%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU814^2 : 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 : n003.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 09:37:26 AM UTC 2026
% Result : Theorem 1.63s 1.31s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 355 ( 80 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 372 ( 11 ~; 9 |; 25 &; 255 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 8 con; 0-2 aty)
% ( 19 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 84 ( 28 ^; 43 !; 13 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
transitiveset: $i > $o ).
thf(f61,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f60,f25]) ).
thf(f25,plain,
( ( in @ sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( transitivesetOp1 = $true )
& ( ( in @ sK2 @ sK0 )
!= $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( transitiveset @ sK0 )
= $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
=> ( ? [X2: $i,X1: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
& ( ( in @ X1 @ sK0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( transitiveset @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i,X1: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
& ( ( in @ X1 @ sK0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( ( in @ sK2 @ sK0 )
!= $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( transitivesetOp1 = $true )
& ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( transitivesetOp1 = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( subsetE = $true )
=> ( ( transitivesetOp1 = $true )
=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( subsetE
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetE
=> ( transitivesetOp1
=> ! [X3: $i] :
( ( transitiveset @ X3 )
=> ! [X0: $i,X2: $i] :
( ( in @ X0 @ X3 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetE
=> ( transitivesetOp1
=> ! [X3: $i] :
( ( transitiveset @ X3 )
=> ! [X0: $i,X2: $i] :
( ( in @ X0 @ X3 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2THF_6238.p',transitivesetOp2) ).
thf(f60,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false = $true )
| ( ( in @ sK2 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f56,f23]) ).
thf(f23,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f56,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( in @ X0 @ sK0 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f52,f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X3 ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X3 ) )
| ( ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X2 @ X3 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ X2 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X2 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f20]) ).
thf(f20,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2THF_6238.p',subsetE) ).
thf(f21,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f52,plain,
( ( subset @ sK1 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( subset @ sK1 @ sK0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f24,f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( ( subset @ X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f27]) ).
thf(f27,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( subset @ X3 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2THF_6238.p',transitiveset) ).
thf(f22,plain,
( ( transitiveset @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f24,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU814^2 : 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
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:40 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SEU814^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.47 % Domain : Set Theory
% 0.26/0.47 % Problem : Transitive Sets
% 0.26/0.47 % Version : Especial > Reduced > Especial.
% 0.26/0.47 % English : (! X:i.transitiveset X -> (! A:i.! x:i.in A X -> in x A ->
% 0.26/0.47 % in x X))
% 0.26/0.47
% 0.26/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.47 % Source : [Bro08]
% 0.26/0.47 % Names : ZFC316l [Bro08]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % 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 v4.1.0, 0.00 v3.7.0
% 0.26/0.47 % Syntax : Number of formulae : 9 ( 3 unt; 5 typ; 3 def)
% 0.26/0.47 % Number of atoms : 20 ( 3 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 6 ( 5 avg)
% 0.26/0.47 % Number of connectives : 32 ( 0 ~; 0 |; 0 &; 22 @)
% 0.26/0.47 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 11 ( 4 avg)
% 0.26/0.47 % Number of types : 2 ( 0 usr)
% 0.26/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.26/0.47 % Number of variables : 10 ( 1 ^; 9 !; 0 ?; 10 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : http://mathgate.info/detsetitem.php?id=502
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(in_type,type,
% 0.26/0.47 in: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(subset_type,type,
% 0.26/0.47 subset: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetE_type,type,
% 0.26/0.47 subsetE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetE,definition,
% 0.26/0.47 ( subsetE
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(transitiveset_type,type,
% 0.26/0.47 transitiveset: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(transitiveset,definition,
% 0.26/0.47 ( transitiveset
% 0.26/0.47 = ( ^ [A: $i] :
% 0.26/0.47 ! [X: $i] :
% 0.26/0.47 ( ( in @ X @ A )
% 0.26/0.47 => ( subset @ X @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(transitivesetOp1_type,type,
% 0.26/0.47 transitivesetOp1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(transitivesetOp1,definition,
% 0.26/0.47 ( transitivesetOp1
% 0.26/0.47 = ( ! [X: $i] :
% 0.26/0.47 ( ( transitiveset @ X )
% 0.26/0.47 => ! [A: $i] :
% 0.26/0.47 ( ( in @ A @ X )
% 0.26/0.47 => ( subset @ A @ X ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(transitivesetOp2,conjecture,
% 0.26/0.47 ( subsetE
% 0.26/0.47 => ( transitivesetOp1
% 0.26/0.47 => ! [X: $i] :
% 0.26/0.47 ( ( transitiveset @ X )
% 0.26/0.47 => ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ A @ X )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 12:34:41 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2DTF6238.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.29 thf(in_type,type,
% 1.44/1.29 in: $i > $i > $o ).
% 1.44/1.29
% 1.44/1.29 thf(subset_type,type,
% 1.44/1.29 subset: $i > $i > $o ).
% 1.44/1.29
% 1.44/1.29 thf(subsetE_type,type,
% 1.44/1.29 subsetE: $o ).
% 1.44/1.29
% 1.44/1.29 thf(subsetE,definition,
% 1.44/1.29 ( subsetE
% 1.44/1.29 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.44/1.29 ( ( subset @ A @ B )
% 1.44/1.29 => ( ( in @ Xx @ A )
% 1.44/1.29 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.44/1.29
% 1.44/1.29 thf(transitiveset_type,type,
% 1.44/1.29 transitiveset: $i > $o ).
% 1.44/1.29
% 1.44/1.29 thf(transitiveset,definition,
% 1.44/1.29 ( transitiveset
% 1.44/1.29 = ( ^ [A: $i] :
% 1.44/1.29 ! [X: $i] :
% 1.44/1.29 ( ( in @ X @ A )
% 1.44/1.29 => ( subset @ X @ A ) ) ) ) ).
% 1.44/1.29
% 1.44/1.29 thf(transitivesetOp1_type,type,
% 1.44/1.29 transitivesetOp1: $o ).
% 1.44/1.29
% 1.44/1.29 thf(transitivesetOp1,definition,
% 1.44/1.29 ( transitivesetOp1
% 1.44/1.29 = ( ! [X: $i] :
% 1.44/1.29 ( ( transitiveset @ X )
% 1.44/1.29 => ! [A: $i] :
% 1.44/1.29 ( ( in @ A @ X )
% 1.44/1.29 => ( subset @ A @ X ) ) ) ) ) ).
% 1.44/1.29
% 1.44/1.29 thf(transitivesetOp2,conjecture,
% 1.44/1.29 ( subsetE
% 1.44/1.29 => ( transitivesetOp1
% 1.44/1.29 => ! [X: $i] :
% 1.44/1.29 ( ( transitiveset @ X )
% 1.44/1.29 => ! [A: $i,Xx: $i] :
% 1.44/1.29 ( ( in @ A @ X )
% 1.44/1.29 => ( ( in @ Xx @ A )
% 1.44/1.29 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.44/1.29 ------------------------
% 1.63/1.31 % (6527)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6238 for (2999ds/183Mi)
% 1.63/1.31 % (6531)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_6238 for (2999ds/2Mi)
% 1.63/1.31 % (6531)Instruction limit reached!
% 1.63/1.31 % (6531)------------------------------
% 1.63/1.31 % (6531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (6531)Termination reason: Unknown
% 1.63/1.31 % (6531)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (6531)Memory used [KB]: 5500
% 1.63/1.31 % (6531)Time elapsed: 0.002 s
% 1.63/1.31 % (6531)Instructions burned: 3 (million)
% 1.63/1.31 % (6531)------------------------------
% 1.63/1.31 % (6531)------------------------------
% 1.63/1.31 % (6527)First to succeed.
% 1.63/1.31 % (6527)Refutation found. Thanks to Tanya!
% 1.63/1.31 % SZS status Theorem for DTF2THF_6238
% 1.63/1.31 % SZS output start Proof for DTF2THF_6238
% 1.63/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.63/1.31 thf(func_def_1, type, subset: $i > $i > $o).
% 1.63/1.31 thf(func_def_4, type, transitiveset: $i > $o).
% 1.63/1.31 thf(f61,plain,(
% 1.63/1.31 $false),
% 1.63/1.31 inference(subsumption_resolution,[status(thm)],[f60,f25])).
% 1.63/1.31 thf(f25,plain,(
% 1.63/1.31 ((in @ sK2 @ sK0) != $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.31 thf(f19,plain,(
% 1.63/1.31 (transitivesetOp1 = $true) & ((((in @ sK2 @ sK0) != $true) & ((in @ sK1 @ sK0) = $true) & ((in @ sK2 @ sK1) = $true)) & ((transitiveset @ sK0) = $true)) & (subsetE = $true)),
% 1.63/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18,f17])).
% 1.63/1.31 thf(f17,plain,(
% 1.63/1.31 ? [X0 : $i] : (? [X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X1 @ X0) = $true) & ((in @ X2 @ X1) = $true)) & ((transitiveset @ X0) = $true)) => (? [X2 : $i,X1 : $i] : (((in @ X2 @ sK0) != $true) & ((in @ X1 @ sK0) = $true) & ((in @ X2 @ X1) = $true)) & ((transitiveset @ sK0) = $true))),
% 1.63/1.31 introduced(definition,[],[choice_axiom])).
% 1.63/1.31 thf(f18,plain,(
% 1.63/1.31 ? [X2 : $i,X1 : $i] : (((in @ X2 @ sK0) != $true) & ((in @ X1 @ sK0) = $true) & ((in @ X2 @ X1) = $true)) => (((in @ sK2 @ sK0) != $true) & ((in @ sK1 @ sK0) = $true) & ((in @ sK2 @ sK1) = $true))),
% 1.63/1.31 introduced(definition,[],[choice_axiom])).
% 1.63/1.31 thf(f16,plain,(
% 1.63/1.31 (transitivesetOp1 = $true) & ? [X0 : $i] : (? [X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X1 @ X0) = $true) & ((in @ X2 @ X1) = $true)) & ((transitiveset @ X0) = $true)) & (subsetE = $true)),
% 1.63/1.31 inference(flattening,[status(thm)],[f15])).
% 1.63/1.31 thf(f15,plain,(
% 1.63/1.31 (? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) & ((in @ X1 @ X0) = $true)) & ((transitiveset @ X0) = $true)) & (transitivesetOp1 = $true)) & (subsetE = $true)),
% 1.63/1.31 inference(ennf_transformation,[status(thm)],[f10])).
% 1.63/1.31 thf(f10,plain,(
% 1.63/1.31 ~((subsetE = $true) => ((transitivesetOp1 = $true) => ! [X0 : $i] : (((transitiveset @ X0) = $true) => ! [X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true))))))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.63/1.31 thf(f9,plain,(
% 1.63/1.31 ~(subsetE => (transitivesetOp1 => ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))))),
% 1.63/1.31 inference(rectify,[status(thm)],[f5])).
% 1.63/1.31 thf(f5,negated_conjecture,(
% 1.63/1.31 ~(subsetE => (transitivesetOp1 => ! [X3 : $i] : ((transitiveset @ X3) => ! [X0 : $i,X2 : $i] : ((in @ X0 @ X3) => ((in @ X2 @ X0) => (in @ X2 @ X3))))))),
% 1.63/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.63/1.31 thf(f4,conjecture,(
% 1.63/1.31 subsetE => (transitivesetOp1 => ! [X3 : $i] : ((transitiveset @ X3) => ! [X0 : $i,X2 : $i] : ((in @ X0 @ X3) => ((in @ X2 @ X0) => (in @ X2 @ X3)))))),
% 1.63/1.31 file('/export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2THF_6238.p',transitivesetOp2)).
% 1.63/1.31 thf(f60,plain,(
% 1.63/1.31 ((in @ sK2 @ sK0) = $true)),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.63/1.31 thf(f57,plain,(
% 1.63/1.31 ($false = $true) | ((in @ sK2 @ sK0) = $true)),
% 1.63/1.31 inference(superposition,[status(thm)],[f56,f23])).
% 1.63/1.31 thf(f23,plain,(
% 1.63/1.31 ((in @ sK2 @ sK1) = $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.31 thf(f56,plain,(
% 1.63/1.31 ( ! [X0 : $i] : (($false = (in @ X0 @ sK1)) | ((in @ X0 @ sK0) = $true)) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.63/1.31 thf(f54,plain,(
% 1.63/1.31 ( ! [X0 : $i] : (($false = $true) | ((in @ X0 @ sK0) = $true) | ($false = (in @ X0 @ sK1))) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f52,f39])).
% 1.63/1.31 thf(f39,plain,(
% 1.63/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X2 @ X3)) | ((in @ X1 @ X3) = $true) | ($false = (in @ X1 @ X2))) )),
% 1.63/1.31 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.63/1.31 thf(f38,plain,(
% 1.63/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X2 @ X3)) | (((in @ X1 @ X2) => (in @ X1 @ X3)) = $true)) )),
% 1.63/1.31 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.63/1.31 thf(f37,plain,(
% 1.63/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((subset @ X2 @ X3) => ((in @ X1 @ X2) => (in @ X1 @ X3))) = $true)) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.63/1.31 thf(f36,plain,(
% 1.63/1.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ X2 @ Y0) => ((in @ X1 @ X2) => (in @ X1 @ Y0)))) @ X3) = $true)) )),
% 1.63/1.31 inference(pi_clausification,[status(thm)],[f35])).
% 1.63/1.31 thf(f35,plain,(
% 1.63/1.31 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ X2 @ Y0) => ((in @ X1 @ X2) => (in @ X1 @ Y0))))) = $true)) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.63/1.31 thf(f34,plain,(
% 1.63/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((in @ X1 @ Y0) => (in @ X1 @ Y1)))))) @ X2) = $true)) )),
% 1.63/1.31 inference(pi_clausification,[status(thm)],[f33])).
% 1.63/1.31 thf(f33,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((in @ X1 @ Y0) => (in @ X1 @ Y1))))))) = $true)) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.63/1.31 thf(f32,plain,(
% 1.63/1.31 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))) @ X1) = $true)) )),
% 1.63/1.31 inference(pi_clausification,[status(thm)],[f30])).
% 1.63/1.31 thf(f30,plain,(
% 1.63/1.31 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) = $true)),
% 1.63/1.31 inference(definition_unfolding,[status(thm)],[f21,f20])).
% 1.63/1.31 thf(f20,plain,(
% 1.63/1.31 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))))),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f8,plain,(
% 1.63/1.31 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.63/1.31 thf(f7,plain,(
% 1.63/1.31 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 1.63/1.31 inference(rectify,[status(thm)],[f1])).
% 1.63/1.31 thf(f1,axiom,(
% 1.63/1.31 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.63/1.31 file('/export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2THF_6238.p',subsetE)).
% 1.63/1.31 thf(f21,plain,(
% 1.63/1.31 (subsetE = $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.31 thf(f52,plain,(
% 1.63/1.31 ((subset @ sK1 @ sK0) = $true)),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.63/1.31 thf(f50,plain,(
% 1.63/1.31 ((subset @ sK1 @ sK0) = $true) | ($false = $true)),
% 1.63/1.31 inference(superposition,[status(thm)],[f24,f47])).
% 1.63/1.31 thf(f47,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (($false = (in @ X1 @ sK0)) | ((subset @ X1 @ sK0) = $true)) )),
% 1.63/1.31 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.63/1.31 thf(f46,plain,(
% 1.63/1.31 ( ! [X1 : $i] : ((((in @ X1 @ sK0) => (subset @ X1 @ sK0)) = $true)) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.63/1.31 thf(f45,plain,(
% 1.63/1.31 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))) @ X1) = $true)) )),
% 1.63/1.31 inference(pi_clausification,[status(thm)],[f44])).
% 1.63/1.31 thf(f44,plain,(
% 1.63/1.31 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0)))) = $true)),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.63/1.31 thf(f29,plain,(
% 1.63/1.31 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ sK0) = $true)),
% 1.63/1.31 inference(definition_unfolding,[status(thm)],[f22,f27])).
% 1.63/1.31 thf(f27,plain,(
% 1.63/1.31 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.31 thf(f14,plain,(
% 1.63/1.31 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f13])).
% 1.63/1.31 thf(f13,plain,(
% 1.63/1.31 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 1.63/1.31 inference(rectify,[status(thm)],[f2])).
% 1.63/1.31 thf(f2,axiom,(
% 1.63/1.31 (transitiveset = (^[X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (subset @ X3 @ X0)))))),
% 1.63/1.31 file('/export/starexec/sandbox/tmp/tmp.bvqh2tzFjn/DTF2THF_6238.p',transitiveset)).
% 1.63/1.31 thf(f22,plain,(
% 1.63/1.31 ((transitiveset @ sK0) = $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.31 thf(f24,plain,(
% 1.63/1.31 ((in @ sK1 @ sK0) = $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.31 % SZS output end Proof for DTF2THF_6238
% 1.63/1.31 % (6527)------------------------------
% 1.63/1.31 % (6527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (6527)Termination reason: Refutation
% 1.63/1.31
% 1.63/1.31 % (6527)Memory used [KB]: 5500
% 1.63/1.31 % (6527)Time elapsed: 0.004 s
% 1.63/1.31 % (6527)Instructions burned: 4 (million)
% 1.63/1.31 % (6527)------------------------------
% 1.63/1.31 % (6527)------------------------------
% 1.63/1.31 % (6526)Success in time 0.013 s
%------------------------------------------------------------------------------