%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU572^2 : 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 : n031.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 09:35:21 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 252 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 328 ( 10 ~; 7 |; 11 &; 241 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 8 con; 0-2 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 89 ( 28 ^; 52 !; 9 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
setadjoin: $i > $i > $i ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(f69,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
$false = $true,
inference(superposition,[status(thm)],[f64,f19]) ).
thf(f19,plain,
( $true
= ( subset @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( subsetTrans = $true )
& ( $true
!= ( subset @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) )
& ( $true
= ( subset @ sK1 @ sK2 ) )
& ( setadjoinSub = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ( ( subset @ X1 @ X2 )
= $true ) )
=> ( ( $true
!= ( subset @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) )
& ( $true
= ( subset @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( subsetTrans = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ( ( subset @ X1 @ X2 )
= $true ) )
& ( setadjoinSub = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ( ( subset @ X1 @ X2 )
= $true ) )
& ( setadjoinSub = $true )
& ( subsetTrans = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
=> ( $true
= ( subset @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( subsetTrans
=> ( setadjoinSub
=> ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetTrans
=> ( setadjoinSub
=> ! [X3: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( subset @ X0 @ ( setadjoin @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetTrans
=> ( setadjoinSub
=> ! [X3: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( subset @ X0 @ ( setadjoin @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2THF_7522.p',setadjoinSub2) ).
thf(f64,plain,
( $false
= ( subset @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false
= ( subset @ sK1 @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f47]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( $false
= ( subset @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( $false
= ( subset @ X2 @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f27,f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( ( subset @ X1 @ X2 )
= $true )
| ( $false
= ( subset @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( subset @ X3 @ X2 )
=> ( subset @ X1 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X1 @ X3 )
=> ( ( subset @ X3 @ X2 )
=> ( subset @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ Y0 @ X2 )
=> ( subset @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ Y0 @ X2 )
=> ( subset @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( subset @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( subset @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y2 @ Y1 )
=> ( subset @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y2 @ Y1 )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f17]) ).
thf(f17,plain,
( subsetTrans
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y2 @ Y1 )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( subsetTrans
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y2 @ Y1 )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( subsetTrans
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetTrans
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2THF_7522.p',subsetTrans) ).
thf(f21,plain,
subsetTrans = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( subset @ Y0 @ ( setadjoin @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ ( setadjoin @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( setadjoin @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f16]) ).
thf(f16,plain,
( setadjoinSub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setadjoinSub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinSub ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X3: $i] :
( ( subset @ X0 @ ( setadjoin @ X3 @ X0 ) )
= setadjoinSub ),
file('/export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2THF_7522.p',setadjoinSub) ).
thf(f18,plain,
setadjoinSub = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f20,plain,
( $true
!= ( subset @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU572^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:28:18 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU572^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! A:i.! x:i.! B:i.subset A B -> subset A (setadjoin x B))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC074l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % 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
% 0.20/0.46 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.20/0.46 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.20/0.46 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 16 @)
% 0.20/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 4 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=478
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans_type,type,
% 0.20/0.46 subsetTrans: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans,definition,
% 0.20/0.46 ( subsetTrans
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ C )
% 0.20/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub_type,type,
% 0.20/0.46 setadjoinSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub,definition,
% 0.20/0.46 ( setadjoinSub
% 0.20/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2,conjecture,
% 0.20/0.46 ( subsetTrans
% 0.20/0.46 => ( setadjoinSub
% 0.20/0.46 => ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 12:28:19 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2DTF7522.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(setadjoin_type,type,
% 1.48/1.28 setadjoin: $i > $i > $i ).
% 1.48/1.28
% 1.48/1.28 thf(subset_type,type,
% 1.48/1.28 subset: $i > $i > $o ).
% 1.48/1.28
% 1.48/1.28 thf(subsetTrans_type,type,
% 1.48/1.28 subsetTrans: $o ).
% 1.48/1.28
% 1.48/1.28 thf(subsetTrans,definition,
% 1.48/1.28 ( subsetTrans
% 1.48/1.28 = ( ! [A: $i,B: $i,C: $i] :
% 1.48/1.28 ( ( subset @ A @ B )
% 1.48/1.28 => ( ( subset @ B @ C )
% 1.48/1.28 => ( subset @ A @ C ) ) ) ) ) ).
% 1.48/1.28
% 1.48/1.28 thf(setadjoinSub_type,type,
% 1.48/1.28 setadjoinSub: $o ).
% 1.48/1.28
% 1.48/1.28 thf(setadjoinSub,definition,
% 1.48/1.28 ( setadjoinSub
% 1.48/1.28 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 1.48/1.28
% 1.48/1.28 thf(setadjoinSub2,conjecture,
% 1.48/1.28 ( subsetTrans
% 1.48/1.28 => ( setadjoinSub
% 1.48/1.28 => ! [A: $i,Xx: $i,B: $i] :
% 1.48/1.28 ( ( subset @ A @ B )
% 1.48/1.28 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (7713)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7522 for (2999ds/2Mi)
% 1.48/1.29 % (7710)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7522 for (2999ds/183Mi)
% 1.48/1.29 % (7713)Instruction limit reached!
% 1.48/1.29 % (7713)------------------------------
% 1.48/1.29 % (7713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (7713)Termination reason: Unknown
% 1.48/1.29 % (7713)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (7713)Memory used [KB]: 5500
% 1.48/1.29 % (7713)Time elapsed: 0.002 s
% 1.48/1.29 % (7713)Instructions burned: 2 (million)
% 1.48/1.29 % (7713)------------------------------
% 1.48/1.29 % (7713)------------------------------
% 1.48/1.30 % (7715)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_7522 for (2999ds/275Mi)
% 1.48/1.30 % (7710)First to succeed.
% 1.64/1.30 % (7710)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_7522
% 1.64/1.30 % SZS output start Proof for DTF2THF_7522
% 1.64/1.30 thf(func_def_0, type, setadjoin: $i > $i > $i).
% 1.64/1.30 thf(func_def_1, type, subset: $i > $i > $o).
% 1.64/1.30 thf(f69,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.64/1.30 thf(f65,plain,(
% 1.64/1.30 ($false = $true)),
% 1.64/1.30 inference(superposition,[status(thm)],[f64,f19])).
% 1.64/1.30 thf(f19,plain,(
% 1.64/1.30 ($true = (subset @ sK1 @ sK2))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 (subsetTrans = $true) & (($true != (subset @ sK1 @ (setadjoin @ sK0 @ sK2))) & ($true = (subset @ sK1 @ sK2))) & (setadjoinSub = $true)),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ (setadjoin @ X0 @ X2))) & ((subset @ X1 @ X2) = $true)) => (($true != (subset @ sK1 @ (setadjoin @ sK0 @ sK2))) & ($true = (subset @ sK1 @ sK2)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 (subsetTrans = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ (setadjoin @ X0 @ X2))) & ((subset @ X1 @ X2) = $true)) & (setadjoinSub = $true)),
% 1.64/1.30 inference(flattening,[status(thm)],[f12])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 (? [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ (setadjoin @ X0 @ X2))) & ((subset @ X1 @ X2) = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 ~((subsetTrans = $true) => ((setadjoinSub = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) = $true) => ($true = (subset @ X1 @ (setadjoin @ X0 @ X2))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 ~(subsetTrans => (setadjoinSub => ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => (subset @ X1 @ (setadjoin @ X0 @ X2)))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,negated_conjecture,(
% 1.64/1.30 ~(subsetTrans => (setadjoinSub => ! [X3 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (subset @ X0 @ (setadjoin @ X3 @ X1)))))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.30 thf(f3,conjecture,(
% 1.64/1.30 subsetTrans => (setadjoinSub => ! [X3 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (subset @ X0 @ (setadjoin @ X3 @ X1))))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2THF_7522.p',setadjoinSub2)).
% 1.64/1.30 thf(f64,plain,(
% 1.64/1.30 ($false = (subset @ sK1 @ sK2))),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.64/1.30 thf(f58,plain,(
% 1.64/1.30 ($false = (subset @ sK1 @ sK2)) | ($true != $true)),
% 1.64/1.30 inference(superposition,[status(thm)],[f20,f47])).
% 1.64/1.30 thf(f47,plain,(
% 1.64/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ (setadjoin @ X1 @ X0)) = $true) | ($false = (subset @ X2 @ X0))) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.64/1.30 thf(f40,plain,(
% 1.64/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ (setadjoin @ X1 @ X0)) = $true) | ($false = (subset @ X2 @ X0)) | ($false = $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f27,f35])).
% 1.64/1.30 thf(f35,plain,(
% 1.64/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X3 @ X2)) | ((subset @ X1 @ X2) = $true) | ($false = (subset @ X1 @ X3))) )),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.64/1.30 thf(f34,plain,(
% 1.64/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X3 @ X2) => (subset @ X1 @ X2))) | ($false = (subset @ X1 @ X3))) )),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.64/1.30 thf(f33,plain,(
% 1.64/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((subset @ X1 @ X3) => ((subset @ X3 @ X2) => (subset @ X1 @ X2))) = $true)) )),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.64/1.30 thf(f32,plain,(
% 1.64/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ Y0) => ((subset @ Y0 @ X2) => (subset @ X1 @ X2)))) @ X3))) )),
% 1.64/1.30 inference(pi_clausification,[status(thm)],[f31])).
% 1.64/1.30 thf(f31,plain,(
% 1.64/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0) => ((subset @ Y0 @ X2) => (subset @ X1 @ X2))))))) )),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.64/1.30 thf(f30,plain,(
% 1.64/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((subset @ Y1 @ Y0) => (subset @ X1 @ Y0)))))) @ X2))) )),
% 1.64/1.30 inference(pi_clausification,[status(thm)],[f29])).
% 1.64/1.30 thf(f29,plain,(
% 1.64/1.30 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((subset @ Y1 @ Y0) => (subset @ X1 @ Y0))))))))) )),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.64/1.30 thf(f28,plain,(
% 1.64/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1)))))))) @ X1) = $true)) )),
% 1.64/1.30 inference(pi_clausification,[status(thm)],[f22])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) = $true)),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f21,f17])).
% 1.64/1.30 thf(f17,plain,(
% 1.64/1.30 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f7])).
% 1.64/1.30 thf(f7,plain,(
% 1.64/1.30 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.30 thf(f6,plain,(
% 1.64/1.30 (subsetTrans = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => ((subset @ X0 @ X1) => (subset @ X2 @ X1))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f1])).
% 1.64/1.30 thf(f1,axiom,(
% 1.64/1.30 (subsetTrans = ! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2THF_7522.p',subsetTrans)).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 (subsetTrans = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.30 thf(f27,plain,(
% 1.64/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X2 @ (setadjoin @ X1 @ X2)))) )),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.64/1.30 thf(f26,plain,(
% 1.64/1.30 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (subset @ Y0 @ (setadjoin @ X1 @ Y0))) @ X2) = $true)) )),
% 1.64/1.30 inference(pi_clausification,[status(thm)],[f25])).
% 1.64/1.30 thf(f25,plain,(
% 1.64/1.30 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setadjoin @ X1 @ Y0)))))) )),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.64/1.30 thf(f24,plain,(
% 1.64/1.30 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1))))) @ X1))) )),
% 1.64/1.30 inference(pi_clausification,[status(thm)],[f23])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f18,f16])).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.30 thf(f9,plain,(
% 1.64/1.30 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.30 thf(f8,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i] : (subset @ X0 @ (setadjoin @ X1 @ X0)) = setadjoinSub)),
% 1.64/1.30 inference(rectify,[status(thm)],[f2])).
% 1.64/1.30 thf(f2,axiom,(
% 1.64/1.30 (! [X0 : $i,X3 : $i] : (subset @ X0 @ (setadjoin @ X3 @ X0)) = setadjoinSub)),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.xwctUZ5SCa/DTF2THF_7522.p',setadjoinSub)).
% 1.64/1.30 thf(f18,plain,(
% 1.64/1.30 (setadjoinSub = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.30 thf(f20,plain,(
% 1.64/1.30 ($true != (subset @ sK1 @ (setadjoin @ sK0 @ sK2)))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.30 % SZS output end Proof for DTF2THF_7522
% 1.64/1.30 % (7710)------------------------------
% 1.64/1.30 % (7710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (7710)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (7710)Memory used [KB]: 5500
% 1.64/1.30 % (7710)Time elapsed: 0.004 s
% 1.64/1.30 % (7710)Instructions burned: 8 (million)
% 1.64/1.30 % (7710)------------------------------
% 1.64/1.30 % (7710)------------------------------
% 1.64/1.30 % (7709)Success in time 0.015 s
%------------------------------------------------------------------------------