%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU564^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:35:18 AM UTC 2026
% Result : Theorem 1.56s 1.36s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 153 ( 9 ~; 2 |; 10 &; 111 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 41 ( 15 ^; 17 !; 9 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(f26,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25,f15]) ).
thf(f15,plain,
( $true
!= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z2U6bphIBb/DTF2THF_2019.p',subsetE) ).
thf(f25,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f21,f16]) ).
thf(f16,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f21,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK1 )
=> ( in @ X1 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f14,f13]) ).
thf(f13,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,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/sandbox/tmp/tmp.z2U6bphIBb/DTF2THF_2019.p',subset) ).
thf(f14,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU564^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n026.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 12:27:25 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
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.40 thf(spec,logic,$$dhol).
% 0.19/0.40 %------------------------------------------------------------------------------
% 0.19/0.40 % File : SEU564^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.40 % Domain : Set Theory
% 0.19/0.40 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.19/0.40 % Version : Especial > Reduced > Especial.
% 0.19/0.40 % English : (! A:i.! B:i.! x:i.subset A B -> in x A -> in x B)
% 0.19/0.40
% 0.19/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.40 % Source : [Bro08]
% 0.19/0.40 % Names : ZFC066l [Bro08]
% 0.19/0.40
% 0.19/0.40 % Status : Theorem
% 0.19/0.40 % 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
% 0.19/0.40 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.19/0.40 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.19/0.40 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.40 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 10 @)
% 0.19/0.40 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.40 % Maximal formula depth : 8 ( 5 avg)
% 0.19/0.40 % Number of types : 2 ( 0 usr)
% 0.19/0.40 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.40 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.19/0.40 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.19/0.40 % SPC : TH0_THM_EQU_NAR
% 0.19/0.40
% 0.19/0.40 % Comments : http://mathgate.info/detsetitem.php?id=152
% 0.19/0.40 %------------------------------------------------------------------------------
% 0.19/0.40 thf(in_type,type,
% 0.19/0.40 in: $i > $i > $o ).
% 0.19/0.40
% 0.19/0.40 thf(subset_type,type,
% 0.19/0.40 subset: $i > $i > $o ).
% 0.19/0.40
% 0.19/0.40 thf(subset,definition,
% 0.19/0.40 ( subset
% 0.19/0.40 = ( ^ [A: $i,B: $i] :
% 0.19/0.40 ! [Xx: $i] :
% 0.19/0.40 ( ( in @ Xx @ A )
% 0.19/0.40 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.40
% 0.19/0.40 thf(subsetE,conjecture,
% 0.19/0.40 ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.40 ( ( subset @ A @ B )
% 0.19/0.40 => ( ( in @ Xx @ A )
% 0.19/0.40 => ( in @ Xx @ B ) ) ) ).
% 0.19/0.40
% 0.19/0.40 %------------------------------------------------------------------------------
% 0.19/0.40 ------------------------
% 1.56/1.33 ---- Embedded in THF ---
% 1.56/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.33 %%% Generated on Tue Feb 24 12:27:26 EST 2026
% 1.56/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.33 %%% Logic specification used:
% 1.56/1.33 %%% thf(spec, logic, $$dhol).
% 1.56/1.33
% 1.56/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.z2U6bphIBb/DTF2DTF2019.p
% See solution above
% 1.56/1.33 ------------------------
% 1.56/1.34 ---- Cleaned THF ---
% 1.56/1.34 thf(in_type,type,
% 1.56/1.34 in: $i > $i > $o ).
% 1.56/1.34
% 1.56/1.34 thf(subset_type,type,
% 1.56/1.34 subset: $i > $i > $o ).
% 1.56/1.34
% 1.56/1.34 thf(subset,definition,
% 1.56/1.34 ( subset
% 1.56/1.34 = ( ^ [A: $i,B: $i] :
% 1.56/1.34 ! [Xx: $i] :
% 1.56/1.34 ( ( in @ Xx @ A )
% 1.56/1.34 => ( in @ Xx @ B ) ) ) ) ).
% 1.56/1.34
% 1.56/1.34 thf(subsetE,conjecture,
% 1.56/1.34 ! [A: $i,B: $i,Xx: $i] :
% 1.56/1.34 ( ( subset @ A @ B )
% 1.56/1.34 => ( ( in @ Xx @ A )
% 1.56/1.34 => ( in @ Xx @ B ) ) ) ).
% 1.56/1.34 ------------------------
% 1.56/1.36 % (2121)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_2019 for (2999ds/275Mi)
% 1.56/1.36 % (2118)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_2019 for (2999ds/27Mi)
% 1.56/1.36 % (2122)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2019 for (2999ds/18Mi)
% 1.56/1.36 % (2119)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2019 for (2999ds/2Mi)
% 1.56/1.36 % (2117)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_2019 for (2999ds/4Mi)
% 1.56/1.36 % (2116)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2019 for (2999ds/183Mi)
% 1.56/1.36 % (2120)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_2019 for (2999ds/2Mi)
% 1.56/1.36 % (2121)Refutation not found, incomplete strategy
% 1.56/1.36 % (2121)------------------------------
% 1.56/1.36 % (2121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (2119)Instruction limit reached!
% 1.56/1.36 % (2119)------------------------------
% 1.56/1.36 % (2119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (2121)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.36
% 1.56/1.36
% 1.56/1.36 % (2121)Memory used [KB]: 5500
% 1.56/1.36 % (2121)Time elapsed: 0.002 s
% 1.56/1.36 % (2121)Instructions burned: 1 (million)
% 1.56/1.36 % (2121)------------------------------
% 1.56/1.36 % (2121)------------------------------
% 1.56/1.36 % (2119)Termination reason: Unknown
% 1.56/1.36 % (2120)Instruction limit reached!
% 1.56/1.36 % (2120)------------------------------
% 1.56/1.36 % (2120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (2120)Termination reason: Unknown
% 1.56/1.36 % (2120)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (2120)Memory used [KB]: 5500
% 1.56/1.36 % (2120)Time elapsed: 0.003 s
% 1.56/1.36 % (2120)Instructions burned: 2 (million)
% 1.56/1.36 % (2120)------------------------------
% 1.56/1.36 % (2120)------------------------------
% 1.56/1.36 % (2119)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (2119)Memory used [KB]: 5500
% 1.56/1.36 % (2119)Time elapsed: 0.003 s
% 1.56/1.36 % (2119)Instructions burned: 2 (million)
% 1.56/1.36 % (2119)------------------------------
% 1.56/1.36 % (2119)------------------------------
% 1.56/1.36 % (2116)First to succeed.
% 1.56/1.36 % (2122)Also succeeded, but the first one will report.
% 1.56/1.36 % (2116)Refutation found. Thanks to Tanya!
% 1.56/1.36 % SZS status Theorem for DTF2THF_2019
% 1.56/1.36 % SZS output start Proof for DTF2THF_2019
% 1.56/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.36 thf(func_def_1, type, subset: $i > $i > $o).
% 1.56/1.36 thf(f26,plain,(
% 1.56/1.36 $false),
% 1.56/1.36 inference(subsumption_resolution,[status(thm)],[f25,f15])).
% 1.56/1.36 thf(f15,plain,(
% 1.56/1.36 ($true != (in @ sK2 @ sK0))),
% 1.56/1.36 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.36 thf(f12,plain,(
% 1.56/1.36 ((in @ sK2 @ sK1) = $true) & ($true != (in @ sK2 @ sK0)) & ($true = (subset @ sK1 @ sK0))),
% 1.56/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.56/1.36 thf(f11,plain,(
% 1.56/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ($true = (subset @ X1 @ X0))) => (((in @ sK2 @ sK1) = $true) & ($true != (in @ sK2 @ sK0)) & ($true = (subset @ sK1 @ sK0)))),
% 1.56/1.36 introduced(definition,[],[choice_axiom])).
% 1.56/1.36 thf(f10,plain,(
% 1.56/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ($true = (subset @ X1 @ X0)))),
% 1.56/1.36 inference(flattening,[status(thm)],[f9])).
% 1.56/1.36 thf(f9,plain,(
% 1.56/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) & ($true = (subset @ X1 @ X0)))),
% 1.56/1.36 inference(ennf_transformation,[status(thm)],[f6])).
% 1.56/1.36 thf(f6,plain,(
% 1.56/1.36 ~! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X0)) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)))),
% 1.56/1.36 inference(fool_elimination,[status(thm)],[f5])).
% 1.56/1.36 thf(f5,plain,(
% 1.56/1.36 ~! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))),
% 1.56/1.36 inference(rectify,[status(thm)],[f3])).
% 1.56/1.36 thf(f3,negated_conjecture,(
% 1.56/1.36 ~! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1)))),
% 1.56/1.36 inference(negated_conjecture,[status(cth)],[f2])).
% 1.56/1.36 thf(f2,conjecture,(
% 1.56/1.36 ! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1)))),
% 1.56/1.36 file('/export/starexec/sandbox/tmp/tmp.z2U6bphIBb/DTF2THF_2019.p',subsetE)).
% 1.56/1.36 thf(f25,plain,(
% 1.56/1.36 ($true = (in @ sK2 @ sK0))),
% 1.56/1.36 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.56/1.36 thf(f22,plain,(
% 1.56/1.36 ($true = (in @ sK2 @ sK0)) | ($false = $true)),
% 1.56/1.36 inference(superposition,[status(thm)],[f21,f16])).
% 1.56/1.36 thf(f16,plain,(
% 1.56/1.36 ((in @ sK2 @ sK1) = $true)),
% 1.56/1.36 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.36 thf(f21,plain,(
% 1.56/1.36 ( ! [X1 : $i] : (($false = (in @ X1 @ sK1)) | ((in @ X1 @ sK0) = $true)) )),
% 1.56/1.36 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.56/1.36 thf(f20,plain,(
% 1.56/1.36 ( ! [X1 : $i] : ((((in @ X1 @ sK1) => (in @ X1 @ sK0)) = $true)) )),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.56/1.36 thf(f19,plain,(
% 1.56/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ sK0))) @ X1) = $true)) )),
% 1.56/1.36 inference(pi_clausification,[status(thm)],[f18])).
% 1.56/1.36 thf(f18,plain,(
% 1.56/1.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ sK0)))))),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.56/1.36 thf(f17,plain,(
% 1.56/1.36 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))) @ sK1 @ sK0) = $true)),
% 1.56/1.36 inference(definition_unfolding,[status(thm)],[f14,f13])).
% 1.56/1.36 thf(f13,plain,(
% 1.56/1.36 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.56/1.36 inference(cnf_transformation,[status(thm)],[f8])).
% 1.56/1.36 thf(f8,plain,(
% 1.56/1.36 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.56/1.36 inference(fool_elimination,[status(thm)],[f7])).
% 1.56/1.36 thf(f7,plain,(
% 1.56/1.36 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))) = subset)),
% 1.56/1.36 inference(rectify,[status(thm)],[f1])).
% 1.56/1.36 thf(f1,axiom,(
% 1.56/1.36 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))) = subset)),
% 1.56/1.36 file('/export/starexec/sandbox/tmp/tmp.z2U6bphIBb/DTF2THF_2019.p',subset)).
% 1.56/1.36 thf(f14,plain,(
% 1.56/1.36 ($true = (subset @ sK1 @ sK0))),
% 1.56/1.36 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.36 % SZS output end Proof for DTF2THF_2019
% 1.56/1.36 % (2116)------------------------------
% 1.56/1.36 % (2116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (2116)Termination reason: Refutation
% 1.56/1.36
% 1.56/1.36 % (2116)Memory used [KB]: 5500
% 1.56/1.36 % (2116)Time elapsed: 0.004 s
% 1.56/1.36 % (2116)Instructions burned: 2 (million)
% 1.56/1.36 % (2116)------------------------------
% 1.56/1.36 % (2116)------------------------------
% 1.56/1.36 % (2115)Success in time 0.019 s
%------------------------------------------------------------------------------