%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU601^2 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:32 AM UTC 2026
% Result : Theorem 1.65s 1.42s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 285 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 397 ( 34 ~; 9 |; 13 &; 282 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 7 con; 0-2 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 44 ^; 39 !; 9 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f42,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
$true != $true,
inference(superposition,[status(thm)],[f20,f40]) ).
thf(f40,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false = $true )
| ( ( in @ sK0 @ sK2 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f38,f19]) ).
thf(f19,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( dsetconstrI = $true )
& ( ( in @ sK0 @ ( setminus @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ( ( in @ sK0 @ ( setminus @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( dsetconstrI = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ! [X2: $i,X0: $i,X4: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> ( in @ X2 @ ( setminus @ X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrI
=> ! [X2: $i,X0: $i,X4: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> ( in @ X2 @ ( setminus @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2THF_32020.p',setminusI) ).
thf(f38,plain,
( ( ( in @ sK0 @ sK2 )
= $true )
| ( $false
= ( in @ sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ~ ( in @ sK0 @ sK2 ) )
= $false )
| ( $false
= ( in @ sK0 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK2 )
@ sK0 )
= $false )
| ( $false
= ( in @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
= ( in @ sK0 @ sK1 ) )
| ( $true != $true )
| ( ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK2 )
@ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f25,f34]) ).
thf(f34,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X3 )
= $false )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i > $o,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f17]) ).
thf(f17,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ( X1 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2THF_32020.p',dsetconstrI) ).
thf(f22,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f25,plain,
( ( in @ sK0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK2 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
!= ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK1
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f18]) ).
thf(f18,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) )
= setminus ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X4: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X4 ) ) )
= setminus ),
file('/export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2THF_32020.p',setminus) ).
thf(f21,plain,
( ( in @ sK0 @ ( setminus @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f20,plain,
( ( in @ sK0 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU601^2 : 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 : n010.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 12:27:48 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
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : SEU601^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.48 % Domain : Set Theory
% 0.31/0.48 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.31/0.48 % Version : Especial > Reduced > Especial.
% 0.31/0.48 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> in x (setminus A B))
% 0.31/0.48
% 0.31/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.48 % Source : [Bro08]
% 0.31/0.48 % Names : ZFC103l [Bro08]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.31/0.48 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.31/0.48 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 4 ( 3 avg)
% 0.31/0.48 % Number of connectives : 27 ( 2 ~; 0 |; 0 &; 20 @)
% 0.31/0.48 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 10 ( 4 avg)
% 0.31/0.48 % Number of types : 2 ( 0 usr)
% 0.31/0.48 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.31/0.48 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.31/0.48 % SPC : TH0_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : http://mathgate.info/detsetitem.php?id=277
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf(in_type,type,
% 0.31/0.48 in: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(dsetconstr_type,type,
% 0.31/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.48
% 0.31/0.48 thf(dsetconstrI_type,type,
% 0.31/0.48 dsetconstrI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dsetconstrI,definition,
% 0.31/0.48 ( dsetconstrI
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( Xphi @ Xx )
% 0.31/0.48 => ( in @ Xx
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminus_type,type,
% 0.31/0.48 setminus: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(setminus,definition,
% 0.31/0.48 ( setminus
% 0.31/0.48 = ( ^ [A: $i,B: $i] :
% 0.31/0.48 ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xx: $i] :
% 0.31/0.48 ~ ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusI,conjecture,
% 0.31/0.48 ( dsetconstrI
% 0.31/0.48 => ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.44/1.38 ---- Embedded in THF ---
% 1.44/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.39 %%% Generated on Tue Feb 24 12:27:49 EST 2026
% 1.44/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.39 %%% Logic specification used:
% 1.44/1.39 %%% thf(spec, logic, $$dhol).
% 1.44/1.39
% 1.44/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2DTF32020.p
% See solution above
% 1.44/1.39 ------------------------
% 1.44/1.39 ---- Cleaned THF ---
% 1.44/1.39 thf(in_type,type,
% 1.44/1.39 in: $i > $i > $o ).
% 1.44/1.39
% 1.44/1.39 thf(dsetconstr_type,type,
% 1.44/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.44/1.39
% 1.44/1.39 thf(dsetconstrI_type,type,
% 1.44/1.39 dsetconstrI: $o ).
% 1.44/1.39
% 1.44/1.39 thf(dsetconstrI,definition,
% 1.44/1.39 ( dsetconstrI
% 1.44/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.44/1.39 ( ( in @ Xx @ A )
% 1.44/1.39 => ( ( Xphi @ Xx )
% 1.44/1.39 => ( in @ Xx
% 1.44/1.39 @ ( dsetconstr @ A
% 1.44/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.44/1.39
% 1.44/1.39 thf(setminus_type,type,
% 1.44/1.39 setminus: $i > $i > $i ).
% 1.44/1.39
% 1.44/1.39 thf(setminus,definition,
% 1.44/1.39 ( setminus
% 1.44/1.39 = ( ^ [A: $i,B: $i] :
% 1.44/1.39 ( dsetconstr @ A
% 1.44/1.39 @ ^ [Xx: $i] :
% 1.44/1.39 ~ ( in @ Xx @ B ) ) ) ) ).
% 1.44/1.39
% 1.44/1.39 thf(setminusI,conjecture,
% 1.44/1.39 ( dsetconstrI
% 1.44/1.39 => ! [A: $i,B: $i,Xx: $i] :
% 1.44/1.39 ( ( in @ Xx @ A )
% 1.44/1.39 => ( ~ ( in @ Xx @ B )
% 1.44/1.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 1.44/1.40 ------------------------
% 1.65/1.41 % (32138)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_32020 for (3000ds/27Mi)
% 1.65/1.41 % (32136)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32020 for (3000ds/183Mi)
% 1.65/1.41 % (32137)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_32020 for (3000ds/4Mi)
% 1.65/1.41 % (32139)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32020 for (3000ds/2Mi)
% 1.65/1.41 % (32140)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_32020 for (3000ds/2Mi)
% 1.65/1.41 % (32142)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32020 for (3000ds/18Mi)
% 1.65/1.41 % (32141)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_32020 for (3000ds/275Mi)
% 1.65/1.42 % (32139)Instruction limit reached!
% 1.65/1.42 % (32139)------------------------------
% 1.65/1.42 % (32139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (32139)Termination reason: Unknown
% 1.65/1.42 % (32139)Termination phase: Saturation
% 1.65/1.42
% 1.65/1.42 % (32139)Memory used [KB]: 5500
% 1.65/1.42 % (32139)Time elapsed: 0.003 s
% 1.65/1.42 % (32139)Instructions burned: 3 (million)
% 1.65/1.42 % (32139)------------------------------
% 1.65/1.42 % (32139)------------------------------
% 1.65/1.42 % (32140)Instruction limit reached!
% 1.65/1.42 % (32140)------------------------------
% 1.65/1.42 % (32140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (32140)Termination reason: Unknown
% 1.65/1.42 % (32140)Termination phase: Saturation
% 1.65/1.42
% 1.65/1.42 % (32140)Memory used [KB]: 5500
% 1.65/1.42 % (32140)Time elapsed: 0.003 s
% 1.65/1.42 % (32140)Instructions burned: 3 (million)
% 1.65/1.42 % (32140)------------------------------
% 1.65/1.42 % (32140)------------------------------
% 1.65/1.42 % (32141)Refutation not found, incomplete strategy
% 1.65/1.42 % (32141)------------------------------
% 1.65/1.42 % (32141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (32141)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.42
% 1.65/1.42
% 1.65/1.42 % (32141)Memory used [KB]: 5500
% 1.65/1.42 % (32141)Time elapsed: 0.003 s
% 1.65/1.42 % (32141)Instructions burned: 2 (million)
% 1.65/1.42 % (32141)------------------------------
% 1.65/1.42 % (32141)------------------------------
% 1.65/1.42 % (32137)Instruction limit reached!
% 1.65/1.42 % (32137)------------------------------
% 1.65/1.42 % (32137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (32137)Termination reason: Unknown
% 1.65/1.42 % (32137)Termination phase: Saturation
% 1.65/1.42
% 1.65/1.42 % (32137)Memory used [KB]: 5500
% 1.65/1.42 % (32137)Time elapsed: 0.004 s
% 1.65/1.42 % (32137)Instructions burned: 4 (million)
% 1.65/1.42 % (32137)------------------------------
% 1.65/1.42 % (32137)------------------------------
% 1.65/1.42 % (32138)First to succeed.
% 1.65/1.42 % (32136)Also succeeded, but the first one will report.
% 1.65/1.42 % (32138)Refutation found. Thanks to Tanya!
% 1.65/1.42 % SZS status Theorem for DTF2THF_32020
% 1.65/1.42 % SZS output start Proof for DTF2THF_32020
% 1.65/1.42 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.42 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.65/1.42 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.65/1.42 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.42 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 1.65/1.42 thf(f42,plain,(
% 1.65/1.42 $false),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.65/1.42 thf(f41,plain,(
% 1.65/1.42 ($true != $true)),
% 1.65/1.42 inference(superposition,[status(thm)],[f20,f40])).
% 1.65/1.42 thf(f40,plain,(
% 1.65/1.42 ((in @ sK0 @ sK2) = $true)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.65/1.42 thf(f39,plain,(
% 1.65/1.42 ($false = $true) | ((in @ sK0 @ sK2) = $true)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f38,f19])).
% 1.65/1.42 thf(f19,plain,(
% 1.65/1.42 ($true = (in @ sK0 @ sK1))),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.42 thf(f16,plain,(
% 1.65/1.42 (dsetconstrI = $true) & (((in @ sK0 @ (setminus @ sK1 @ sK2)) != $true) & ((in @ sK0 @ sK2) != $true) & ($true = (in @ sK0 @ sK1)))),
% 1.65/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.65/1.42 thf(f15,plain,(
% 1.65/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true)) => (((in @ sK0 @ (setminus @ sK1 @ sK2)) != $true) & ((in @ sK0 @ sK2) != $true) & ($true = (in @ sK0 @ sK1)))),
% 1.65/1.42 introduced(definition,[],[choice_axiom])).
% 1.65/1.42 thf(f14,plain,(
% 1.65/1.42 (dsetconstrI = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true))),
% 1.65/1.42 inference(flattening,[status(thm)],[f13])).
% 1.65/1.42 thf(f13,plain,(
% 1.65/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true)) & ((in @ X0 @ X1) = $true)) & (dsetconstrI = $true)),
% 1.65/1.42 inference(ennf_transformation,[status(thm)],[f12])).
% 1.65/1.42 thf(f12,plain,(
% 1.65/1.42 ~((dsetconstrI = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) != $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true))))),
% 1.65/1.42 inference(flattening,[status(thm)],[f7])).
% 1.65/1.42 thf(f7,plain,(
% 1.65/1.42 ~((dsetconstrI = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (~((in @ X0 @ X2) = $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true))))),
% 1.65/1.42 inference(fool_elimination,[status(thm)],[f6])).
% 1.65/1.42 thf(f6,plain,(
% 1.65/1.42 ~(dsetconstrI => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))))),
% 1.65/1.42 inference(rectify,[status(thm)],[f4])).
% 1.65/1.42 thf(f4,negated_conjecture,(
% 1.65/1.42 ~(dsetconstrI => ! [X2 : $i,X0 : $i,X4 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X4) => (in @ X2 @ (setminus @ X0 @ X4)))))),
% 1.65/1.42 inference(negated_conjecture,[status(cth)],[f3])).
% 1.65/1.42 thf(f3,conjecture,(
% 1.65/1.42 dsetconstrI => ! [X2 : $i,X0 : $i,X4 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X4) => (in @ X2 @ (setminus @ X0 @ X4))))),
% 1.65/1.42 file('/export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2THF_32020.p',setminusI)).
% 1.65/1.42 thf(f38,plain,(
% 1.65/1.42 ((in @ sK0 @ sK2) = $true) | ($false = (in @ sK0 @ sK1))),
% 1.65/1.42 inference(not_proxy_clausification,[status(thm)],[f37])).
% 1.65/1.42 thf(f37,plain,(
% 1.65/1.42 ((~ (in @ sK0 @ sK2)) = $false) | ($false = (in @ sK0 @ sK1))),
% 1.65/1.42 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.65/1.42 thf(f36,plain,(
% 1.65/1.42 (((^[Y0 : $i]: (~ (in @ Y0 @ sK2))) @ sK0) = $false) | ($false = (in @ sK0 @ sK1))),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.65/1.42 thf(f35,plain,(
% 1.65/1.42 ($false = (in @ sK0 @ sK1)) | ($true != $true) | (((^[Y0 : $i]: (~ (in @ Y0 @ sK2))) @ sK0) = $false)),
% 1.65/1.42 inference(superposition,[status(thm)],[f25,f34])).
% 1.65/1.42 thf(f34,plain,(
% 1.65/1.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ (dsetconstr @ X1 @ X2)) = $true) | ((X2 @ X3) = $false) | ($false = (in @ X3 @ X1))) )),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.65/1.42 thf(f33,plain,(
% 1.65/1.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((X2 @ X3) => (in @ X3 @ (dsetconstr @ X1 @ X2))) = $true) | ($false = (in @ X3 @ X1))) )),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.65/1.42 thf(f32,plain,(
% 1.65/1.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((in @ X3 @ X1) => ((X2 @ X3) => (in @ X3 @ (dsetconstr @ X1 @ X2)))) = $true)) )),
% 1.65/1.42 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.65/1.42 thf(f31,plain,(
% 1.65/1.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ X2))))) @ X3) = $true)) )),
% 1.65/1.42 inference(pi_clausification,[status(thm)],[f30])).
% 1.65/1.42 thf(f30,plain,(
% 1.65/1.42 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ X2)))))) = $true)) )),
% 1.65/1.42 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.65/1.42 thf(f29,plain,(
% 1.65/1.42 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ X1 @ Y0))))))) @ X2) = $true)) )),
% 1.65/1.42 inference(pi_clausification,[status(thm)],[f28])).
% 1.65/1.42 thf(f28,plain,(
% 1.65/1.42 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ X1 @ Y0)))))))))) )),
% 1.65/1.42 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.65/1.42 thf(f27,plain,(
% 1.65/1.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))))))) @ X1) = $true)) )),
% 1.65/1.42 inference(pi_clausification,[status(thm)],[f26])).
% 1.65/1.42 thf(f26,plain,(
% 1.65/1.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1)))))))))) = $true)),
% 1.65/1.42 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.65/1.42 thf(f23,plain,(
% 1.65/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 1.65/1.42 inference(definition_unfolding,[status(thm)],[f22,f17])).
% 1.65/1.42 thf(f17,plain,(
% 1.65/1.42 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.42 thf(f11,plain,(
% 1.65/1.42 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 1.65/1.42 inference(fool_elimination,[status(thm)],[f10])).
% 1.65/1.42 thf(f10,plain,(
% 1.65/1.42 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ X2) => ((X1 @ X0) => (in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.65/1.42 inference(rectify,[status(thm)],[f1])).
% 1.65/1.42 thf(f1,axiom,(
% 1.65/1.42 (! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.65/1.42 file('/export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2THF_32020.p',dsetconstrI)).
% 1.65/1.42 thf(f22,plain,(
% 1.65/1.42 (dsetconstrI = $true)),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.42 thf(f25,plain,(
% 1.65/1.42 ((in @ sK0 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (~ (in @ Y0 @ sK2))))) != $true)),
% 1.65/1.42 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.65/1.42 thf(f24,plain,(
% 1.65/1.42 ($true != (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))) @ sK1 @ sK2)))),
% 1.65/1.42 inference(definition_unfolding,[status(thm)],[f21,f18])).
% 1.65/1.42 thf(f18,plain,(
% 1.65/1.42 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.42 thf(f9,plain,(
% 1.65/1.42 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 1.65/1.42 inference(fool_elimination,[status(thm)],[f8])).
% 1.65/1.42 thf(f8,plain,(
% 1.65/1.42 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X1))))) = setminus)),
% 1.65/1.42 inference(rectify,[status(thm)],[f2])).
% 1.65/1.42 thf(f2,axiom,(
% 1.65/1.42 ((^[X0 : $i, X4 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X4))))) = setminus)),
% 1.65/1.42 file('/export/starexec/sandbox/tmp/tmp.cGxDTP3IIF/DTF2THF_32020.p',setminus)).
% 1.65/1.42 thf(f21,plain,(
% 1.65/1.42 ((in @ sK0 @ (setminus @ sK1 @ sK2)) != $true)),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.42 thf(f20,plain,(
% 1.65/1.42 ((in @ sK0 @ sK2) != $true)),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.42 % SZS output end Proof for DTF2THF_32020
% 1.65/1.42 % (32138)------------------------------
% 1.65/1.42 % (32138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (32138)Termination reason: Refutation
% 1.65/1.42
% 1.65/1.42 % (32138)Memory used [KB]: 5500
% 1.65/1.42 % (32138)Time elapsed: 0.005 s
% 1.65/1.42 % (32138)Instructions burned: 4 (million)
% 1.65/1.42 % (32138)------------------------------
% 1.65/1.42 % (32138)------------------------------
% 1.65/1.42 % (32135)Success in time 0.018 s
%------------------------------------------------------------------------------