%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU571^2 : 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 : n020.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 09:35:20 AM UTC 2026
% Result : Theorem 1.44s 1.29s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 406 ( 10 ~; 12 |; 6 &; 306 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 7 con; 0-2 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 106 ( 37 ^; 63 !; 6 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_17,type,
sK3: $i > $i > $i ).
thf(f60,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
$true != $true,
inference(superposition,[status(thm)],[f17,f56]) ).
thf(f56,plain,
! [X0: $i,X1: $i] :
( ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f31,f42]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( setadjoin @ X1 @ X2 ) ) @ X2 ) )
| ( ( subset @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( $false
= ( in @ ( sK3 @ X0 @ ( setadjoin @ X1 @ X2 ) ) @ X2 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f30,f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f19,f16]) ).
thf(f16,plain,
setadjoinIR = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( subsetI1 = $true )
& ( ( subset @ sK1 @ ( setadjoin @ sK0 @ sK1 ) )
!= $true )
& ( setadjoinIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
=> ( ( subset @ sK1 @ ( setadjoin @ sK0 @ sK1 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( subsetI1 = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
& ( setadjoinIR = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( setadjoinIR = $true )
=> ( ( subsetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( setadjoinIR
=> ( subsetI1
=> ! [X0: $i,X1: $i] : ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setadjoinIR
=> ( subsetI1
=> ! [X0: $i,X1: $i] : ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setadjoinIR
=> ( subsetI1
=> ! [X0: $i,X1: $i] : ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2THF_20703.p',setadjoinSub) ).
thf(f19,plain,
( setadjoinIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setadjoinIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= setadjoinIR ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= setadjoinIR ),
file('/export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2THF_20703.p',setadjoinIR) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X2 ) @ X2 )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK3 @ X1 @ X2 ) ) )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f18]) ).
thf(f18,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f20,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: $i,X1: $i] :
( ( ! [X0: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ X3 ) )
=> ( subset @ X1 @ X3 ) )
= subsetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2THF_20703.p',subsetI1) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f17,plain,
( ( subset @ sK1 @ ( setadjoin @ sK0 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU571^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.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 12:27:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU571^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (! x:i.! A:i.subset A (setadjoin x A))
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC073l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.19/0.47 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 3 ( 4 avg)
% 0.19/0.47 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 16 @)
% 0.19/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=458
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(in_type,type,
% 0.19/0.47 in: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoin_type,type,
% 0.19/0.47 setadjoin: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIR_type,type,
% 0.19/0.47 setadjoinIR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIR,definition,
% 0.19/0.47 ( setadjoinIR
% 0.19/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subset_type,type,
% 0.19/0.47 subset: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetI1_type,type,
% 0.19/0.47 subsetI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetI1,definition,
% 0.19/0.47 ( subsetI1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ B ) )
% 0.19/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinSub,conjecture,
% 0.19/0.47 ( setadjoinIR
% 0.19/0.47 => ( subsetI1
% 0.19/0.47 => ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.44/1.26 ---- Embedded in THF ---
% 1.44/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.26 %%% Generated on Tue Feb 24 12:27:28 EST 2026
% 1.44/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.26 %%% Logic specification used:
% 1.44/1.26 %%% thf(spec, logic, $$dhol).
% 1.44/1.26
% 1.44/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2DTF20703.p
% See solution above
% 1.44/1.26 ------------------------
% 1.44/1.27 ---- Cleaned THF ---
% 1.44/1.27 thf(in_type,type,
% 1.44/1.27 in: $i > $i > $o ).
% 1.44/1.27
% 1.44/1.27 thf(setadjoin_type,type,
% 1.44/1.27 setadjoin: $i > $i > $i ).
% 1.44/1.27
% 1.44/1.27 thf(setadjoinIR_type,type,
% 1.44/1.27 setadjoinIR: $o ).
% 1.44/1.27
% 1.44/1.27 thf(setadjoinIR,definition,
% 1.44/1.27 ( setadjoinIR
% 1.44/1.27 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.44/1.27 ( ( in @ Xy @ A )
% 1.44/1.27 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.44/1.27
% 1.44/1.27 thf(subset_type,type,
% 1.44/1.27 subset: $i > $i > $o ).
% 1.44/1.27
% 1.44/1.27 thf(subsetI1_type,type,
% 1.44/1.27 subsetI1: $o ).
% 1.44/1.27
% 1.44/1.27 thf(subsetI1,definition,
% 1.44/1.27 ( subsetI1
% 1.44/1.27 = ( ! [A: $i,B: $i] :
% 1.44/1.27 ( ! [Xx: $i] :
% 1.44/1.27 ( ( in @ Xx @ A )
% 1.44/1.27 => ( in @ Xx @ B ) )
% 1.44/1.27 => ( subset @ A @ B ) ) ) ) ).
% 1.44/1.27
% 1.44/1.27 thf(setadjoinSub,conjecture,
% 1.44/1.27 ( setadjoinIR
% 1.44/1.27 => ( subsetI1
% 1.44/1.27 => ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 1.44/1.27 ------------------------
% 1.44/1.28 % (20817)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20703 for (3000ds/183Mi)
% 1.44/1.29 % (20817)First to succeed.
% 1.44/1.29 % (20823)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20703 for (3000ds/18Mi)
% 1.44/1.29 % (20817)Refutation found. Thanks to Tanya!
% 1.44/1.29 % SZS status Theorem for DTF2THF_20703
% 1.44/1.29 % SZS output start Proof for DTF2THF_20703
% 1.44/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.44/1.29 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.44/1.29 thf(func_def_4, type, subset: $i > $i > $o).
% 1.44/1.29 thf(func_def_17, type, sK3: $i > $i > $i).
% 1.44/1.29 thf(f60,plain,(
% 1.44/1.29 $false),
% 1.44/1.29 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.44/1.29 thf(f59,plain,(
% 1.44/1.29 ($true != $true)),
% 1.44/1.29 inference(superposition,[status(thm)],[f17,f56])).
% 1.44/1.29 thf(f56,plain,(
% 1.44/1.29 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (setadjoin @ X1 @ X0)) = $true)) )),
% 1.44/1.29 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.44/1.29 thf(f55,plain,(
% 1.44/1.29 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (setadjoin @ X1 @ X0)) = $true) | ($false = $true)) )),
% 1.44/1.29 inference(duplicate_literal_removal,[status(thm)],[f51])).
% 1.44/1.29 thf(f51,plain,(
% 1.44/1.29 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((subset @ X0 @ (setadjoin @ X1 @ X0)) = $true) | ((subset @ X0 @ (setadjoin @ X1 @ X0)) = $true)) )),
% 1.44/1.29 inference(superposition,[status(thm)],[f31,f42])).
% 1.44/1.29 thf(f42,plain,(
% 1.44/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (setadjoin @ X1 @ X2)) @ X2)) | ((subset @ X0 @ (setadjoin @ X1 @ X2)) = $true)) )),
% 1.44/1.29 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.44/1.29 thf(f39,plain,(
% 1.44/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ (setadjoin @ X1 @ X2)) = $true) | ($false = (in @ (sK3 @ X0 @ (setadjoin @ X1 @ X2)) @ X2)) | ($false = $true)) )),
% 1.44/1.29 inference(superposition,[status(thm)],[f30,f38])).
% 1.44/1.29 thf(f38,plain,(
% 1.44/1.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X3 @ X2)) = $true) | ((in @ X1 @ X2) = $false)) )),
% 1.44/1.29 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.44/1.29 thf(f37,plain,(
% 1.44/1.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X2) => (in @ X1 @ (setadjoin @ X3 @ X2))) = $true)) )),
% 1.44/1.29 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.44/1.29 thf(f36,plain,(
% 1.44/1.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ X2) => (in @ X1 @ (setadjoin @ Y0 @ X2)))) @ X3) = $true)) )),
% 1.44/1.29 inference(pi_clausification,[status(thm)],[f35])).
% 1.44/1.29 thf(f35,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ X2) => (in @ X1 @ (setadjoin @ Y0 @ X2))))) = $true)) )),
% 1.44/1.29 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.44/1.29 thf(f34,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => (in @ X1 @ (setadjoin @ Y1 @ Y0)))))) @ X2) = $true)) )),
% 1.44/1.29 inference(pi_clausification,[status(thm)],[f33])).
% 1.44/1.29 thf(f33,plain,(
% 1.44/1.29 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => (in @ X1 @ (setadjoin @ Y1 @ Y0))))))) = $true)) )),
% 1.44/1.29 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.44/1.29 thf(f32,plain,(
% 1.44/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (setadjoin @ Y2 @ Y1)))))))) @ X1) = $true)) )),
% 1.44/1.29 inference(pi_clausification,[status(thm)],[f21])).
% 1.44/1.29 thf(f21,plain,(
% 1.44/1.29 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) = $true)),
% 1.44/1.29 inference(definition_unfolding,[status(thm)],[f19,f16])).
% 1.44/1.29 thf(f16,plain,(
% 1.44/1.29 (setadjoinIR = $true)),
% 1.44/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.44/1.29 thf(f15,plain,(
% 1.44/1.29 (subsetI1 = $true) & ((subset @ sK1 @ (setadjoin @ sK0 @ sK1)) != $true) & (setadjoinIR = $true)),
% 1.44/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.44/1.29 thf(f14,plain,(
% 1.44/1.29 ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) != $true) => ((subset @ sK1 @ (setadjoin @ sK0 @ sK1)) != $true)),
% 1.44/1.29 introduced(definition,[],[choice_axiom])).
% 1.44/1.29 thf(f13,plain,(
% 1.44/1.29 (subsetI1 = $true) & ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) != $true) & (setadjoinIR = $true)),
% 1.44/1.29 inference(flattening,[status(thm)],[f12])).
% 1.44/1.29 thf(f12,plain,(
% 1.44/1.29 (? [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) != $true) & (subsetI1 = $true)) & (setadjoinIR = $true)),
% 1.44/1.29 inference(ennf_transformation,[status(thm)],[f7])).
% 1.44/1.29 thf(f7,plain,(
% 1.44/1.29 ~((setadjoinIR = $true) => ((subsetI1 = $true) => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true)))),
% 1.44/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.44/1.29 thf(f6,plain,(
% 1.44/1.29 ~(setadjoinIR => (subsetI1 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1))))),
% 1.44/1.29 inference(rectify,[status(thm)],[f4])).
% 1.44/1.29 thf(f4,negated_conjecture,(
% 1.44/1.29 ~(setadjoinIR => (subsetI1 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1))))),
% 1.44/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.44/1.29 thf(f3,conjecture,(
% 1.44/1.29 setadjoinIR => (subsetI1 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)))),
% 1.44/1.29 file('/export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2THF_20703.p',setadjoinSub)).
% 1.44/1.29 thf(f19,plain,(
% 1.44/1.29 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))))),
% 1.44/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.44/1.29 thf(f9,plain,(
% 1.44/1.29 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))))),
% 1.44/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.44/1.29 thf(f8,plain,(
% 1.44/1.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinIR)),
% 1.44/1.29 inference(rectify,[status(thm)],[f1])).
% 1.44/1.29 thf(f1,axiom,(
% 1.44/1.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinIR)),
% 1.44/1.29 file('/export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2THF_20703.p',setadjoinIR)).
% 1.44/1.29 thf(f30,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X2) @ X2) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.44/1.29 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.44/1.29 thf(f29,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : ((((in @ (sK3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X1 @ X2) @ X2)) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.44/1.29 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.44/1.29 thf(f28,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK3 @ X1 @ X2))) | ((subset @ X1 @ X2) = $true)) )),
% 1.44/1.29 inference(sigma_clausification,[status(thm)],[f27])).
% 1.44/1.29 thf(f27,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.44/1.29 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.44/1.29 thf(f26,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)) = $true)) )),
% 1.44/1.29 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.44/1.29 thf(f25,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2) = $true)) )),
% 1.44/1.29 inference(pi_clausification,[status(thm)],[f24])).
% 1.44/1.29 thf(f24,plain,(
% 1.44/1.29 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))) = $true)) )),
% 1.44/1.29 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.44/1.29 thf(f23,plain,(
% 1.44/1.29 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1))) )),
% 1.44/1.29 inference(pi_clausification,[status(thm)],[f22])).
% 1.44/1.29 thf(f22,plain,(
% 1.44/1.29 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) = $true)),
% 1.44/1.29 inference(definition_unfolding,[status(thm)],[f20,f18])).
% 1.44/1.29 thf(f18,plain,(
% 1.44/1.29 (subsetI1 = $true)),
% 1.44/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.44/1.29 thf(f20,plain,(
% 1.44/1.29 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.44/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.44/1.29 thf(f11,plain,(
% 1.44/1.29 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.44/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.44/1.29 thf(f10,plain,(
% 1.44/1.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 1.44/1.29 inference(rectify,[status(thm)],[f2])).
% 1.44/1.29 thf(f2,axiom,(
% 1.44/1.29 (! [X3 : $i,X1 : $i] : (! [X0 : $i] : ((in @ X0 @ X1) => (in @ X0 @ X3)) => (subset @ X1 @ X3)) = subsetI1)),
% 1.44/1.29 file('/export/starexec/sandbox2/tmp/tmp.byEizhnGGE/DTF2THF_20703.p',subsetI1)).
% 1.44/1.29 thf(f31,plain,(
% 1.44/1.29 ( ! [X2 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X2) @ X1) = $true) | ((subset @ X1 @ X2) = $true)) )),
% 1.44/1.29 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.44/1.29 thf(f17,plain,(
% 1.44/1.29 ((subset @ sK1 @ (setadjoin @ sK0 @ sK1)) != $true)),
% 1.44/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.44/1.29 % SZS output end Proof for DTF2THF_20703
% 1.44/1.29 % (20817)------------------------------
% 1.44/1.29 % (20817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.29 % (20817)Termination reason: Refutation
% 1.44/1.29
% 1.44/1.29 % (20817)Memory used [KB]: 5500
% 1.44/1.29 % (20817)Time elapsed: 0.005 s
% 1.44/1.29 % (20817)Instructions burned: 6 (million)
% 1.44/1.29 % (20817)------------------------------
% 1.44/1.29 % (20817)------------------------------
% 1.44/1.29 % (20816)Success in time 0.007 s
%------------------------------------------------------------------------------