%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU775^2 : 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 : 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 09:37:05 AM UTC 2026
% Result : Theorem 1.68s 1.48s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 274 ( 10 ~; 0 |; 6 &; 239 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 6 con; 0-3 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 98 ( 76 ^; 18 !; 4 ?; 98 :)
% 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,
breln1invset: $i > $i > $i ).
thf(f38,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f31,f37]) ).
thf(f37,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( subset @ ( dpsetconstr @ X1 @ X1 @ X2 ) @ ( cartprod @ X1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ^ [Y0: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X1 @ Y0 ) @ ( cartprod @ X1 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X1 @ Y0 ) @ ( cartprod @ X1 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26,f25,f27]) ).
thf(f27,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)],[f21,f20]) ).
thf(f20,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,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.LTfVuILXxC/DTF2THF_29815.p',breln) ).
thf(f21,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/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln1) ).
thf(f25,plain,
setOfPairsIsBReln1 = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( setOfPairsIsBReln1 = $true )
& ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= $true ) )
=> ( ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( setOfPairsIsBReln1 = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setOfPairsIsBReln1 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( setOfPairsIsBReln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( setOfPairsIsBReln1
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( setOfPairsIsBReln1
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln1invprop) ).
thf(f26,plain,
( setOfPairsIsBReln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( breln1 @ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( setOfPairsIsBReln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( breln1 @ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( setOfPairsIsBReln1
= ( ! [X0: $i > $i > $o,X1: $i] :
( breln1 @ X1
@ ( dpsetconstr @ X1 @ X1
@ ^ [X2: $i,X3: $i] : ( X0 @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setOfPairsIsBReln1
= ( ! [X4: $i > $i > $o,X0: $i] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X5: $i,X6: $i] : ( X4 @ X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',setOfPairsIsBReln1) ).
thf(f31,plain,
( $true
!= ( subset
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK1 ) )
@ ( cartprod @ sK0 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
@ sK0
@ sK1 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f23,f27,f22]) ).
thf(f22,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: $i,X1: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ X1 ) ) )
= breln1invset ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X3: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X5: $i,X6: $i] : ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) )
= breln1invset ),
file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln1invset) ).
thf(f23,plain,
( ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU775^2 : TPTP v9.2.1. Released v3.7.0.
% 0.14/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n019.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:33:39 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.48 ---- Original DTF file ---
% 0.33/0.48 thf(spec,logic,$$dhol).
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 % File : SEU775^2 : TPTP v9.2.1. Released v3.7.0.
% 0.33/0.48 % Domain : Set Theory
% 0.33/0.48 % Problem : Binary Relations on a Set
% 0.33/0.48 % Version : Especial > Reduced > Especial.
% 0.33/0.48 % English : (! A:i.! R:i.breln1 A R -> breln1 A (breln1invset A R))
% 0.33/0.48
% 0.33/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.33/0.48 % Source : [Bro08]
% 0.33/0.48 % Names : ZFC277l [Bro08]
% 0.33/0.48
% 0.33/0.48 % Status : Theorem
% 0.33/0.48 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 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 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.33/0.48 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.33/0.48 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.33/0.48 % Maximal formula atoms : 3 ( 2 avg)
% 0.33/0.48 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 27 @)
% 0.33/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.33/0.48 % Maximal formula depth : 8 ( 2 avg)
% 0.33/0.48 % Number of types : 2 ( 0 usr)
% 0.33/0.48 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.33/0.48 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.33/0.48 % Number of variables : 15 ( 11 ^; 4 !; 0 ?; 15 :)
% 0.33/0.48 % SPC : TH0_THM_EQU_NAR
% 0.33/0.48
% 0.33/0.48 % Comments : http://mathgate.info/detsetitem.php?id=335
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 thf(in_type,type,
% 0.33/0.48 in: $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(subset_type,type,
% 0.33/0.48 subset: $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(kpair_type,type,
% 0.33/0.48 kpair: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(cartprod_type,type,
% 0.33/0.48 cartprod: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(breln_type,type,
% 0.33/0.48 breln: $i > $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(breln,definition,
% 0.33/0.48 ( breln
% 0.33/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(dpsetconstr_type,type,
% 0.33/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.33/0.48
% 0.33/0.48 thf(breln1_type,type,
% 0.33/0.48 breln1: $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(breln1,definition,
% 0.33/0.48 ( breln1
% 0.33/0.48 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setOfPairsIsBReln1_type,type,
% 0.33/0.48 setOfPairsIsBReln1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setOfPairsIsBReln1,definition,
% 0.33/0.48 ( setOfPairsIsBReln1
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.33/0.48 ( breln1 @ A
% 0.33/0.48 @ ( dpsetconstr @ A @ A
% 0.33/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(breln1invset_type,type,
% 0.33/0.48 breln1invset: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(breln1invset,definition,
% 0.33/0.48 ( breln1invset
% 0.33/0.48 = ( ^ [A: $i,R: $i] :
% 0.33/0.48 ( dpsetconstr @ A @ A
% 0.33/0.48 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(breln1invprop,conjecture,
% 0.33/0.48 ( setOfPairsIsBReln1
% 0.33/0.48 => ! [A: $i,R: $i] :
% 0.33/0.48 ( ( breln1 @ A @ R )
% 0.33/0.48 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 1.68/1.45 ---- Embedded in THF ---
% 1.68/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.45 %%% Generated on Tue Feb 24 12:33:40 EST 2026
% 1.68/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.45 %%% Logic specification used:
% 1.68/1.45 %%% thf(spec, logic, $$dhol).
% 1.68/1.45
% 1.68/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2DTF29815.p
% See solution above
% 1.68/1.45 ------------------------
% 1.68/1.46 ---- Cleaned THF ---
% 1.68/1.46 thf(in_type,type,
% 1.68/1.46 in: $i > $i > $o ).
% 1.68/1.46
% 1.68/1.46 thf(subset_type,type,
% 1.68/1.46 subset: $i > $i > $o ).
% 1.68/1.46
% 1.68/1.46 thf(kpair_type,type,
% 1.68/1.46 kpair: $i > $i > $i ).
% 1.68/1.46
% 1.68/1.46 thf(cartprod_type,type,
% 1.68/1.46 cartprod: $i > $i > $i ).
% 1.68/1.46
% 1.68/1.46 thf(breln_type,type,
% 1.68/1.46 breln: $i > $i > $i > $o ).
% 1.68/1.46
% 1.68/1.46 thf(breln,definition,
% 1.68/1.46 ( breln
% 1.68/1.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.68/1.46
% 1.68/1.46 thf(dpsetconstr_type,type,
% 1.68/1.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.68/1.46
% 1.68/1.46 thf(breln1_type,type,
% 1.68/1.46 breln1: $i > $i > $o ).
% 1.68/1.46
% 1.68/1.46 thf(breln1,definition,
% 1.68/1.46 ( breln1
% 1.68/1.46 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.68/1.46
% 1.68/1.46 thf(setOfPairsIsBReln1_type,type,
% 1.68/1.46 setOfPairsIsBReln1: $o ).
% 1.68/1.46
% 1.68/1.46 thf(setOfPairsIsBReln1,definition,
% 1.68/1.46 ( setOfPairsIsBReln1
% 1.68/1.46 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 1.68/1.46 ( breln1 @ A
% 1.68/1.46 @ ( dpsetconstr @ A @ A
% 1.68/1.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 1.68/1.46
% 1.68/1.46 thf(breln1invset_type,type,
% 1.68/1.46 breln1invset: $i > $i > $i ).
% 1.68/1.46
% 1.68/1.46 thf(breln1invset,definition,
% 1.68/1.46 ( breln1invset
% 1.68/1.46 = ( ^ [A: $i,R: $i] :
% 1.68/1.46 ( dpsetconstr @ A @ A
% 1.68/1.46 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 1.68/1.46
% 1.68/1.46 thf(breln1invprop,conjecture,
% 1.68/1.46 ( setOfPairsIsBReln1
% 1.68/1.46 => ! [A: $i,R: $i] :
% 1.68/1.46 ( ( breln1 @ A @ R )
% 1.68/1.46 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ).
% 1.68/1.46 ------------------------
% 1.68/1.48 % (29915)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29815 for (2999ds/2Mi)
% 1.68/1.48 % (29918)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29815 for (2999ds/18Mi)
% 1.68/1.48 % (29912)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29815 for (2999ds/183Mi)
% 1.68/1.48 % (29914)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_29815 for (2999ds/27Mi)
% 1.68/1.48 % (29913)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_29815 for (2999ds/4Mi)
% 1.68/1.48 % (29916)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_29815 for (2999ds/2Mi)
% 1.68/1.48 % (29917)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_29815 for (2999ds/275Mi)
% 1.68/1.48 % (29915)Instruction limit reached!
% 1.68/1.48 % (29915)------------------------------
% 1.68/1.48 % (29915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (29915)Termination reason: Unknown
% 1.68/1.48 % (29916)Instruction limit reached!
% 1.68/1.48 % (29916)------------------------------
% 1.68/1.48 % (29916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (29915)Termination phase: Function definition elimination
% 1.68/1.48
% 1.68/1.48 % (29915)Memory used [KB]: 1023
% 1.68/1.48 % (29915)Time elapsed: 0.003 s
% 1.68/1.48 % (29915)Instructions burned: 2 (million)
% 1.68/1.48 % (29915)------------------------------
% 1.68/1.48 % (29915)------------------------------
% 1.68/1.48 % (29916)Termination reason: Unknown
% 1.68/1.48 % (29916)Termination phase: Property scanning
% 1.68/1.48
% 1.68/1.48 % (29916)Memory used [KB]: 895
% 1.68/1.48 % (29916)Time elapsed: 0.003 s
% 1.68/1.48 % (29916)Instructions burned: 3 (million)
% 1.68/1.48 % (29916)------------------------------
% 1.68/1.48 % (29916)------------------------------
% 1.68/1.48 % (29913)First to succeed.
% 1.68/1.48 % (29917)Refutation not found, incomplete strategy
% 1.68/1.48 % (29917)------------------------------
% 1.68/1.48 % (29917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (29917)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.48
% 1.68/1.48
% 1.68/1.48 % (29917)Memory used [KB]: 5500
% 1.68/1.48 % (29917)Time elapsed: 0.003 s
% 1.68/1.48 % (29917)Instructions burned: 2 (million)
% 1.68/1.48 % (29917)------------------------------
% 1.68/1.48 % (29917)------------------------------
% 1.68/1.48 % (29912)Also succeeded, but the first one will report.
% 1.68/1.48 % (29913)Refutation found. Thanks to Tanya!
% 1.68/1.48 % SZS status Theorem for DTF2THF_29815
% 1.68/1.48 % SZS output start Proof for DTF2THF_29815
% 1.68/1.48 thf(func_def_0, type, in: $i > $i > $o).
% 1.68/1.48 thf(func_def_1, type, subset: $i > $i > $o).
% 1.68/1.48 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.68/1.48 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.68/1.48 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.68/1.48 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.68/1.48 thf(func_def_7, type, breln1: $i > $i > $o).
% 1.68/1.48 thf(func_def_9, type, breln1invset: $i > $i > $i).
% 1.68/1.48 thf(f38,plain,(
% 1.68/1.48 $false),
% 1.68/1.48 inference(subsumption_resolution,[status(thm)],[f31,f37])).
% 1.68/1.48 thf(f37,plain,(
% 1.68/1.48 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (subset @ (dpsetconstr @ X1 @ X1 @ X2) @ (cartprod @ X1 @ X1)))) )),
% 1.68/1.48 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.68/1.48 thf(f36,plain,(
% 1.68/1.48 ( ! [X2 : $i > $i > $o,X1 : $i] : ((((^[Y0 : $i > $i > $o]: (subset @ (dpsetconstr @ X1 @ X1 @ Y0) @ (cartprod @ X1 @ X1))) @ X2) = $true)) )),
% 1.68/1.48 inference(pi_clausification,[status(thm)],[f35])).
% 1.68/1.48 thf(f35,plain,(
% 1.68/1.48 ( ! [X1 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (subset @ (dpsetconstr @ X1 @ X1 @ Y0) @ (cartprod @ X1 @ X1)))) = $true)) )),
% 1.68/1.48 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.68/1.48 thf(f34,plain,(
% 1.68/1.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y0 @ Y1) @ (cartprod @ Y0 @ Y0))))) @ X1))) )),
% 1.68/1.48 inference(pi_clausification,[status(thm)],[f33])).
% 1.68/1.48 thf(f33,plain,(
% 1.68/1.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y0 @ Y1) @ (cartprod @ Y0 @ Y0)))))) = $true)),
% 1.68/1.48 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.68/1.48 thf(f30,plain,(
% 1.68/1.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))))))) = $true)),
% 1.68/1.48 inference(definition_unfolding,[status(thm)],[f26,f25,f27])).
% 1.68/1.48 thf(f27,plain,(
% 1.68/1.48 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 1.68/1.48 inference(definition_unfolding,[status(thm)],[f21,f20])).
% 1.68/1.48 thf(f20,plain,(
% 1.68/1.48 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f10])).
% 1.68/1.48 thf(f10,plain,(
% 1.68/1.48 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f1])).
% 1.68/1.48 thf(f1,axiom,(
% 1.68/1.48 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 1.68/1.48 file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln)).
% 1.68/1.48 thf(f21,plain,(
% 1.68/1.48 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f9])).
% 1.68/1.48 thf(f9,plain,(
% 1.68/1.48 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f8])).
% 1.68/1.48 thf(f8,plain,(
% 1.68/1.48 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)),
% 1.68/1.48 inference(rectify,[status(thm)],[f2])).
% 1.68/1.48 thf(f2,axiom,(
% 1.68/1.48 ((^[X0 : $i, X3 : $i] : (breln @ X0 @ X0 @ X3)) = breln1)),
% 1.68/1.48 file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln1)).
% 1.68/1.48 thf(f25,plain,(
% 1.68/1.48 (setOfPairsIsBReln1 = $true)),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.48 thf(f19,plain,(
% 1.68/1.48 (setOfPairsIsBReln1 = $true) & (($true = (breln1 @ sK0 @ sK1)) & ((breln1 @ sK0 @ (breln1invset @ sK0 @ sK1)) != $true))),
% 1.68/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18])).
% 1.68/1.48 thf(f18,plain,(
% 1.68/1.48 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ((breln1 @ X0 @ (breln1invset @ X0 @ X1)) != $true)) => (($true = (breln1 @ sK0 @ sK1)) & ((breln1 @ sK0 @ (breln1invset @ sK0 @ sK1)) != $true))),
% 1.68/1.48 introduced(definition,[],[choice_axiom])).
% 1.68/1.48 thf(f17,plain,(
% 1.68/1.48 (setOfPairsIsBReln1 = $true) & ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ((breln1 @ X0 @ (breln1invset @ X0 @ X1)) != $true))),
% 1.68/1.48 inference(ennf_transformation,[status(thm)],[f12])).
% 1.68/1.48 thf(f12,plain,(
% 1.68/1.48 ~((setOfPairsIsBReln1 = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ((breln1 @ X0 @ (breln1invset @ X0 @ X1)) = $true)))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f11])).
% 1.68/1.48 thf(f11,plain,(
% 1.68/1.48 ~(setOfPairsIsBReln1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => (breln1 @ X0 @ (breln1invset @ X0 @ X1))))),
% 1.68/1.48 inference(rectify,[status(thm)],[f6])).
% 1.68/1.48 thf(f6,negated_conjecture,(
% 1.68/1.48 ~(setOfPairsIsBReln1 => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => (breln1 @ X0 @ (breln1invset @ X0 @ X3))))),
% 1.68/1.48 inference(negated_conjecture,[status(cth)],[f5])).
% 1.68/1.48 thf(f5,conjecture,(
% 1.68/1.48 setOfPairsIsBReln1 => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => (breln1 @ X0 @ (breln1invset @ X0 @ X3)))),
% 1.68/1.48 file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln1invprop)).
% 1.68/1.48 thf(f26,plain,(
% 1.68/1.48 (setOfPairsIsBReln1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (breln1 @ Y0 @ (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))))))))),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f16])).
% 1.68/1.48 thf(f16,plain,(
% 1.68/1.48 (setOfPairsIsBReln1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (breln1 @ Y0 @ (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))))))))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f15])).
% 1.68/1.48 thf(f15,plain,(
% 1.68/1.48 (setOfPairsIsBReln1 = ! [X0 : $i > $i > $o,X1 : $i] : (breln1 @ X1 @ (dpsetconstr @ X1 @ X1 @ (^[X2 : $i, X3 : $i] : (X0 @ X2 @ X3)))))),
% 1.68/1.48 inference(rectify,[status(thm)],[f3])).
% 1.68/1.48 thf(f3,axiom,(
% 1.68/1.48 (setOfPairsIsBReln1 = ! [X4 : $i > $i > $o,X0 : $i] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X5 : $i, X6 : $i] : (X4 @ X5 @ X6)))))),
% 1.68/1.48 file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',setOfPairsIsBReln1)).
% 1.68/1.48 thf(f31,plain,(
% 1.68/1.48 ($true != (subset @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK1))))) @ (cartprod @ sK0 @ sK0)))),
% 1.68/1.48 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.68/1.48 thf(f29,plain,(
% 1.68/1.48 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK0 @ sK1)) != $true)),
% 1.68/1.48 inference(definition_unfolding,[status(thm)],[f23,f27,f22])).
% 1.68/1.48 thf(f22,plain,(
% 1.68/1.48 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f14])).
% 1.68/1.48 thf(f14,plain,(
% 1.68/1.48 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f13])).
% 1.68/1.48 thf(f13,plain,(
% 1.68/1.48 ((^[X0 : $i, X1 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (in @ (kpair @ X3 @ X2) @ X1)))) = breln1invset)),
% 1.68/1.48 inference(rectify,[status(thm)],[f4])).
% 1.68/1.48 thf(f4,axiom,(
% 1.68/1.48 ((^[X0 : $i, X3 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X5 : $i, X6 : $i] : (in @ (kpair @ X6 @ X5) @ X3)))) = breln1invset)),
% 1.68/1.48 file('/export/starexec/sandbox/tmp/tmp.LTfVuILXxC/DTF2THF_29815.p',breln1invset)).
% 1.68/1.48 thf(f23,plain,(
% 1.68/1.48 ((breln1 @ sK0 @ (breln1invset @ sK0 @ sK1)) != $true)),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.48 % SZS output end Proof for DTF2THF_29815
% 1.68/1.48 % (29913)------------------------------
% 1.68/1.48 % (29913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (29913)Termination reason: Refutation
% 1.68/1.48
% 1.68/1.48 % (29913)Memory used [KB]: 5500
% 1.68/1.48 % (29913)Time elapsed: 0.005 s
% 1.68/1.48 % (29913)Instructions burned: 3 (million)
% 1.68/1.48 % (29913)------------------------------
% 1.68/1.48 % (29913)------------------------------
% 1.68/1.48 % (29911)Success in time 0.019 s
%------------------------------------------------------------------------------