%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU667^2 : 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 : n019.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 09:36:04 AM UTC 2026
% Result : Theorem 1.53s 1.21s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 45 equ; 0 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 529 ( 10 ~; 0 |; 44 &; 428 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 11 usr; 7 con; 0-3 aty)
% ( 18 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 159 ( 119 ^; 30 !; 10 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
kpair: $i > $i > $i ).
thf(func_def_4,type,
cartprod: $i > $i > $i ).
thf(func_def_5,type,
breln: $i > $i > $i > $o ).
thf(func_def_7,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_22,type,
sK1: $i > $i > $o ).
thf(f32,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f24,f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( $true
= ( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( X3 @ Y1 @ Y2 )
& ( in @ Y2 @ X2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ X1 ) ) ) )
@ ( cartprod @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( in @ Y3 @ X2 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) )
& ( in @ Y2 @ X1 ) ) ) )
@ ( cartprod @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( in @ Y3 @ X2 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) )
& ( in @ Y2 @ X1 ) ) ) )
@ ( cartprod @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ Y0 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
& ( in @ Y4 @ Y0 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) )
& ( in @ Y3 @ X1 ) ) ) )
@ ( cartprod @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ Y0 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
& ( in @ Y4 @ Y0 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) )
& ( in @ Y3 @ X1 ) ) ) )
@ ( cartprod @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( subset
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y3 @ Y4 )
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ?? @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
& ( in @ Y8 @ Y4 )
& ( ( kpair @ Y7 @ Y8 )
= Y6 ) ) )
& ( in @ Y7 @ Y3 ) ) ) )
@ Y0
@ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f18,f20]) ).
thf(f20,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( ( kpair @ X4 @ X5 )
= X3 )
& ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X3: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X4: $i] :
? [X5: $i] :
( ( in @ X5 @ X0 )
& ? [X6: $i] :
( ( ( kpair @ X5 @ X6 )
= X4 )
& ( in @ X6 @ X1 )
& ( X3 @ X5 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',dpsetconstr) ).
thf(f18,plain,
dpsetconstrSub = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
!= ( breln @ sK0 @ sK2
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) )
& ( dpsetconstrSub = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i > $i > $o,X2: $i] :
( $true
!= ( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
=> ( $true
!= ( breln @ sK0 @ sK2
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i > $i > $o,X2: $i] :
( $true
!= ( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( dpsetconstrSub = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( dpsetconstrSub = $true )
=> ! [X0: $i,X1: $i > $i > $o,X2: $i] :
( $true
= ( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( dpsetconstrSub
=> ! [X0: $i,X1: $i > $i > $o,X2: $i] :
( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( dpsetconstrSub
=> ! [X0: $i,X3: $i > $i > $o,X1: $i] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X3 @ X5 @ X6 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( dpsetconstrSub
=> ! [X0: $i,X3: $i > $i > $o,X1: $i] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X3 @ X5 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',setOfPairsIsBReln) ).
thf(f21,plain,
( dpsetconstrSub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( dpsetconstrSub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( dpsetconstrSub
= ( ! [X0: $i > $i > $o,X1: $i,X2: $i] :
( subset
@ ( dpsetconstr @ X2 @ X1
@ ^ [X3: $i,X4: $i] : ( X0 @ X3 @ X4 ) )
@ ( cartprod @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( dpsetconstrSub
= ( ! [X3: $i > $i > $o,X1: $i,X0: $i] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X3 @ X5 @ X6 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',dpsetconstrSub) ).
thf(f24,plain,
( $true
!= ( subset
@ ( dsetconstr @ ( cartprod @ sK0 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK0 ) ) ) )
@ ( cartprod @ sK0 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK0
@ sK2
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK0
@ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f17,f20]) ).
thf(f17,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',breln) ).
thf(f19,plain,
( $true
!= ( breln @ sK0 @ sK2
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU667^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:30:24 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEU667^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.45 % Domain : Set Theory
% 0.30/0.45 % Problem : Ordered Pairs - Sets of Pairs
% 0.30/0.45 % Version : Especial > Reduced > Especial.
% 0.30/0.45 % English : (! A:i.! B:i.! phi:i>(i>o).breln A B (dpsetconstr A B
% 0.30/0.45 % (^ x,y:i.phi x y)))
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.45 % Source : [Bro08]
% 0.30/0.45 % Names : ZFC169l [Bro08]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 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
% 0.30/0.45 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 3 def)
% 0.30/0.45 % Number of atoms : 12 ( 4 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 2 ( 3 avg)
% 0.30/0.45 % Number of connectives : 37 ( 0 ~; 0 |; 3 &; 33 @)
% 0.30/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 11 ( 4 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 9 ( 8 usr; 1 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 19 ( 11 ^; 6 !; 2 ?; 19 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : http://mathgate.info/detsetitem.php?id=232
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(in_type,type,
% 0.30/0.45 in: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstr_type,type,
% 0.30/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(subset_type,type,
% 0.30/0.45 subset: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(kpair_type,type,
% 0.30/0.45 kpair: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(cartprod_type,type,
% 0.30/0.45 cartprod: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(breln_type,type,
% 0.30/0.45 breln: $i > $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(breln,definition,
% 0.30/0.45 ( breln
% 0.30/0.45 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(dpsetconstr_type,type,
% 0.30/0.45 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(dpsetconstr,definition,
% 0.30/0.45 ( dpsetconstr
% 0.30/0.45 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.45 ( dsetconstr @ ( cartprod @ A @ B )
% 0.30/0.45 @ ^ [Xu: $i] :
% 0.30/0.45 ? [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 & ? [Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ B )
% 0.30/0.45 & ( Xphi @ Xx @ Xy )
% 0.30/0.45 & ( Xu
% 0.30/0.45 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(dpsetconstrSub_type,type,
% 0.30/0.45 dpsetconstrSub: $o ).
% 0.30/0.45
% 0.30/0.45 thf(dpsetconstrSub,definition,
% 0.30/0.45 ( dpsetconstrSub
% 0.30/0.45 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.45 ( subset
% 0.30/0.45 @ ( dpsetconstr @ A @ B
% 0.30/0.45 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.30/0.45 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setOfPairsIsBReln,conjecture,
% 0.30/0.45 ( dpsetconstrSub
% 0.30/0.45 => ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.45 ( breln @ A @ B
% 0.30/0.45 @ ( dpsetconstr @ A @ B
% 0.30/0.45 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.43/1.18 ---- Embedded in THF ---
% 1.43/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.18 %%% Generated on Tue Feb 24 12:30:25 EST 2026
% 1.43/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.18 %%% Logic specification used:
% 1.43/1.18 %%% thf(spec, logic, $$dhol).
% 1.43/1.18
% 1.43/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2DTF16159.p
% See solution above
% 1.43/1.18 ------------------------
% 1.43/1.19 ---- Cleaned THF ---
% 1.43/1.19 thf(in_type,type,
% 1.43/1.19 in: $i > $i > $o ).
% 1.43/1.19
% 1.43/1.19 thf(dsetconstr_type,type,
% 1.43/1.19 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.43/1.19
% 1.43/1.19 thf(subset_type,type,
% 1.43/1.19 subset: $i > $i > $o ).
% 1.43/1.19
% 1.43/1.19 thf(kpair_type,type,
% 1.43/1.19 kpair: $i > $i > $i ).
% 1.43/1.19
% 1.43/1.19 thf(cartprod_type,type,
% 1.43/1.19 cartprod: $i > $i > $i ).
% 1.43/1.19
% 1.43/1.19 thf(breln_type,type,
% 1.43/1.19 breln: $i > $i > $i > $o ).
% 1.43/1.19
% 1.43/1.19 thf(breln,definition,
% 1.43/1.19 ( breln
% 1.43/1.19 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.43/1.19
% 1.43/1.19 thf(dpsetconstr_type,type,
% 1.43/1.19 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.43/1.19
% 1.43/1.19 thf(dpsetconstr,definition,
% 1.43/1.19 ( dpsetconstr
% 1.43/1.19 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.43/1.19 ( dsetconstr @ ( cartprod @ A @ B )
% 1.43/1.19 @ ^ [Xu: $i] :
% 1.43/1.19 ? [Xx: $i] :
% 1.43/1.19 ( ( in @ Xx @ A )
% 1.43/1.19 & ? [Xy: $i] :
% 1.43/1.19 ( ( in @ Xy @ B )
% 1.43/1.19 & ( Xphi @ Xx @ Xy )
% 1.43/1.19 & ( Xu
% 1.43/1.19 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 1.43/1.19
% 1.43/1.19 thf(dpsetconstrSub_type,type,
% 1.43/1.19 dpsetconstrSub: $o ).
% 1.43/1.19
% 1.43/1.19 thf(dpsetconstrSub,definition,
% 1.43/1.19 ( dpsetconstrSub
% 1.43/1.19 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.43/1.19 ( subset
% 1.43/1.19 @ ( dpsetconstr @ A @ B
% 1.43/1.19 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 1.43/1.19 @ ( cartprod @ A @ B ) ) ) ) ).
% 1.43/1.19
% 1.43/1.19 thf(setOfPairsIsBReln,conjecture,
% 1.43/1.19 ( dpsetconstrSub
% 1.43/1.19 => ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.43/1.19 ( breln @ A @ B
% 1.43/1.19 @ ( dpsetconstr @ A @ B
% 1.43/1.19 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ).
% 1.43/1.19 ------------------------
% 1.53/1.21 % (16256)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16159 for (3000ds/183Mi)
% 1.53/1.21 % (16258)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_16159 for (3000ds/27Mi)
% 1.53/1.21 % (16260)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_16159 for (3000ds/2Mi)
% 1.53/1.21 % (16256)First to succeed.
% 1.53/1.21 % (16260)Instruction limit reached!
% 1.53/1.21 % (16260)------------------------------
% 1.53/1.21 % (16260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.21 % (16260)Termination reason: Unknown
% 1.53/1.21 % (16260)Termination phase: Saturation
% 1.53/1.21
% 1.53/1.21 % (16260)Memory used [KB]: 5500
% 1.53/1.21 % (16260)Time elapsed: 0.003 s
% 1.53/1.21 % (16260)Instructions burned: 4 (million)
% 1.53/1.21 % (16260)------------------------------
% 1.53/1.21 % (16260)------------------------------
% 1.53/1.21 % (16258)Also succeeded, but the first one will report.
% 1.53/1.21 % (16256)Refutation found. Thanks to Tanya!
% 1.53/1.21 % SZS status Theorem for DTF2THF_16159
% 1.53/1.21 % SZS output start Proof for DTF2THF_16159
% 1.53/1.21 thf(func_def_0, type, in: $i > $i > $o).
% 1.53/1.21 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.53/1.21 thf(func_def_2, type, subset: $i > $i > $o).
% 1.53/1.21 thf(func_def_3, type, kpair: $i > $i > $i).
% 1.53/1.21 thf(func_def_4, type, cartprod: $i > $i > $i).
% 1.53/1.21 thf(func_def_5, type, breln: $i > $i > $i > $o).
% 1.53/1.21 thf(func_def_7, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.53/1.21 thf(func_def_22, type, sK1: $i > $i > $o).
% 1.53/1.21 thf(f32,plain,(
% 1.53/1.21 $false),
% 1.53/1.21 inference(subsumption_resolution,[status(thm)],[f24,f31])).
% 1.53/1.21 thf(f31,plain,(
% 1.53/1.21 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (($true = (subset @ (dsetconstr @ (cartprod @ X1 @ X2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) & (in @ Y2 @ X2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ X1)))))) @ (cartprod @ X1 @ X2)))) )),
% 1.53/1.21 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.53/1.21 thf(f30,plain,(
% 1.53/1.21 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $i > $o]: (subset @ (dsetconstr @ (cartprod @ X1 @ X2) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (in @ Y3 @ X2)) & ((kpair @ Y2 @ Y3) = Y1)))) & (in @ Y2 @ X1)))))) @ (cartprod @ X1 @ X2))) @ X3))) )),
% 1.53/1.21 inference(pi_clausification,[status(thm)],[f29])).
% 1.53/1.21 thf(f29,plain,(
% 1.53/1.21 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (subset @ (dsetconstr @ (cartprod @ X1 @ X2) @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (in @ Y3 @ X2)) & ((kpair @ Y2 @ Y3) = Y1)))) & (in @ Y2 @ X1)))))) @ (cartprod @ X1 @ X2)))))) )),
% 1.53/1.21 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.53/1.21 thf(f28,plain,(
% 1.53/1.21 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (subset @ (dsetconstr @ (cartprod @ X1 @ Y0) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (in @ Y4 @ Y0)) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ X1)))))) @ (cartprod @ X1 @ Y0))))) @ X2))) )),
% 1.53/1.21 inference(pi_clausification,[status(thm)],[f27])).
% 1.53/1.21 thf(f27,plain,(
% 1.53/1.21 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (subset @ (dsetconstr @ (cartprod @ X1 @ Y0) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (in @ Y4 @ Y0)) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ X1)))))) @ (cartprod @ X1 @ Y0)))))))) )),
% 1.53/1.21 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.53/1.21 thf(f26,plain,(
% 1.53/1.21 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0)))))) @ (cartprod @ Y0 @ Y1))))))) @ X1))) )),
% 1.53/1.21 inference(pi_clausification,[status(thm)],[f25])).
% 1.53/1.21 thf(f25,plain,(
% 1.53/1.21 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0)))))) @ (cartprod @ Y0 @ Y1)))))))))),
% 1.53/1.21 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.53/1.21 thf(f23,plain,(
% 1.53/1.21 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y3 @ Y4) @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((?? @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) & (in @ Y8 @ Y4)) & ((kpair @ Y7 @ Y8) = Y6)))) & (in @ Y7 @ Y3))))))))))) @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y0 @ Y1)))))))))),
% 1.53/1.21 inference(definition_unfolding,[status(thm)],[f21,f18,f20])).
% 1.53/1.21 thf(f20,plain,(
% 1.53/1.21 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.21 thf(f12,plain,(
% 1.53/1.21 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.53/1.21 inference(fool_elimination,[status(thm)],[f11])).
% 1.53/1.21 thf(f11,plain,(
% 1.53/1.21 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X0) & ? [X5 : $i] : (((kpair @ X4 @ X5) = X3) & (in @ X5 @ X1) & (X2 @ X4 @ X5))))))))),
% 1.53/1.21 inference(rectify,[status(thm)],[f2])).
% 1.53/1.21 thf(f2,axiom,(
% 1.53/1.21 (dpsetconstr = (^[X0 : $i, X1 : $i, X3 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X4 : $i] : (? [X5 : $i] : ((in @ X5 @ X0) & ? [X6 : $i] : (((kpair @ X5 @ X6) = X4) & (in @ X6 @ X1) & (X3 @ X5 @ X6))))))))),
% 1.53/1.21 file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',dpsetconstr)).
% 1.53/1.21 thf(f18,plain,(
% 1.53/1.21 (dpsetconstrSub = $true)),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f16])).
% 1.53/1.21 thf(f16,plain,(
% 1.53/1.21 ($true != (breln @ sK0 @ sK2 @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) & (dpsetconstrSub = $true)),
% 1.53/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.53/1.21 thf(f15,plain,(
% 1.53/1.21 ? [X0 : $i,X1 : $i > $i > $o,X2 : $i] : ($true != (breln @ X0 @ X2 @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) => ($true != (breln @ sK0 @ sK2 @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
% 1.53/1.21 introduced(definition,[],[choice_axiom])).
% 1.53/1.21 thf(f14,plain,(
% 1.53/1.21 ? [X0 : $i,X1 : $i > $i > $o,X2 : $i] : ($true != (breln @ X0 @ X2 @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) & (dpsetconstrSub = $true)),
% 1.53/1.21 inference(ennf_transformation,[status(thm)],[f8])).
% 1.53/1.21 thf(f8,plain,(
% 1.53/1.21 ~((dpsetconstrSub = $true) => ! [X0 : $i,X1 : $i > $i > $o,X2 : $i] : ($true = (breln @ X0 @ X2 @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))))),
% 1.53/1.21 inference(fool_elimination,[status(thm)],[f7])).
% 1.53/1.21 thf(f7,plain,(
% 1.53/1.21 ~(dpsetconstrSub => ! [X0 : $i,X1 : $i > $i > $o,X2 : $i] : (breln @ X0 @ X2 @ (dpsetconstr @ X0 @ X2 @ (^[X3 : $i, X4 : $i] : (X1 @ X3 @ X4)))))),
% 1.53/1.21 inference(rectify,[status(thm)],[f5])).
% 1.53/1.21 thf(f5,negated_conjecture,(
% 1.53/1.21 ~(dpsetconstrSub => ! [X0 : $i,X3 : $i > $i > $o,X1 : $i] : (breln @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))))),
% 1.53/1.21 inference(negated_conjecture,[status(cth)],[f4])).
% 1.53/1.21 thf(f4,conjecture,(
% 1.53/1.21 dpsetconstrSub => ! [X0 : $i,X3 : $i > $i > $o,X1 : $i] : (breln @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))))),
% 1.53/1.21 file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',setOfPairsIsBReln)).
% 1.53/1.21 thf(f21,plain,(
% 1.53/1.21 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y0 @ Y1)))))))))),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.21 thf(f10,plain,(
% 1.53/1.21 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y0 @ Y1)))))))))),
% 1.53/1.21 inference(fool_elimination,[status(thm)],[f9])).
% 1.53/1.21 thf(f9,plain,(
% 1.53/1.21 (dpsetconstrSub = ! [X0 : $i > $i > $o,X1 : $i,X2 : $i] : (subset @ (dpsetconstr @ X2 @ X1 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4))) @ (cartprod @ X2 @ X1)))),
% 1.53/1.21 inference(rectify,[status(thm)],[f3])).
% 1.53/1.21 thf(f3,axiom,(
% 1.53/1.21 (dpsetconstrSub = ! [X3 : $i > $i > $o,X1 : $i,X0 : $i] : (subset @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))) @ (cartprod @ X0 @ X1)))),
% 1.53/1.21 file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',dpsetconstrSub)).
% 1.53/1.21 thf(f24,plain,(
% 1.53/1.21 ($true != (subset @ (dsetconstr @ (cartprod @ sK0 @ sK2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK0)))))) @ (cartprod @ sK0 @ sK2)))),
% 1.53/1.21 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.53/1.21 thf(f22,plain,(
% 1.53/1.21 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK0 @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))) @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
% 1.53/1.21 inference(definition_unfolding,[status(thm)],[f19,f17,f20])).
% 1.53/1.21 thf(f17,plain,(
% 1.53/1.21 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.21 thf(f13,plain,(
% 1.53/1.21 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.53/1.21 inference(fool_elimination,[status(thm)],[f1])).
% 1.53/1.21 thf(f1,axiom,(
% 1.53/1.21 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.53/1.21 file('/export/starexec/sandbox2/tmp/tmp.BNDf9h8L3I/DTF2THF_16159.p',breln)).
% 1.53/1.21 thf(f19,plain,(
% 1.53/1.21 ($true != (breln @ sK0 @ sK2 @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
% 1.53/1.21 inference(cnf_transformation,[status(thm)],[f16])).
% 1.53/1.21 % SZS output end Proof for DTF2THF_16159
% 1.53/1.21 % (16256)------------------------------
% 1.53/1.21 % (16256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.21 % (16256)Termination reason: Refutation
% 1.53/1.21
% 1.53/1.21 % (16256)Memory used [KB]: 5500
% 1.53/1.21 % (16256)Time elapsed: 0.004 s
% 1.53/1.21 % (16256)Instructions burned: 5 (million)
% 1.53/1.21 % (16256)------------------------------
% 1.53/1.21 % (16256)------------------------------
% 1.53/1.21 % (16255)Success in time 0.002 s
%------------------------------------------------------------------------------