%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU771^2 : 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 : n016.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 09:37:04 AM UTC 2026
% Result : Theorem 1.52s 1.30s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 142 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 282 ( 10 ~; 0 |; 2 &; 247 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 5 con; 0-3 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 81 ^; 26 !; 4 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
subset: $i > $i > $o ).
thf(func_def_1,type,
cartprod: $i > $i > $i ).
thf(func_def_2,type,
breln: $i > $i > $i > $o ).
thf(func_def_4,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_6,type,
breln1: $i > $i > $o ).
thf(func_def_16,type,
sK1: $i > $i > $o ).
thf(f33,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25,f32]) ).
thf(f32,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( $true
= ( subset @ ( dpsetconstr @ X3 @ X1 @ X2 ) @ ( cartprod @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ X1 @ X2 ) @ ( cartprod @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ X1 @ X2 ) @ ( cartprod @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ X1 @ Y0 ) @ ( cartprod @ Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ X1 @ Y0 ) @ ( cartprod @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f18,f21]) ).
thf(f21,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,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',breln) ).
thf(f18,plain,
setOfPairsIsBReln = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( breln1 @ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
!= $true )
& ( setOfPairsIsBReln = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i > $i > $o] :
( ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true )
=> ( ( breln1 @ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i > $i > $o] :
( ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true )
& ( setOfPairsIsBReln = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setOfPairsIsBReln = $true )
=> ! [X0: $i,X1: $i > $i > $o] :
( ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setOfPairsIsBReln
=> ! [X0: $i,X1: $i > $i > $o] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setOfPairsIsBReln
=> ! [X0: $i,X3: $i > $i > $o] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X4: $i,X5: $i] : ( X3 @ X4 @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setOfPairsIsBReln
=> ! [X0: $i,X3: $i > $i > $o] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X4: $i,X5: $i] : ( X3 @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',setOfPairsIsBReln1) ).
thf(f20,plain,
( setOfPairsIsBReln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( breln @ Y2 @ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( setOfPairsIsBReln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( breln @ Y2 @ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) ) )
= setOfPairsIsBReln ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X3: $i > $i > $o,X1: $i] :
( ( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X4: $i,X5: $i] : ( X3 @ X4 @ X5 ) ) )
= setOfPairsIsBReln ),
file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',setOfPairsIsBReln) ).
thf(f25,plain,
( ( subset @ ( dpsetconstr @ sK0 @ sK0 @ sK1 ) @ ( cartprod @ sK0 @ sK0 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f22]) ).
thf(f22,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)],[f17,f21]) ).
thf(f17,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) )
= breln1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X6: $i] : ( breln @ X0 @ X0 @ X6 ) )
= breln1 ),
file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',breln1) ).
thf(f19,plain,
( ( breln1 @ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU771^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:33:51 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU771^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Binary Relations on a Set
% 0.19/0.45 % Version : Especial > Reduced > Especial.
% 0.19/0.45 % English : (! A:i.! phi:i>(i>o).breln1 A (dpsetconstr A A (^ x,y:i.phi x y)))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC273l [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 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 v4.0.1, 0.33 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.19/0.45 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.45 % Number of connectives : 23 ( 0 ~; 0 |; 0 &; 22 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 10 ( 3 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% 0.19/0.45 % Number of variables : 14 ( 9 ^; 5 !; 0 ?; 14 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=334
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(subset_type,type,
% 0.19/0.45 subset: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cartprod_type,type,
% 0.19/0.45 cartprod: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(breln_type,type,
% 0.19/0.45 breln: $i > $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(breln,definition,
% 0.19/0.45 ( breln
% 0.19/0.45 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(dpsetconstr_type,type,
% 0.19/0.45 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(setOfPairsIsBReln_type,type,
% 0.19/0.45 setOfPairsIsBReln: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setOfPairsIsBReln,definition,
% 0.19/0.45 ( setOfPairsIsBReln
% 0.19/0.45 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.19/0.45 ( breln @ A @ B
% 0.19/0.45 @ ( dpsetconstr @ A @ B
% 0.19/0.45 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(breln1_type,type,
% 0.19/0.45 breln1: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(breln1,definition,
% 0.19/0.45 ( breln1
% 0.19/0.45 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setOfPairsIsBReln1,conjecture,
% 0.19/0.45 ( setOfPairsIsBReln
% 0.19/0.45 => ! [A: $i,Xphi: $i > $i > $o] :
% 0.19/0.45 ( breln1 @ A
% 0.19/0.45 @ ( dpsetconstr @ A @ A
% 0.19/0.45 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.52/1.26 ---- Embedded in THF ---
% 1.52/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.26 %%% Generated on Tue Feb 24 12:33:51 EST 2026
% 1.52/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.26 %%% Logic specification used:
% 1.52/1.26 %%% thf(spec, logic, $$dhol).
% 1.52/1.26
% 1.52/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2DTF997.p
% See solution above
% 1.52/1.26 ------------------------
% 1.52/1.27 ---- Cleaned THF ---
% 1.52/1.27 thf(subset_type,type,
% 1.52/1.27 subset: $i > $i > $o ).
% 1.52/1.27
% 1.52/1.27 thf(cartprod_type,type,
% 1.52/1.27 cartprod: $i > $i > $i ).
% 1.52/1.27
% 1.52/1.27 thf(breln_type,type,
% 1.52/1.27 breln: $i > $i > $i > $o ).
% 1.52/1.27
% 1.52/1.27 thf(breln,definition,
% 1.52/1.27 ( breln
% 1.52/1.27 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(dpsetconstr_type,type,
% 1.52/1.27 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.52/1.27
% 1.52/1.27 thf(setOfPairsIsBReln_type,type,
% 1.52/1.27 setOfPairsIsBReln: $o ).
% 1.52/1.27
% 1.52/1.27 thf(setOfPairsIsBReln,definition,
% 1.52/1.27 ( setOfPairsIsBReln
% 1.52/1.27 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.52/1.27 ( breln @ A @ B
% 1.52/1.27 @ ( dpsetconstr @ A @ B
% 1.52/1.27 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(breln1_type,type,
% 1.52/1.27 breln1: $i > $i > $o ).
% 1.52/1.27
% 1.52/1.27 thf(breln1,definition,
% 1.52/1.27 ( breln1
% 1.52/1.27 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(setOfPairsIsBReln1,conjecture,
% 1.52/1.27 ( setOfPairsIsBReln
% 1.52/1.27 => ! [A: $i,Xphi: $i > $i > $o] :
% 1.52/1.27 ( breln1 @ A
% 1.52/1.27 @ ( dpsetconstr @ A @ A
% 1.52/1.27 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ).
% 1.52/1.27 ------------------------
% 1.52/1.28 % (1309)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_997 for (2999ds/2Mi)
% 1.52/1.29 % (1309)Instruction limit reached!
% 1.52/1.29 % (1309)------------------------------
% 1.52/1.29 % (1309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (1309)Termination reason: Unknown
% 1.52/1.29 % (1309)Termination phase: Saturation
% 1.52/1.29
% 1.52/1.29 % (1309)Memory used [KB]: 5500
% 1.52/1.29 % (1309)Time elapsed: 0.003 s
% 1.52/1.29 % (1309)Instructions burned: 3 (million)
% 1.52/1.29 % (1309)------------------------------
% 1.52/1.29 % (1309)------------------------------
% 1.52/1.29 % (1306)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_997 for (2999ds/183Mi)
% 1.52/1.29 % (1307)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_997 for (2999ds/4Mi)
% 1.52/1.29 % (1308)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_997 for (2999ds/27Mi)
% 1.52/1.29 % (1310)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_997 for (2999ds/2Mi)
% 1.52/1.29 % (1311)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_997 for (2999ds/275Mi)
% 1.52/1.29 % (1312)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_997 for (2999ds/18Mi)
% 1.52/1.29 % (1310)Instruction limit reached!
% 1.52/1.29 % (1310)------------------------------
% 1.52/1.29 % (1310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (1310)Termination reason: Unknown
% 1.52/1.29 % (1310)Termination phase: Function definition elimination
% 1.52/1.29
% 1.52/1.29 % (1310)Memory used [KB]: 895
% 1.52/1.29 % (1310)Time elapsed: 0.003 s
% 1.52/1.29 % (1310)Instructions burned: 2 (million)
% 1.52/1.29 % (1310)------------------------------
% 1.52/1.29 % (1310)------------------------------
% 1.52/1.29 % (1307)First to succeed.
% 1.52/1.30 % (1306)Also succeeded, but the first one will report.
% 1.52/1.30 % (1307)Refutation found. Thanks to Tanya!
% 1.52/1.30 % SZS status Theorem for DTF2THF_997
% 1.52/1.30 % SZS output start Proof for DTF2THF_997
% 1.52/1.30 thf(func_def_0, type, subset: $i > $i > $o).
% 1.52/1.30 thf(func_def_1, type, cartprod: $i > $i > $i).
% 1.52/1.30 thf(func_def_2, type, breln: $i > $i > $i > $o).
% 1.52/1.30 thf(func_def_4, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.52/1.30 thf(func_def_6, type, breln1: $i > $i > $o).
% 1.52/1.30 thf(func_def_16, type, sK1: $i > $i > $o).
% 1.52/1.30 thf(f33,plain,(
% 1.52/1.30 $false),
% 1.52/1.30 inference(subsumption_resolution,[status(thm)],[f25,f32])).
% 1.52/1.30 thf(f32,plain,(
% 1.52/1.30 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (subset @ (dpsetconstr @ X3 @ X1 @ X2) @ (cartprod @ X3 @ X1)))) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.52/1.30 thf(f31,plain,(
% 1.52/1.30 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (subset @ (dpsetconstr @ Y0 @ X1 @ X2) @ (cartprod @ Y0 @ X1))) @ X3) = $true)) )),
% 1.52/1.30 inference(pi_clausification,[status(thm)],[f30])).
% 1.52/1.30 thf(f30,plain,(
% 1.52/1.30 ( ! [X2 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (subset @ (dpsetconstr @ Y0 @ X1 @ X2) @ (cartprod @ Y0 @ X1)))) = $true)) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.52/1.30 thf(f29,plain,(
% 1.52/1.30 ( ! [X2 : $i > $i > $o,X1 : $i] : ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ X1 @ Y0) @ (cartprod @ Y1 @ X1))))) @ X2) = $true)) )),
% 1.52/1.30 inference(pi_clausification,[status(thm)],[f28])).
% 1.52/1.30 thf(f28,plain,(
% 1.52/1.30 ( ! [X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ X1 @ Y0) @ (cartprod @ Y1 @ X1)))))))) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.52/1.30 thf(f27,plain,(
% 1.52/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 1.52/1.30 inference(pi_clausification,[status(thm)],[f26])).
% 1.52/1.30 thf(f26,plain,(
% 1.52/1.30 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) = $true)),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.52/1.30 thf(f24,plain,(
% 1.52/1.30 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))) = $true)),
% 1.52/1.30 inference(definition_unfolding,[status(thm)],[f20,f18,f21])).
% 1.52/1.30 thf(f21,plain,(
% 1.52/1.30 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.52/1.30 thf(f13,plain,(
% 1.52/1.30 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f1])).
% 1.52/1.30 thf(f1,axiom,(
% 1.52/1.30 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',breln)).
% 1.52/1.30 thf(f18,plain,(
% 1.52/1.30 (setOfPairsIsBReln = $true)),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.52/1.30 thf(f16,plain,(
% 1.52/1.30 ((breln1 @ sK0 @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) != $true) & (setOfPairsIsBReln = $true)),
% 1.52/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15])).
% 1.52/1.30 thf(f15,plain,(
% 1.52/1.30 ? [X0 : $i,X1 : $i > $i > $o] : ((breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true) => ((breln1 @ sK0 @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) != $true)),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f14,plain,(
% 1.52/1.30 ? [X0 : $i,X1 : $i > $i > $o] : ((breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true) & (setOfPairsIsBReln = $true)),
% 1.52/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.52/1.30 thf(f8,plain,(
% 1.52/1.30 ~((setOfPairsIsBReln = $true) => ! [X0 : $i,X1 : $i > $i > $o] : ((breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.52/1.30 thf(f7,plain,(
% 1.52/1.30 ~(setOfPairsIsBReln => ! [X0 : $i,X1 : $i > $i > $o] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (X1 @ X2 @ X3)))))),
% 1.52/1.30 inference(rectify,[status(thm)],[f5])).
% 1.52/1.30 thf(f5,negated_conjecture,(
% 1.52/1.30 ~(setOfPairsIsBReln => ! [X0 : $i,X3 : $i > $i > $o] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (X3 @ X4 @ X5)))))),
% 1.52/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.52/1.30 thf(f4,conjecture,(
% 1.52/1.30 setOfPairsIsBReln => ! [X0 : $i,X3 : $i > $i > $o] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (X3 @ X4 @ X5))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',setOfPairsIsBReln1)).
% 1.52/1.30 thf(f20,plain,(
% 1.52/1.30 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.52/1.30 thf(f10,plain,(
% 1.52/1.30 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.52/1.30 thf(f9,plain,(
% 1.52/1.30 (! [X0 : $i,X1 : $i > $i > $o,X2 : $i] : (breln @ X0 @ X2 @ (dpsetconstr @ X0 @ X2 @ (^[X3 : $i, X4 : $i] : (X1 @ X3 @ X4)))) = setOfPairsIsBReln)),
% 1.52/1.30 inference(rectify,[status(thm)],[f2])).
% 1.52/1.30 thf(f2,axiom,(
% 1.52/1.30 (! [X0 : $i,X3 : $i > $i > $o,X1 : $i] : (breln @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X4 : $i, X5 : $i] : (X3 @ X4 @ X5)))) = setOfPairsIsBReln)),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',setOfPairsIsBReln)).
% 1.52/1.30 thf(f25,plain,(
% 1.52/1.30 ((subset @ (dpsetconstr @ sK0 @ sK0 @ sK1) @ (cartprod @ sK0 @ sK0)) != $true)),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.52/1.30 thf(f23,plain,(
% 1.52/1.30 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
% 1.52/1.30 inference(definition_unfolding,[status(thm)],[f19,f22])).
% 1.52/1.30 thf(f22,plain,(
% 1.52/1.30 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 1.52/1.30 inference(definition_unfolding,[status(thm)],[f17,f21])).
% 1.52/1.30 thf(f17,plain,(
% 1.52/1.30 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.52/1.30 thf(f12,plain,(
% 1.52/1.30 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.52/1.30 thf(f11,plain,(
% 1.52/1.30 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)),
% 1.52/1.30 inference(rectify,[status(thm)],[f3])).
% 1.52/1.30 thf(f3,axiom,(
% 1.52/1.30 ((^[X0 : $i, X6 : $i] : (breln @ X0 @ X0 @ X6)) = breln1)),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.K8KyLolQbz/DTF2THF_997.p',breln1)).
% 1.52/1.30 thf(f19,plain,(
% 1.52/1.30 ((breln1 @ sK0 @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) != $true)),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.30 % SZS output end Proof for DTF2THF_997
% 1.65/1.30 % (1307)------------------------------
% 1.65/1.30 % (1307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (1307)Termination reason: Refutation
% 1.65/1.30
% 1.65/1.30 % (1307)Memory used [KB]: 5500
% 1.65/1.30 % (1307)Time elapsed: 0.005 s
% 1.65/1.30 % (1307)Instructions burned: 3 (million)
% 1.65/1.30 % (1307)------------------------------
% 1.65/1.30 % (1307)------------------------------
% 1.65/1.30 % (1305)Success in time 0.021 s
%------------------------------------------------------------------------------