%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU778^2 : 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 : n024.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 09:37:07 AM UTC 2026
% Result : Theorem 1.59s 1.31s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 223 ( 49 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 388 ( 13 ~; 0 |; 24 &; 323 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 8 con; 0-3 aty)
% ( 10 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 117 ( 85 ^; 22 !; 10 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_6,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_7,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_27,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f43,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
$true != $true,
inference(superposition,[status(thm)],[f39,f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( subset @ ( dpsetconstr @ X2 @ X2 @ X1 ) @ ( cartprod @ X2 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ Y0 @ X1 ) @ ( cartprod @ Y0 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ Y0 @ X1 ) @ ( cartprod @ Y0 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ Y1 @ Y0 ) @ ( cartprod @ Y1 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ Y1 @ Y0 ) @ ( cartprod @ Y1 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y1
@ ( dpsetconstr @ Y1 @ Y1
@ ^ [Y2: $i,Y3: $i] : ( Y0 @ Y2 @ Y3 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f21,f29]) ).
thf(f29,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f28]) ).
thf(f28,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln) ).
thf(f26,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) )
= breln1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X3: $i] : ( breln @ X0 @ X0 @ X3 ) )
= breln1 ),
file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln1) ).
thf(f21,plain,
setOfPairsIsBReln1 = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( ( breln1 @ sK0 @ sK2 )
= $true )
& ( ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK2 ) )
!= $true )
& ( setOfPairsIsBReln1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) )
=> ( ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ? [X2: $i] :
( ( ( breln1 @ sK0 @ X2 )
= $true )
& ( $true
!= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ X2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK0 @ X2 )
= $true )
& ( $true
!= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ X2 ) ) ) )
=> ( ( ( breln1 @ sK0 @ sK2 )
= $true )
& ( ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) )
& ( setOfPairsIsBReln1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( setOfPairsIsBReln1 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ( $true
= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( setOfPairsIsBReln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( setOfPairsIsBReln1
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X7: $i] :
( ( breln1 @ X0 @ X7 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X3 @ X7 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( setOfPairsIsBReln1
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X7: $i] :
( ( breln1 @ X0 @ X7 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X3 @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln1compprop) ).
thf(f27,plain,
( setOfPairsIsBReln1
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( breln1 @ Y1
@ ( dpsetconstr @ Y1 @ Y1
@ ^ [Y2: $i,Y3: $i] : ( Y0 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( setOfPairsIsBReln1
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( breln1 @ Y1
@ ( dpsetconstr @ Y1 @ Y1
@ ^ [Y2: $i,Y3: $i] : ( Y0 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i > $i > $o] :
( ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) )
= setOfPairsIsBReln1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X4: $i > $i > $o] :
( ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X5: $i,X6: $i] : ( X4 @ X5 @ X6 ) ) )
= setOfPairsIsBReln1 ),
file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',setOfPairsIsBReln1) ).
thf(f39,plain,
( ( subset
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ Y2 @ sK0 ) ) ) )
@ ( cartprod @ sK0 @ sK0 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ Y5 @ Y0 ) ) ) )
@ sK0
@ sK1
@ sK2 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f22,f29,f25]) ).
thf(f25,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ Y5 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ Y5 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ X5 @ X0 )
& ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 ) ) ) )
= breln1compset ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X3: $i,X7: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X5: $i,X6: $i] :
? [X8: $i] :
( ( in @ X8 @ X0 )
& ( in @ ( kpair @ X8 @ X6 ) @ X7 )
& ( in @ ( kpair @ X5 @ X8 ) @ X3 ) ) ) )
= breln1compset ),
file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln1compset) ).
thf(f22,plain,
( ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU778^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.26 % Computer : n024.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue Feb 24 07:33:25 EST 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.26 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.35 ---- Original DTF file ---
% 0.18/0.35 thf(spec,logic,$$dhol).
% 0.18/0.35 %------------------------------------------------------------------------------
% 0.18/0.35 % File : SEU778^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.35 % Domain : Set Theory
% 0.18/0.35 % Problem : Binary Relations on a Set
% 0.18/0.35 % Version : Especial > Reduced > Especial.
% 0.18/0.35 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S ->
% 0.18/0.35 % breln1 A (breln1compset A R S)))
% 0.18/0.35
% 0.18/0.35 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.35 % Source : [Bro08]
% 0.18/0.35 % Names : ZFC280l [Bro08]
% 0.18/0.35
% 0.18/0.35 % Status : Theorem
% 0.18/0.35 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.18/0.35 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.18/0.35 % Number of atoms : 17 ( 4 equ; 0 cnn)
% 0.18/0.35 % Maximal formula atoms : 4 ( 3 avg)
% 0.18/0.35 % Number of connectives : 41 ( 0 ~; 0 |; 2 &; 36 @)
% 0.18/0.35 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.35 % Maximal formula depth : 11 ( 3 avg)
% 0.18/0.35 % Number of types : 2 ( 0 usr)
% 0.18/0.35 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.18/0.35 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.18/0.35 % Number of variables : 18 ( 12 ^; 5 !; 1 ?; 18 :)
% 0.18/0.35 % SPC : TH0_THM_EQU_NAR
% 0.18/0.35
% 0.18/0.35 % Comments : http://mathgate.info/detsetitem.php?id=344
% 0.18/0.35 %------------------------------------------------------------------------------
% 0.18/0.35 thf(in_type,type,
% 0.18/0.35 in: $i > $i > $o ).
% 0.18/0.35
% 0.18/0.35 thf(subset_type,type,
% 0.18/0.35 subset: $i > $i > $o ).
% 0.18/0.35
% 0.18/0.35 thf(kpair_type,type,
% 0.18/0.35 kpair: $i > $i > $i ).
% 0.18/0.35
% 0.18/0.35 thf(cartprod_type,type,
% 0.18/0.35 cartprod: $i > $i > $i ).
% 0.18/0.35
% 0.18/0.35 thf(breln_type,type,
% 0.18/0.35 breln: $i > $i > $i > $o ).
% 0.18/0.35
% 0.18/0.35 thf(breln,definition,
% 0.18/0.35 ( breln
% 0.18/0.35 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.35
% 0.18/0.35 thf(dpsetconstr_type,type,
% 0.18/0.35 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.18/0.35
% 0.18/0.35 thf(breln1_type,type,
% 0.18/0.35 breln1: $i > $i > $o ).
% 0.18/0.35
% 0.18/0.35 thf(breln1,definition,
% 0.18/0.35 ( breln1
% 0.18/0.35 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.18/0.35
% 0.18/0.35 thf(setOfPairsIsBReln1_type,type,
% 0.18/0.35 setOfPairsIsBReln1: $o ).
% 0.18/0.35
% 0.18/0.35 thf(setOfPairsIsBReln1,definition,
% 0.18/0.35 ( setOfPairsIsBReln1
% 0.18/0.35 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.18/0.35 ( breln1 @ A
% 0.18/0.35 @ ( dpsetconstr @ A @ A
% 0.18/0.35 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.18/0.35
% 0.18/0.35 thf(breln1compset_type,type,
% 0.18/0.35 breln1compset: $i > $i > $i > $i ).
% 0.18/0.35
% 0.18/0.35 thf(breln1compset,definition,
% 0.18/0.35 ( breln1compset
% 0.18/0.35 = ( ^ [A: $i,R: $i,S: $i] :
% 0.18/0.35 ( dpsetconstr @ A @ A
% 0.18/0.35 @ ^ [Xx: $i,Xy: $i] :
% 0.18/0.35 ? [Xz: $i] :
% 0.18/0.35 ( ( in @ Xz @ A )
% 0.18/0.35 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.18/0.35 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 0.18/0.35
% 0.18/0.35 thf(breln1compprop,conjecture,
% 0.18/0.35 ( setOfPairsIsBReln1
% 0.18/0.35 => ! [A: $i,R: $i] :
% 0.18/0.35 ( ( breln1 @ A @ R )
% 0.18/0.35 => ! [S: $i] :
% 0.18/0.35 ( ( breln1 @ A @ S )
% 0.18/0.35 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ).
% 0.18/0.35
% 0.18/0.35 %------------------------------------------------------------------------------
% 0.18/0.35 ------------------------
% 1.41/1.27 ---- Embedded in THF ---
% 1.41/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.41/1.27 %%% Generated on Tue Feb 24 07:33:26 EST 2026
% 1.41/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.41/1.27 %%% Logic specification used:
% 1.41/1.27 %%% thf(spec, logic, $$dhol).
% 1.41/1.27
% 1.41/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2DTF9014.p
% See solution above
% 1.41/1.27 ------------------------
% 1.41/1.28 ---- Cleaned THF ---
% 1.41/1.28 thf(in_type,type,
% 1.41/1.28 in: $i > $i > $o ).
% 1.41/1.28
% 1.41/1.28 thf(subset_type,type,
% 1.41/1.28 subset: $i > $i > $o ).
% 1.41/1.28
% 1.41/1.28 thf(kpair_type,type,
% 1.41/1.28 kpair: $i > $i > $i ).
% 1.41/1.28
% 1.41/1.28 thf(cartprod_type,type,
% 1.41/1.28 cartprod: $i > $i > $i ).
% 1.41/1.28
% 1.41/1.28 thf(breln_type,type,
% 1.41/1.28 breln: $i > $i > $i > $o ).
% 1.41/1.28
% 1.41/1.28 thf(breln,definition,
% 1.41/1.28 ( breln
% 1.41/1.28 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.41/1.28
% 1.41/1.28 thf(dpsetconstr_type,type,
% 1.41/1.28 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.41/1.28
% 1.41/1.28 thf(breln1_type,type,
% 1.41/1.28 breln1: $i > $i > $o ).
% 1.41/1.28
% 1.41/1.28 thf(breln1,definition,
% 1.41/1.28 ( breln1
% 1.41/1.28 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.41/1.28
% 1.41/1.28 thf(setOfPairsIsBReln1_type,type,
% 1.41/1.28 setOfPairsIsBReln1: $o ).
% 1.41/1.28
% 1.41/1.28 thf(setOfPairsIsBReln1,definition,
% 1.41/1.28 ( setOfPairsIsBReln1
% 1.41/1.28 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 1.41/1.28 ( breln1 @ A
% 1.41/1.28 @ ( dpsetconstr @ A @ A
% 1.41/1.28 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 1.41/1.28
% 1.41/1.28 thf(breln1compset_type,type,
% 1.41/1.28 breln1compset: $i > $i > $i > $i ).
% 1.41/1.28
% 1.41/1.28 thf(breln1compset,definition,
% 1.41/1.28 ( breln1compset
% 1.41/1.28 = ( ^ [A: $i,R: $i,S: $i] :
% 1.41/1.28 ( dpsetconstr @ A @ A
% 1.41/1.28 @ ^ [Xx: $i,Xy: $i] :
% 1.41/1.28 ? [Xz: $i] :
% 1.41/1.28 ( ( in @ Xz @ A )
% 1.41/1.28 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.41/1.28 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 1.41/1.28
% 1.41/1.28 thf(breln1compprop,conjecture,
% 1.41/1.28 ( setOfPairsIsBReln1
% 1.41/1.28 => ! [A: $i,R: $i] :
% 1.41/1.28 ( ( breln1 @ A @ R )
% 1.41/1.28 => ! [S: $i] :
% 1.41/1.28 ( ( breln1 @ A @ S )
% 1.41/1.28 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ).
% 1.41/1.28 ------------------------
% 1.59/1.30 % (9112)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_9014 for (2999ds/4Mi)
% 1.59/1.30 % (9113)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_9014 for (2999ds/27Mi)
% 1.59/1.30 % (9114)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9014 for (2999ds/2Mi)
% 1.59/1.30 % (9115)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_9014 for (2999ds/2Mi)
% 1.59/1.30 % (9116)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_9014 for (2999ds/275Mi)
% 1.59/1.30 % (9111)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9014 for (2999ds/183Mi)
% 1.59/1.30 % (9117)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9014 for (2999ds/18Mi)
% 1.59/1.30 % (9114)Instruction limit reached!
% 1.59/1.30 % (9114)------------------------------
% 1.59/1.30 % (9114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (9114)Termination reason: Unknown
% 1.59/1.30 % (9114)Termination phase: Saturation
% 1.59/1.30 % (9115)Instruction limit reached!
% 1.59/1.30 % (9115)------------------------------
% 1.59/1.30 % (9115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (9115)Termination reason: Unknown
% 1.59/1.30 % (9115)Termination phase: Property scanning
% 1.59/1.30
% 1.59/1.30 % (9115)Memory used [KB]: 1023
% 1.59/1.30 % (9115)Time elapsed: 0.003 s
% 1.59/1.30 % (9115)Instructions burned: 3 (million)
% 1.59/1.30 % (9115)------------------------------
% 1.59/1.30 % (9115)------------------------------
% 1.59/1.30
% 1.59/1.30 % (9114)Memory used [KB]: 1023
% 1.59/1.30 % (9114)Time elapsed: 0.003 s
% 1.59/1.30 % (9114)Instructions burned: 3 (million)
% 1.59/1.30 % (9114)------------------------------
% 1.59/1.30 % (9114)------------------------------
% 1.59/1.30 % (9112)Instruction limit reached!
% 1.59/1.30 % (9112)------------------------------
% 1.59/1.30 % (9112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (9116)Refutation not found, incomplete strategy
% 1.59/1.30 % (9116)------------------------------
% 1.59/1.30 % (9116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (9116)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.30
% 1.59/1.30
% 1.59/1.30 % (9116)Memory used [KB]: 5500
% 1.59/1.30 % (9116)Time elapsed: 0.003 s
% 1.59/1.30 % (9116)Instructions burned: 3 (million)
% 1.59/1.30 % (9116)------------------------------
% 1.59/1.30 % (9116)------------------------------
% 1.59/1.30 % (9112)Termination reason: Unknown
% 1.59/1.30 % (9112)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (9112)Memory used [KB]: 5500
% 1.59/1.30 % (9112)Time elapsed: 0.004 s
% 1.59/1.30 % (9112)Instructions burned: 4 (million)
% 1.59/1.30 % (9112)------------------------------
% 1.59/1.30 % (9112)------------------------------
% 1.59/1.31 % (9113)First to succeed.
% 1.59/1.31 % (9111)Also succeeded, but the first one will report.
% 1.59/1.31 % (9113)Refutation found. Thanks to Tanya!
% 1.59/1.31 % SZS status Theorem for DTF2THF_9014
% 1.59/1.31 % SZS output start Proof for DTF2THF_9014
% 1.59/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.59/1.31 thf(func_def_1, type, subset: $i > $i > $o).
% 1.59/1.31 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.59/1.31 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.59/1.31 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.59/1.31 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.59/1.31 thf(func_def_7, type, breln1: $i > $i > $o).
% 1.59/1.31 thf(func_def_9, type, breln1compset: $i > $i > $i > $i).
% 1.59/1.31 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.59/1.31 thf(func_def_27, type, ph4: !>[X0: $tType]:(X0)).
% 1.59/1.31 thf(f43,plain,(
% 1.59/1.31 $false),
% 1.59/1.31 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.59/1.31 thf(f42,plain,(
% 1.59/1.31 ($true != $true)),
% 1.59/1.31 inference(superposition,[status(thm)],[f39,f38])).
% 1.59/1.31 thf(f38,plain,(
% 1.59/1.31 ( ! [X2 : $i,X1 : $i > $i > $o] : (((subset @ (dpsetconstr @ X2 @ X2 @ X1) @ (cartprod @ X2 @ X2)) = $true)) )),
% 1.59/1.31 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.59/1.31 thf(f37,plain,(
% 1.59/1.31 ( ! [X2 : $i,X1 : $i > $i > $o] : ((((^[Y0 : $i]: (subset @ (dpsetconstr @ Y0 @ Y0 @ X1) @ (cartprod @ Y0 @ Y0))) @ X2) = $true)) )),
% 1.59/1.31 inference(pi_clausification,[status(thm)],[f36])).
% 1.59/1.31 thf(f36,plain,(
% 1.59/1.31 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (subset @ (dpsetconstr @ Y0 @ Y0 @ X1) @ (cartprod @ Y0 @ Y0)))) = $true)) )),
% 1.59/1.31 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.59/1.31 thf(f35,plain,(
% 1.59/1.31 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ Y1 @ Y0) @ (cartprod @ Y1 @ Y1))))) @ X1) = $true)) )),
% 1.59/1.31 inference(pi_clausification,[status(thm)],[f34])).
% 1.59/1.31 thf(f34,plain,(
% 1.59/1.31 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ Y1 @ Y0) @ (cartprod @ Y1 @ Y1)))))))),
% 1.59/1.31 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.59/1.31 thf(f33,plain,(
% 1.59/1.31 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ (dpsetconstr @ Y1 @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y2 @ Y3)))))))))))),
% 1.59/1.31 inference(definition_unfolding,[status(thm)],[f27,f21,f29])).
% 1.59/1.31 thf(f29,plain,(
% 1.59/1.31 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 1.59/1.31 inference(definition_unfolding,[status(thm)],[f26,f28])).
% 1.59/1.31 thf(f28,plain,(
% 1.59/1.31 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.59/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.31 thf(f14,plain,(
% 1.59/1.31 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.59/1.31 inference(fool_elimination,[status(thm)],[f1])).
% 1.59/1.31 thf(f1,axiom,(
% 1.59/1.31 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 1.59/1.31 file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln)).
% 1.59/1.31 thf(f26,plain,(
% 1.59/1.31 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.59/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.31 thf(f9,plain,(
% 1.59/1.31 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.59/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.59/1.31 thf(f8,plain,(
% 1.59/1.31 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)),
% 1.59/1.31 inference(rectify,[status(thm)],[f2])).
% 1.59/1.31 thf(f2,axiom,(
% 1.59/1.31 ((^[X0 : $i, X3 : $i] : (breln @ X0 @ X0 @ X3)) = breln1)),
% 1.59/1.31 file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln1)).
% 1.59/1.31 thf(f21,plain,(
% 1.59/1.31 (setOfPairsIsBReln1 = $true)),
% 1.59/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.31 thf(f20,plain,(
% 1.59/1.31 (($true = (breln1 @ sK0 @ sK1)) & (((breln1 @ sK0 @ sK2) = $true) & ((breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK2)) != $true))) & (setOfPairsIsBReln1 = $true)),
% 1.59/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18])).
% 1.59/1.31 thf(f18,plain,(
% 1.59/1.31 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2))))) => (($true = (breln1 @ sK0 @ sK1)) & ? [X2 : $i] : (((breln1 @ sK0 @ X2) = $true) & ($true != (breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ X2)))))),
% 1.59/1.31 introduced(definition,[],[choice_axiom])).
% 1.59/1.31 thf(f19,plain,(
% 1.59/1.31 ? [X2 : $i] : (((breln1 @ sK0 @ X2) = $true) & ($true != (breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ X2)))) => (((breln1 @ sK0 @ sK2) = $true) & ((breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK2)) != $true))),
% 1.59/1.31 introduced(definition,[],[choice_axiom])).
% 1.59/1.31 thf(f17,plain,(
% 1.59/1.31 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2))))) & (setOfPairsIsBReln1 = $true)),
% 1.59/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.59/1.31 thf(f13,plain,(
% 1.59/1.31 ~((setOfPairsIsBReln1 = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ($true = (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2))))))),
% 1.59/1.31 inference(fool_elimination,[status(thm)],[f12])).
% 1.59/1.31 thf(f12,plain,(
% 1.59/1.31 ~(setOfPairsIsBReln1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))))),
% 1.59/1.31 inference(rectify,[status(thm)],[f6])).
% 1.59/1.31 thf(f6,negated_conjecture,(
% 1.59/1.31 ~(setOfPairsIsBReln1 => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X7 : $i] : ((breln1 @ X0 @ X7) => (breln1 @ X0 @ (breln1compset @ X0 @ X3 @ X7)))))),
% 1.59/1.31 inference(negated_conjecture,[status(cth)],[f5])).
% 1.59/1.31 thf(f5,conjecture,(
% 1.59/1.31 setOfPairsIsBReln1 => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X7 : $i] : ((breln1 @ X0 @ X7) => (breln1 @ X0 @ (breln1compset @ X0 @ X3 @ X7))))),
% 1.59/1.31 file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln1compprop)).
% 1.59/1.31 thf(f27,plain,(
% 1.59/1.31 (setOfPairsIsBReln1 = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (breln1 @ Y1 @ (dpsetconstr @ Y1 @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y2 @ Y3)))))))))))),
% 1.59/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.59/1.31 thf(f16,plain,(
% 1.59/1.31 (setOfPairsIsBReln1 = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (breln1 @ Y1 @ (dpsetconstr @ Y1 @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y2 @ Y3)))))))))))),
% 1.59/1.31 inference(fool_elimination,[status(thm)],[f15])).
% 1.59/1.31 thf(f15,plain,(
% 1.59/1.31 (! [X0 : $i,X1 : $i > $i > $o] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (X1 @ X2 @ X3)))) = setOfPairsIsBReln1)),
% 1.59/1.31 inference(rectify,[status(thm)],[f3])).
% 1.59/1.31 thf(f3,axiom,(
% 1.59/1.31 (! [X0 : $i,X4 : $i > $i > $o] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X5 : $i, X6 : $i] : (X4 @ X5 @ X6)))) = setOfPairsIsBReln1)),
% 1.59/1.31 file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',setOfPairsIsBReln1)).
% 1.59/1.31 thf(f39,plain,(
% 1.59/1.31 ((subset @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK1) & (in @ (kpair @ Y2 @ Y1) @ sK2)) & (in @ Y2 @ sK0)))))))) @ (cartprod @ sK0 @ sK0)) != $true)),
% 1.59/1.31 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.59/1.31 thf(f32,plain,(
% 1.59/1.31 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ (kpair @ Y5 @ Y4) @ Y2)) & (in @ Y5 @ Y0))))))))))))) @ sK0 @ sK1 @ sK2)) != $true)),
% 1.59/1.31 inference(definition_unfolding,[status(thm)],[f22,f29,f25])).
% 1.59/1.31 thf(f25,plain,(
% 1.59/1.31 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ (kpair @ Y5 @ Y4) @ Y2)) & (in @ Y5 @ Y0))))))))))))))),
% 1.59/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.59/1.31 thf(f11,plain,(
% 1.59/1.31 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ (kpair @ Y5 @ Y4) @ Y2)) & (in @ Y5 @ Y0))))))))))))))),
% 1.59/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.59/1.31 thf(f10,plain,(
% 1.59/1.31 ((^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5 : $i] : ((in @ X5 @ X0) & (in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1)))))) = breln1compset)),
% 1.59/1.31 inference(rectify,[status(thm)],[f4])).
% 1.59/1.31 thf(f4,axiom,(
% 1.59/1.31 ((^[X0 : $i, X3 : $i, X7 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X5 : $i, X6 : $i] : (? [X8 : $i] : ((in @ X8 @ X0) & (in @ (kpair @ X8 @ X6) @ X7) & (in @ (kpair @ X5 @ X8) @ X3)))))) = breln1compset)),
% 1.59/1.31 file('/export/starexec/sandbox2/tmp/tmp.A20c5LtEhI/DTF2THF_9014.p',breln1compset)).
% 1.59/1.31 thf(f22,plain,(
% 1.59/1.31 ((breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK2)) != $true)),
% 1.59/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.59/1.31 % SZS output end Proof for DTF2THF_9014
% 1.59/1.31 % (9113)------------------------------
% 1.59/1.31 % (9113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (9113)Termination reason: Refutation
% 1.59/1.31
% 1.59/1.31 % (9113)Memory used [KB]: 5500
% 1.59/1.31 % (9113)Time elapsed: 0.006 s
% 1.59/1.31 % (9113)Instructions burned: 4 (million)
% 1.59/1.31 % (9113)------------------------------
% 1.59/1.31 % (9113)------------------------------
% 1.59/1.31 % (9110)Success in time 0.02 s
%------------------------------------------------------------------------------