%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU769^2 : 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 09:37:03 AM UTC 2026
% Result : Theorem 1.07s 0.94s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 353 ( 11 ~; 3 |; 6 &; 294 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 6 con; 0-3 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 114 ( 81 ^; 29 !; 4 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
breln: $i > $i > $i > $o ).
thf(func_def_8,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1Set: $i > $i ).
thf(func_def_23,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f64,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
$true = $false,
inference(superposition,[status(thm)],[f60,f44]) ).
thf(f44,plain,
( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) )
= $false )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
!= ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f24,f28]) ).
thf(f28,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)],[f23,f21]) ).
thf(f21,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( breln
= ( ^ [X0: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln) ).
thf(f23,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)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X6: $i] : ( breln @ X0 @ X0 @ X6 ) )
= breln1 ),
file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln1) ).
thf(f24,plain,
( $true
!= ( breln1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( dsetconstrER = $true )
& ( $true
= ( in @ sK1 @ ( breln1Set @ sK0 ) ) )
& ( $true
!= ( breln1 @ sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( breln1Set @ X0 ) ) )
& ( $true
!= ( breln1 @ X0 @ X1 ) ) )
=> ( ( $true
= ( in @ sK1 @ ( breln1Set @ sK0 ) ) )
& ( $true
!= ( breln1 @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( breln1Set @ X0 ) ) )
& ( $true
!= ( breln1 @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( breln1Set @ X0 ) ) )
=> ( $true
= ( breln1 @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X6: $i] :
( ( in @ X6 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X6 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrER
=> ! [X0: $i,X6: $i] :
( ( in @ X6 @ ( breln1Set @ X0 ) )
=> ( breln1 @ X0 @ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln1SetBreln1) ).
thf(f60,plain,
( $true
= ( subset @ sK1 @ ( cartprod @ sK0 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK0 @ sK0 ) )
@ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK0 @ sK0 ) )
@ sK1 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f34,f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
= $false )
| ( ( X1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f22]) ).
thf(f22,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',dsetconstrER) ).
thf(f26,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f34,plain,
( $true
= ( in @ sK1
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK0 @ sK0 ) )
@ ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ sK0 @ sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( in @ sK1
@ ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f29]) ).
thf(f29,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f28]) ).
thf(f27,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] : ( breln1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( breln1Set
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y0 ) )
@ ^ [Y1: $i] : ( breln1 @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( breln1Set
= ( ^ [X0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X0 ) )
@ ^ [X1: $i] : ( breln1 @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( breln1Set
= ( ^ [X0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X0 ) )
@ ^ [X6: $i] : ( breln1 @ X0 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln1Set) ).
thf(f25,plain,
( $true
= ( in @ sK1 @ ( breln1Set @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU769^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 07:33:10 EST 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SEU769^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.31 % Domain : Set Theory
% 0.07/0.31 % Problem : Binary Relations on a Set
% 0.07/0.31 % Version : Especial > Reduced > Especial.
% 0.07/0.31 % English : (! A:i.! R:i.in R (breln1Set A) -> breln1 A R)
% 0.07/0.31
% 0.07/0.31 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.31 % Source : [Bro08]
% 0.07/0.31 % Names : ZFC271l [Bro08]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % 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, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 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 v5.1.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.07/0.31 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.07/0.31 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 3 ( 2 avg)
% 0.07/0.31 % Number of connectives : 28 ( 0 ~; 0 |; 0 &; 25 @)
% 0.07/0.31 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 7 ( 2 avg)
% 0.07/0.31 % Number of types : 2 ( 0 usr)
% 0.07/0.31 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.07/0.31 % Number of variables : 13 ( 8 ^; 5 !; 0 ?; 13 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : http://mathgate.info/detsetitem.php?id=375
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(in_type,type,
% 0.07/0.31 in: $i > $i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(powerset_type,type,
% 0.07/0.31 powerset: $i > $i ).
% 0.07/0.31
% 0.07/0.31 thf(dsetconstr_type,type,
% 0.07/0.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.07/0.31
% 0.07/0.31 thf(dsetconstrER_type,type,
% 0.07/0.31 dsetconstrER: $o ).
% 0.07/0.31
% 0.07/0.31 thf(dsetconstrER,definition,
% 0.07/0.31 ( dsetconstrER
% 0.07/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.31 ( ( in @ Xx
% 0.07/0.31 @ ( dsetconstr @ A
% 0.07/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.31 => ( Xphi @ Xx ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(subset_type,type,
% 0.07/0.31 subset: $i > $i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(cartprod_type,type,
% 0.07/0.31 cartprod: $i > $i > $i ).
% 0.07/0.31
% 0.07/0.31 thf(breln_type,type,
% 0.07/0.31 breln: $i > $i > $i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(breln,definition,
% 0.07/0.31 ( breln
% 0.07/0.31 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(breln1_type,type,
% 0.07/0.31 breln1: $i > $i > $o ).
% 0.07/0.31
% 0.07/0.31 thf(breln1,definition,
% 0.07/0.31 ( breln1
% 0.07/0.31 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(breln1Set_type,type,
% 0.07/0.31 breln1Set: $i > $i ).
% 0.07/0.31
% 0.07/0.31 thf(breln1Set,definition,
% 0.07/0.31 ( breln1Set
% 0.07/0.31 = ( ^ [A: $i] :
% 0.07/0.31 ( dsetconstr @ ( powerset @ ( cartprod @ A @ A ) )
% 0.07/0.31 @ ^ [R: $i] : ( breln1 @ A @ R ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(breln1SetBreln1,conjecture,
% 0.07/0.31 ( dsetconstrER
% 0.07/0.31 => ! [A: $i,R: $i] :
% 0.07/0.31 ( ( in @ R @ ( breln1Set @ A ) )
% 0.07/0.31 => ( breln1 @ A @ R ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 1.07/0.91 ---- Embedded in THF ---
% 1.07/0.91 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.07/0.91 %%% Generated on Tue Feb 24 07:33:11 EST 2026
% 1.07/0.91 %%% using '$$dhol' embedding, version 1.3.0.
% 1.07/0.91 %%% Logic specification used:
% 1.07/0.91 %%% thf(spec, logic, $$dhol).
% 1.07/0.91
% 1.07/0.91 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2DTF7645.p
% See solution above
% 1.07/0.91 ------------------------
% 1.07/0.92 ---- Cleaned THF ---
% 1.07/0.92 thf(in_type,type,
% 1.07/0.92 in: $i > $i > $o ).
% 1.07/0.92
% 1.07/0.92 thf(powerset_type,type,
% 1.07/0.92 powerset: $i > $i ).
% 1.07/0.92
% 1.07/0.92 thf(dsetconstr_type,type,
% 1.07/0.92 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.07/0.92
% 1.07/0.92 thf(dsetconstrER_type,type,
% 1.07/0.92 dsetconstrER: $o ).
% 1.07/0.92
% 1.07/0.92 thf(dsetconstrER,definition,
% 1.07/0.92 ( dsetconstrER
% 1.07/0.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.07/0.92 ( ( in @ Xx
% 1.07/0.92 @ ( dsetconstr @ A
% 1.07/0.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.07/0.92 => ( Xphi @ Xx ) ) ) ) ).
% 1.07/0.92
% 1.07/0.92 thf(subset_type,type,
% 1.07/0.92 subset: $i > $i > $o ).
% 1.07/0.92
% 1.07/0.92 thf(cartprod_type,type,
% 1.07/0.92 cartprod: $i > $i > $i ).
% 1.07/0.92
% 1.07/0.92 thf(breln_type,type,
% 1.07/0.92 breln: $i > $i > $i > $o ).
% 1.07/0.92
% 1.07/0.92 thf(breln,definition,
% 1.07/0.92 ( breln
% 1.07/0.92 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.07/0.92
% 1.07/0.92 thf(breln1_type,type,
% 1.07/0.92 breln1: $i > $i > $o ).
% 1.07/0.92
% 1.07/0.92 thf(breln1,definition,
% 1.07/0.92 ( breln1
% 1.07/0.92 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.07/0.92
% 1.07/0.92 thf(breln1Set_type,type,
% 1.07/0.92 breln1Set: $i > $i ).
% 1.07/0.92
% 1.07/0.92 thf(breln1Set,definition,
% 1.07/0.92 ( breln1Set
% 1.07/0.92 = ( ^ [A: $i] :
% 1.07/0.92 ( dsetconstr @ ( powerset @ ( cartprod @ A @ A ) )
% 1.07/0.92 @ ^ [R: $i] : ( breln1 @ A @ R ) ) ) ) ).
% 1.07/0.92
% 1.07/0.92 thf(breln1SetBreln1,conjecture,
% 1.07/0.92 ( dsetconstrER
% 1.07/0.92 => ! [A: $i,R: $i] :
% 1.07/0.92 ( ( in @ R @ ( breln1Set @ A ) )
% 1.07/0.92 => ( breln1 @ A @ R ) ) ) ).
% 1.07/0.92 ------------------------
% 1.07/0.93 % (7765)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_7645 for (3000ds/4Mi)
% 1.07/0.93 % (7766)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_7645 for (3000ds/27Mi)
% 1.07/0.93 % (7765)First to succeed.
% 1.07/0.94 % (7766)Also succeeded, but the first one will report.
% 1.07/0.94 % (7770)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7645 for (3000ds/18Mi)
% 1.07/0.94 % (7765)Refutation found. Thanks to Tanya!
% 1.07/0.94 % SZS status Theorem for DTF2THF_7645
% 1.07/0.94 % SZS output start Proof for DTF2THF_7645
% 1.07/0.94 thf(func_def_0, type, in: $i > $i > $o).
% 1.07/0.94 thf(func_def_1, type, powerset: $i > $i).
% 1.07/0.94 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.07/0.94 thf(func_def_5, type, subset: $i > $i > $o).
% 1.07/0.94 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.07/0.94 thf(func_def_7, type, breln: $i > $i > $i > $o).
% 1.07/0.94 thf(func_def_8, type, breln1: $i > $i > $o).
% 1.07/0.94 thf(func_def_9, type, breln1Set: $i > $i).
% 1.07/0.94 thf(func_def_23, type, ph3: !>[X0: $tType]:(X0)).
% 1.07/0.94 thf(f64,plain,(
% 1.07/0.94 $false),
% 1.07/0.94 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.07/0.94 thf(f62,plain,(
% 1.07/0.94 ($true = $false)),
% 1.07/0.94 inference(superposition,[status(thm)],[f60,f44])).
% 1.07/0.94 thf(f44,plain,(
% 1.07/0.94 ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false)),
% 1.07/0.94 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.07/0.94 thf(f43,plain,(
% 1.07/0.94 ((subset @ sK1 @ (cartprod @ sK0 @ sK0)) = $false) | ($true != $true)),
% 1.07/0.94 inference(fool_paramodulation,[status(thm)],[f33])).
% 1.07/0.94 thf(f33,plain,(
% 1.07/0.94 ($true != (subset @ sK1 @ (cartprod @ sK0 @ sK0)))),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.07/0.94 thf(f32,plain,(
% 1.07/0.94 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ sK1))),
% 1.07/0.94 inference(definition_unfolding,[status(thm)],[f24,f28])).
% 1.07/0.94 thf(f28,plain,(
% 1.07/0.94 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 1.07/0.94 inference(definition_unfolding,[status(thm)],[f23,f21])).
% 1.07/0.94 thf(f21,plain,(
% 1.07/0.94 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f17])).
% 1.07/0.94 thf(f17,plain,(
% 1.07/0.94 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.07/0.94 inference(fool_elimination,[status(thm)],[f16])).
% 1.07/0.94 thf(f16,plain,(
% 1.07/0.94 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 1.07/0.94 inference(rectify,[status(thm)],[f2])).
% 1.07/0.94 thf(f2,axiom,(
% 1.07/0.94 (breln = (^[X0 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X4))))),
% 1.07/0.94 file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln)).
% 1.07/0.94 thf(f23,plain,(
% 1.07/0.94 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f9])).
% 1.07/0.94 thf(f9,plain,(
% 1.07/0.94 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.07/0.94 inference(fool_elimination,[status(thm)],[f8])).
% 1.07/0.94 thf(f8,plain,(
% 1.07/0.94 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)),
% 1.07/0.94 inference(rectify,[status(thm)],[f3])).
% 1.07/0.94 thf(f3,axiom,(
% 1.07/0.94 ((^[X0 : $i, X6 : $i] : (breln @ X0 @ X0 @ X6)) = breln1)),
% 1.07/0.94 file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln1)).
% 1.07/0.94 thf(f24,plain,(
% 1.07/0.94 ($true != (breln1 @ sK0 @ sK1))),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f20])).
% 1.07/0.94 thf(f20,plain,(
% 1.07/0.94 (dsetconstrER = $true) & (($true = (in @ sK1 @ (breln1Set @ sK0))) & ($true != (breln1 @ sK0 @ sK1)))),
% 1.07/0.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19])).
% 1.07/0.94 thf(f19,plain,(
% 1.07/0.94 ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (breln1Set @ X0))) & ($true != (breln1 @ X0 @ X1))) => (($true = (in @ sK1 @ (breln1Set @ sK0))) & ($true != (breln1 @ sK0 @ sK1)))),
% 1.07/0.94 introduced(definition,[],[choice_axiom])).
% 1.07/0.94 thf(f18,plain,(
% 1.07/0.94 (dsetconstrER = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (breln1Set @ X0))) & ($true != (breln1 @ X0 @ X1)))),
% 1.07/0.94 inference(ennf_transformation,[status(thm)],[f13])).
% 1.07/0.94 thf(f13,plain,(
% 1.07/0.94 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (breln1Set @ X0))) => ($true = (breln1 @ X0 @ X1))))),
% 1.07/0.94 inference(fool_elimination,[status(thm)],[f12])).
% 1.07/0.94 thf(f12,plain,(
% 1.07/0.94 ~(dsetconstrER => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (breln1Set @ X0)) => (breln1 @ X0 @ X1)))),
% 1.07/0.94 inference(rectify,[status(thm)],[f6])).
% 1.07/0.94 thf(f6,negated_conjecture,(
% 1.07/0.94 ~(dsetconstrER => ! [X0 : $i,X6 : $i] : ((in @ X6 @ (breln1Set @ X0)) => (breln1 @ X0 @ X6)))),
% 1.07/0.94 inference(negated_conjecture,[status(cth)],[f5])).
% 1.07/0.94 thf(f5,conjecture,(
% 1.07/0.94 dsetconstrER => ! [X0 : $i,X6 : $i] : ((in @ X6 @ (breln1Set @ X0)) => (breln1 @ X0 @ X6))),
% 1.07/0.94 file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln1SetBreln1)).
% 1.07/0.94 thf(f60,plain,(
% 1.07/0.94 ($true = (subset @ sK1 @ (cartprod @ sK0 @ sK0)))),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.07/0.94 thf(f59,plain,(
% 1.07/0.94 ($true = ((^[Y0 : $i]: (subset @ Y0 @ (cartprod @ sK0 @ sK0))) @ sK1))),
% 1.07/0.94 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.07/0.94 thf(f55,plain,(
% 1.07/0.94 ($true = ((^[Y0 : $i]: (subset @ Y0 @ (cartprod @ sK0 @ sK0))) @ sK1)) | ($true = $false)),
% 1.07/0.94 inference(superposition,[status(thm)],[f34,f42])).
% 1.07/0.94 thf(f42,plain,(
% 1.07/0.94 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X3 @ (dsetconstr @ X2 @ X1)) = $false) | ((X1 @ X3) = $true)) )),
% 1.07/0.94 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.07/0.94 thf(f41,plain,(
% 1.07/0.94 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((in @ X3 @ (dsetconstr @ X2 @ X1)) => (X1 @ X3)))) )),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.07/0.94 thf(f40,plain,(
% 1.07/0.94 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ X1)) => (X1 @ Y0))) @ X3))) )),
% 1.07/0.94 inference(pi_clausification,[status(thm)],[f39])).
% 1.07/0.94 thf(f39,plain,(
% 1.07/0.94 ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ X1)) => (X1 @ Y0)))))) )),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.07/0.94 thf(f38,plain,(
% 1.07/0.94 ( ! [X2 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ Y0 @ X1)) => (X1 @ Y1))))) @ X2))) )),
% 1.07/0.94 inference(pi_clausification,[status(thm)],[f37])).
% 1.07/0.94 thf(f37,plain,(
% 1.07/0.94 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ Y0 @ X1)) => (X1 @ Y1)))))))) )),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.07/0.94 thf(f36,plain,(
% 1.07/0.94 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2))))))) @ X1))) )),
% 1.07/0.94 inference(pi_clausification,[status(thm)],[f35])).
% 1.07/0.94 thf(f35,plain,(
% 1.07/0.94 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))))),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.07/0.94 thf(f30,plain,(
% 1.07/0.94 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))),
% 1.07/0.94 inference(definition_unfolding,[status(thm)],[f26,f22])).
% 1.07/0.94 thf(f22,plain,(
% 1.07/0.94 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f15])).
% 1.07/0.94 thf(f15,plain,(
% 1.07/0.94 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))),
% 1.07/0.94 inference(fool_elimination,[status(thm)],[f14])).
% 1.07/0.94 thf(f14,plain,(
% 1.07/0.94 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X0)))),
% 1.07/0.94 inference(rectify,[status(thm)],[f1])).
% 1.07/0.94 thf(f1,axiom,(
% 1.07/0.94 (dsetconstrER = ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.07/0.94 file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',dsetconstrER)).
% 1.07/0.94 thf(f26,plain,(
% 1.07/0.94 (dsetconstrER = $true)),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f20])).
% 1.07/0.94 thf(f34,plain,(
% 1.07/0.94 ($true = (in @ sK1 @ (dsetconstr @ (powerset @ (cartprod @ sK0 @ sK0)) @ (^[Y0 : $i]: (subset @ Y0 @ (cartprod @ sK0 @ sK0))))))),
% 1.07/0.94 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.07/0.94 thf(f31,plain,(
% 1.07/0.94 ($true = (in @ sK1 @ ((^[Y0 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y0)) @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1)))) @ sK0)))),
% 1.07/0.94 inference(definition_unfolding,[status(thm)],[f25,f29])).
% 1.07/0.94 thf(f29,plain,(
% 1.07/0.94 (breln1Set = (^[Y0 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y0)) @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1)))))),
% 1.07/0.94 inference(definition_unfolding,[status(thm)],[f27,f28])).
% 1.07/0.94 thf(f27,plain,(
% 1.07/0.94 (breln1Set = (^[Y0 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y0)) @ (^[Y1 : $i]: (breln1 @ Y0 @ Y1)))))),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f11])).
% 1.07/0.94 thf(f11,plain,(
% 1.07/0.94 (breln1Set = (^[Y0 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y0)) @ (^[Y1 : $i]: (breln1 @ Y0 @ Y1)))))),
% 1.07/0.94 inference(fool_elimination,[status(thm)],[f10])).
% 1.07/0.94 thf(f10,plain,(
% 1.07/0.94 (breln1Set = (^[X0 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X0)) @ (^[X1 : $i] : (breln1 @ X0 @ X1)))))),
% 1.07/0.94 inference(rectify,[status(thm)],[f4])).
% 1.07/0.94 thf(f4,axiom,(
% 1.07/0.94 (breln1Set = (^[X0 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X0)) @ (^[X6 : $i] : (breln1 @ X0 @ X6)))))),
% 1.07/0.94 file('/export/starexec/sandbox2/tmp/tmp.HPwaPyCUhz/DTF2THF_7645.p',breln1Set)).
% 1.07/0.94 thf(f25,plain,(
% 1.07/0.94 ($true = (in @ sK1 @ (breln1Set @ sK0)))),
% 1.07/0.94 inference(cnf_transformation,[status(thm)],[f20])).
% 1.07/0.94 % SZS output end Proof for DTF2THF_7645
% 1.07/0.94 % (7765)------------------------------
% 1.07/0.94 % (7765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.07/0.94 % (7765)Termination reason: Refutation
% 1.07/0.94
% 1.07/0.94 % (7765)Memory used [KB]: 5500
% 1.07/0.94 % (7765)Time elapsed: 0.004 s
% 1.07/0.94 % (7765)Instructions burned: 3 (million)
% 1.07/0.94 % (7765)------------------------------
% 1.07/0.94 % (7765)------------------------------
% 1.07/0.94 % (7763)Success in time 0.013 s
%------------------------------------------------------------------------------