%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU777^2 : 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 : n001.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 09:37:06 AM UTC 2026
% Result : Theorem 1.56s 1.26s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 395 ( 101 equ; 0 cnn)
% Maximal formula atoms : 10 ( 11 avg)
% Number of connectives : 567 ( 32 ~; 17 |; 41 &; 448 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 160 ( 56 ^; 71 !; 33 ?; 160 :)
% 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_8,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1invset: $i > $i > $i ).
thf(func_def_17,type,
sK1: $i > $i > $o ).
thf(func_def_27,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f53,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f52,f34]) ).
thf(f34,plain,
( $true
!= ( in @ ( kpair @ sK7 @ sK8 ) @ sK6 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( dpsetconstrER = $true )
& ( ( in @ sK7 @ sK5 )
= $true )
& ( ( in @ sK8 @ sK5 )
= $true )
& ( $true
= ( in @ ( kpair @ sK8 @ sK7 ) @ ( breln1invset @ sK5 @ sK6 ) ) )
& ( $true
!= ( in @ ( kpair @ sK7 @ sK8 ) @ sK6 ) )
& ( ( breln1 @ sK5 @ sK6 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f18,f26,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
& ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
!= $true ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK5 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK5 ) )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ sK5 @ sK6 ) )
= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ sK6 )
!= $true ) ) )
& ( ( breln1 @ sK5 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK5 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK5 ) )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ sK5 @ sK6 ) )
= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ sK6 )
!= $true ) ) )
=> ( ( ( in @ sK7 @ sK5 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK5 ) )
& ( $true
= ( in @ ( kpair @ X3 @ sK7 ) @ ( breln1invset @ sK5 @ sK6 ) ) )
& ( ( in @ ( kpair @ sK7 @ X3 ) @ sK6 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK5 ) )
& ( $true
= ( in @ ( kpair @ X3 @ sK7 ) @ ( breln1invset @ sK5 @ sK6 ) ) )
& ( ( in @ ( kpair @ sK7 @ X3 ) @ sK6 )
!= $true ) )
=> ( ( ( in @ sK8 @ sK5 )
= $true )
& ( $true
= ( in @ ( kpair @ sK8 @ sK7 ) @ ( breln1invset @ sK5 @ sK6 ) ) )
& ( $true
!= ( in @ ( kpair @ sK7 @ sK8 ) @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( dpsetconstrER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
& ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
!= $true ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( dpsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( dpsetconstrER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( dpsetconstrER
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrER
=> ! [X0: $i,X8: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ ( breln1invset @ X0 @ X8 ) )
=> ( in @ ( kpair @ X4 @ X5 ) @ X8 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dpsetconstrER
=> ! [X0: $i,X8: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ ( breln1invset @ X0 @ X8 ) )
=> ( in @ ( kpair @ X4 @ X5 ) @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2THF_13031.p',breln1invE) ).
thf(f52,plain,
( $true
= ( in @ ( kpair @ sK7 @ sK8 ) @ sK6 ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK6 )
@ sK8
@ sK7 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK6 )
@ sK8
@ sK7 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f47,f48]) ).
thf(f48,plain,
( ( in @ ( kpair @ sK8 @ sK7 )
@ ( dpsetconstr @ sK5 @ sK5
@ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK6 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( ( in @ ( kpair @ sK8 @ sK7 )
@ ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
@ sK5
@ sK6 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f35,f32]) ).
thf(f32,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( breln1invset
= ( ^ [X0: $i,X1: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( breln1invset
= ( ^ [X0: $i,X8: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X4: $i,X5: $i] : ( in @ ( kpair @ X5 @ X4 ) @ X8 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2THF_13031.p',breln1invset) ).
thf(f35,plain,
( $true
= ( in @ ( kpair @ sK8 @ sK7 ) @ ( breln1invset @ sK5 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i > $o,X4: $i] :
( ( ( in @ ( kpair @ X0 @ X2 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) )
!= $true )
| ( ( X1 @ X0 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i > $o,X4: $i] :
( ( ( X1 @ X0 @ X2 )
= $true )
| ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i > $o,X4: $i] :
( ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true )
| ( ( X1 @ X0 @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f31,f38]) ).
thf(f38,plain,
dpsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i > $o,X4: $i] :
( ( ( X1 @ X0 @ X2 )
= $true )
| ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true )
| ( dpsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( X1 @ X0 @ X2 )
= $true )
| ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ( ( ( sK1 @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ ( kpair @ sK0 @ sK2 )
@ ( dpsetconstr @ sK4 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f22]) ).
thf(f22,plain,
( ? [X5: $i,X6: $i > $i > $o,X7: $i,X8: $i,X9: $i] :
( ( $true
!= ( X6 @ X5 @ X7 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X7 )
@ ( dpsetconstr @ X9 @ X8
@ ^ [Y0: $i,Y1: $i] : ( X6 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( sK1 @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ ( kpair @ sK0 @ sK2 )
@ ( dpsetconstr @ sK4 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( X1 @ X0 @ X2 )
= $true )
| ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ? [X5: $i,X6: $i > $i > $o,X7: $i,X8: $i,X9: $i] :
( ( $true
!= ( X6 @ X5 @ X7 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X7 )
@ ( dpsetconstr @ X9 @ X8
@ ^ [Y0: $i,Y1: $i] : ( X6 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( X1 @ X0 @ X2 )
= $true )
| ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( X1 @ X0 @ X2 )
!= $true )
& ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( X1 @ X0 @ X2 )
= $true )
| ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true ) )
<=> ( dpsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
= $true )
=> ( ( X1 @ X0 @ X2 )
= $true ) )
<=> ( dpsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( ( in @ ( kpair @ X0 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) )
=> ( X1 @ X0 @ X2 ) )
= dpsetconstrER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: $i,X3: $i > $i > $o,X5: $i,X1: $i,X0: $i] :
( ( ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X6: $i,X7: $i] : ( X3 @ X6 @ X7 ) ) )
=> ( X3 @ X4 @ X5 ) )
= dpsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2THF_13031.p',dpsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU777^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n001.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:34:20 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.44 ---- Original DTF file ---
% 0.29/0.44 thf(spec,logic,$$dhol).
% 0.29/0.44 %------------------------------------------------------------------------------
% 0.29/0.44 % File : SEU777^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.44 % Domain : Set Theory
% 0.29/0.44 % Problem : Binary Relations on a Set
% 0.29/0.44 % Version : Especial > Reduced > Especial.
% 0.29/0.44 % English : (! A:i.! R:i.breln1 A R -> (! x:i.in x A -> (! y:i.in y A ->
% 0.29/0.44 % in (kpair y x) (breln1invset A R) -> in (kpair x y) R)))
% 0.29/0.44
% 0.29/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.44 % Source : [Bro08]
% 0.29/0.44 % Names : ZFC279l [Bro08]
% 0.29/0.44
% 0.29/0.44 % Status : Theorem
% 0.29/0.44 % 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, 0.14 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 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.29/0.44 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.29/0.44 % Number of atoms : 17 ( 4 equ; 0 cnn)
% 0.29/0.44 % Maximal formula atoms : 6 ( 3 avg)
% 0.29/0.44 % Number of connectives : 47 ( 0 ~; 0 |; 0 &; 41 @)
% 0.29/0.44 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.29/0.44 % Maximal formula depth : 14 ( 4 avg)
% 0.29/0.44 % Number of types : 2 ( 0 usr)
% 0.29/0.44 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.29/0.44 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.29/0.44 % Number of variables : 20 ( 11 ^; 9 !; 0 ?; 20 :)
% 0.29/0.44 % SPC : TH0_THM_EQU_NAR
% 0.29/0.44
% 0.29/0.44 % Comments : http://mathgate.info/detsetitem.php?id=342
% 0.29/0.44 %------------------------------------------------------------------------------
% 0.29/0.44 thf(in_type,type,
% 0.29/0.44 in: $i > $i > $o ).
% 0.29/0.44
% 0.29/0.44 thf(subset_type,type,
% 0.29/0.44 subset: $i > $i > $o ).
% 0.29/0.44
% 0.29/0.44 thf(kpair_type,type,
% 0.29/0.44 kpair: $i > $i > $i ).
% 0.29/0.44
% 0.29/0.44 thf(cartprod_type,type,
% 0.29/0.44 cartprod: $i > $i > $i ).
% 0.29/0.44
% 0.29/0.44 thf(breln_type,type,
% 0.29/0.44 breln: $i > $i > $i > $o ).
% 0.29/0.44
% 0.29/0.44 thf(breln,definition,
% 0.29/0.44 ( breln
% 0.29/0.44 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.44
% 0.29/0.44 thf(dpsetconstr_type,type,
% 0.29/0.44 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.44
% 0.29/0.44 thf(dpsetconstrER_type,type,
% 0.29/0.44 dpsetconstrER: $o ).
% 0.29/0.44
% 0.29/0.44 thf(dpsetconstrER,definition,
% 0.29/0.44 ( dpsetconstrER
% 0.29/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.44 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.44 @ ( dpsetconstr @ A @ B
% 0.29/0.44 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.44 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.44
% 0.29/0.44 thf(breln1_type,type,
% 0.29/0.44 breln1: $i > $i > $o ).
% 0.29/0.44
% 0.29/0.44 thf(breln1,definition,
% 0.29/0.44 ( breln1
% 0.29/0.44 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.29/0.44
% 0.29/0.44 thf(breln1invset_type,type,
% 0.29/0.44 breln1invset: $i > $i > $i ).
% 0.29/0.44
% 0.29/0.44 thf(breln1invset,definition,
% 0.29/0.44 ( breln1invset
% 0.29/0.44 = ( ^ [A: $i,R: $i] :
% 0.29/0.44 ( dpsetconstr @ A @ A
% 0.29/0.44 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 0.29/0.44
% 0.29/0.44 thf(breln1invE,conjecture,
% 0.29/0.44 ( dpsetconstrER
% 0.29/0.44 => ! [A: $i,R: $i] :
% 0.29/0.44 ( ( breln1 @ A @ R )
% 0.29/0.44 => ! [Xx: $i] :
% 0.29/0.44 ( ( in @ Xx @ A )
% 0.29/0.44 => ! [Xy: $i] :
% 0.29/0.44 ( ( in @ Xy @ A )
% 0.29/0.44 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.29/0.44 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.29/0.44
% 0.29/0.44 %------------------------------------------------------------------------------
% 0.29/0.44 ------------------------
% 1.56/1.23 ---- Embedded in THF ---
% 1.56/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.23 %%% Generated on Tue Feb 24 12:34:21 EST 2026
% 1.56/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.23 %%% Logic specification used:
% 1.56/1.23 %%% thf(spec, logic, $$dhol).
% 1.56/1.23
% 1.56/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2DTF13031.p
% See solution above
% 1.56/1.23 ------------------------
% 1.56/1.24 ---- Cleaned THF ---
% 1.56/1.24 thf(in_type,type,
% 1.56/1.24 in: $i > $i > $o ).
% 1.56/1.24
% 1.56/1.24 thf(subset_type,type,
% 1.56/1.24 subset: $i > $i > $o ).
% 1.56/1.24
% 1.56/1.24 thf(kpair_type,type,
% 1.56/1.24 kpair: $i > $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(cartprod_type,type,
% 1.56/1.24 cartprod: $i > $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(breln_type,type,
% 1.56/1.24 breln: $i > $i > $i > $o ).
% 1.56/1.24
% 1.56/1.24 thf(breln,definition,
% 1.56/1.24 ( breln
% 1.56/1.24 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(dpsetconstr_type,type,
% 1.56/1.24 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.56/1.24
% 1.56/1.24 thf(dpsetconstrER_type,type,
% 1.56/1.24 dpsetconstrER: $o ).
% 1.56/1.24
% 1.56/1.24 thf(dpsetconstrER,definition,
% 1.56/1.24 ( dpsetconstrER
% 1.56/1.24 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 1.56/1.24 ( ( in @ ( kpair @ Xx @ Xy )
% 1.56/1.24 @ ( dpsetconstr @ A @ B
% 1.56/1.24 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 1.56/1.24 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(breln1_type,type,
% 1.56/1.24 breln1: $i > $i > $o ).
% 1.56/1.24
% 1.56/1.24 thf(breln1,definition,
% 1.56/1.24 ( breln1
% 1.56/1.24 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(breln1invset_type,type,
% 1.56/1.24 breln1invset: $i > $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(breln1invset,definition,
% 1.56/1.24 ( breln1invset
% 1.56/1.24 = ( ^ [A: $i,R: $i] :
% 1.56/1.24 ( dpsetconstr @ A @ A
% 1.56/1.24 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(breln1invE,conjecture,
% 1.56/1.24 ( dpsetconstrER
% 1.56/1.24 => ! [A: $i,R: $i] :
% 1.56/1.24 ( ( breln1 @ A @ R )
% 1.56/1.24 => ! [Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ A )
% 1.56/1.24 => ! [Xy: $i] :
% 1.56/1.24 ( ( in @ Xy @ A )
% 1.56/1.24 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 1.56/1.24 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.56/1.24 ------------------------
% 1.56/1.25 % (13180)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_13031 for (3000ds/27Mi)
% 1.56/1.25 % (13184)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13031 for (3000ds/18Mi)
% 1.56/1.25 % (13184)First to succeed.
% 1.56/1.26 % (13184)Refutation found. Thanks to Tanya!
% 1.56/1.26 % SZS status Theorem for DTF2THF_13031
% 1.56/1.26 % SZS output start Proof for DTF2THF_13031
% 1.56/1.26 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.26 thf(func_def_1, type, subset: $i > $i > $o).
% 1.56/1.26 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.56/1.26 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.56/1.26 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.56/1.26 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.56/1.26 thf(func_def_8, type, breln1: $i > $i > $o).
% 1.56/1.26 thf(func_def_9, type, breln1invset: $i > $i > $i).
% 1.56/1.26 thf(func_def_17, type, sK1: $i > $i > $o).
% 1.56/1.26 thf(func_def_27, type, ph10: !>[X0: $tType]:(X0)).
% 1.56/1.26 thf(f53,plain,(
% 1.56/1.26 $false),
% 1.56/1.26 inference(subsumption_resolution,[status(thm)],[f52,f34])).
% 1.56/1.26 thf(f34,plain,(
% 1.56/1.26 ($true != (in @ (kpair @ sK7 @ sK8) @ sK6))),
% 1.56/1.26 inference(cnf_transformation,[status(thm)],[f27])).
% 1.56/1.26 thf(f27,plain,(
% 1.56/1.26 (dpsetconstrER = $true) & ((((in @ sK7 @ sK5) = $true) & (((in @ sK8 @ sK5) = $true) & ($true = (in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK5 @ sK6))) & ($true != (in @ (kpair @ sK7 @ sK8) @ sK6)))) & ((breln1 @ sK5 @ sK6) = $true))),
% 1.56/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f18,f26,f25,f24])).
% 1.56/1.26 thf(f24,plain,(
% 1.56/1.26 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ($true = (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))) & ((in @ (kpair @ X2 @ X3) @ X1) != $true))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i] : (($true = (in @ X2 @ sK5)) & ? [X3 : $i] : (($true = (in @ X3 @ sK5)) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ sK5 @ sK6)) = $true) & ((in @ (kpair @ X2 @ X3) @ sK6) != $true))) & ((breln1 @ sK5 @ sK6) = $true))),
% 1.56/1.26 introduced(definition,[],[choice_axiom])).
% 1.56/1.26 thf(f25,plain,(
% 1.56/1.26 ? [X2 : $i] : (($true = (in @ X2 @ sK5)) & ? [X3 : $i] : (($true = (in @ X3 @ sK5)) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ sK5 @ sK6)) = $true) & ((in @ (kpair @ X2 @ X3) @ sK6) != $true))) => (((in @ sK7 @ sK5) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ sK5)) & ($true = (in @ (kpair @ X3 @ sK7) @ (breln1invset @ sK5 @ sK6))) & ((in @ (kpair @ sK7 @ X3) @ sK6) != $true)))),
% 1.56/1.26 introduced(definition,[],[choice_axiom])).
% 1.56/1.26 thf(f26,plain,(
% 1.56/1.26 ? [X3 : $i] : (($true = (in @ X3 @ sK5)) & ($true = (in @ (kpair @ X3 @ sK7) @ (breln1invset @ sK5 @ sK6))) & ((in @ (kpair @ sK7 @ X3) @ sK6) != $true)) => (((in @ sK8 @ sK5) = $true) & ($true = (in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK5 @ sK6))) & ($true != (in @ (kpair @ sK7 @ sK8) @ sK6)))),
% 1.56/1.26 introduced(definition,[],[choice_axiom])).
% 1.56/1.26 thf(f18,plain,(
% 1.56/1.26 (dpsetconstrER = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ($true = (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))) & ((in @ (kpair @ X2 @ X3) @ X1) != $true))) & ($true = (breln1 @ X0 @ X1)))),
% 1.56/1.26 inference(flattening,[status(thm)],[f17])).
% 1.56/1.26 thf(f17,plain,(
% 1.56/1.26 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X2 @ X3) @ X1) != $true) & ($true = (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)))) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ X0) = $true)) & ($true = (breln1 @ X0 @ X1))) & (dpsetconstrER = $true)),
% 1.56/1.26 inference(ennf_transformation,[status(thm)],[f14])).
% 1.56/1.26 thf(f14,plain,(
% 1.56/1.26 ~((dpsetconstrER = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (($true = (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))) => ((in @ (kpair @ X2 @ X3) @ X1) = $true))))))),
% 1.56/1.26 inference(fool_elimination,[status(thm)],[f13])).
% 1.56/1.26 thf(f13,plain,(
% 1.56/1.26 ~(dpsetconstrER => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) => (in @ (kpair @ X2 @ X3) @ X1))))))),
% 1.56/1.26 inference(rectify,[status(thm)],[f6])).
% 1.56/1.26 thf(f6,negated_conjecture,(
% 1.56/1.26 ~(dpsetconstrER => ! [X0 : $i,X8 : $i] : ((breln1 @ X0 @ X8) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X8)) => (in @ (kpair @ X4 @ X5) @ X8))))))),
% 1.56/1.26 inference(negated_conjecture,[status(cth)],[f5])).
% 1.56/1.26 thf(f5,conjecture,(
% 1.56/1.26 dpsetconstrER => ! [X0 : $i,X8 : $i] : ((breln1 @ X0 @ X8) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X8)) => (in @ (kpair @ X4 @ X5) @ X8)))))),
% 1.56/1.26 file('/export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2THF_13031.p',breln1invE)).
% 1.56/1.26 thf(f52,plain,(
% 1.56/1.26 ($true = (in @ (kpair @ sK7 @ sK8) @ sK6))),
% 1.56/1.26 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.56/1.26 thf(f51,plain,(
% 1.56/1.26 (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK6)))) @ sK8 @ sK7) = $true)),
% 1.56/1.26 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.56/1.26 thf(f50,plain,(
% 1.56/1.26 (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK6)))) @ sK8 @ sK7) = $true) | ($true != $true)),
% 1.56/1.26 inference(superposition,[status(thm)],[f47,f48])).
% 1.56/1.26 thf(f48,plain,(
% 1.56/1.26 ((in @ (kpair @ sK8 @ sK7) @ (dpsetconstr @ sK5 @ sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK6)))))) = $true)),
% 1.56/1.26 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.56/1.26 thf(f44,plain,(
% 1.56/1.26 ((in @ (kpair @ sK8 @ sK7) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK5 @ sK6)) = $true)),
% 1.56/1.26 inference(definition_unfolding,[status(thm)],[f35,f32])).
% 1.56/1.26 thf(f32,plain,(
% 1.56/1.26 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 1.56/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.56/1.26 thf(f10,plain,(
% 1.56/1.26 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 1.56/1.26 inference(fool_elimination,[status(thm)],[f9])).
% 1.56/1.26 thf(f9,plain,(
% 1.56/1.26 (breln1invset = (^[X0 : $i, X1 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (in @ (kpair @ X3 @ X2) @ X1)))))),
% 1.56/1.26 inference(rectify,[status(thm)],[f4])).
% 1.56/1.26 thf(f4,axiom,(
% 1.56/1.26 (breln1invset = (^[X0 : $i, X8 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (in @ (kpair @ X5 @ X4) @ X8)))))),
% 1.56/1.26 file('/export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2THF_13031.p',breln1invset)).
% 1.56/1.26 thf(f35,plain,(
% 1.56/1.26 ($true = (in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK5 @ sK6)))),
% 1.56/1.26 inference(cnf_transformation,[status(thm)],[f27])).
% 1.56/1.26 thf(f47,plain,(
% 1.56/1.26 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $i > $o,X4 : $i] : (((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ X1)) != $true) | ((X1 @ X0 @ X2) = $true)) )),
% 1.56/1.26 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.56/1.26 thf(f46,plain,(
% 1.56/1.26 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $i > $o,X4 : $i] : (((X1 @ X0 @ X2) = $true) | ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true)) )),
% 1.56/1.26 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.56/1.26 thf(f41,plain,(
% 1.56/1.26 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $i > $o,X4 : $i] : (((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true) | ((X1 @ X0 @ X2) = $true) | ($true != $true)) )),
% 1.56/1.26 inference(definition_unfolding,[status(thm)],[f31,f38])).
% 1.56/1.26 thf(f38,plain,(
% 1.56/1.26 (dpsetconstrER = $true)),
% 1.56/1.26 inference(cnf_transformation,[status(thm)],[f27])).
% 1.56/1.26 thf(f31,plain,(
% 1.56/1.26 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $i > $o,X4 : $i] : (((X1 @ X0 @ X2) = $true) | ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true) | (dpsetconstrER != $true)) )),
% 1.56/1.26 inference(cnf_transformation,[status(thm)],[f23])).
% 1.56/1.26 thf(f23,plain,(
% 1.56/1.26 (! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : (((X1 @ X0 @ X2) = $true) | ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | (((sK1 @ sK0 @ sK2) != $true) & ($true = (in @ (kpair @ sK0 @ sK2) @ (dpsetconstr @ sK4 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))))),
% 1.56/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f22])).
% 1.56/1.26 thf(f22,plain,(
% 1.56/1.26 ? [X5 : $i,X6 : $i > $i > $o,X7 : $i,X8 : $i,X9 : $i] : (($true != (X6 @ X5 @ X7)) & ($true = (in @ (kpair @ X5 @ X7) @ (dpsetconstr @ X9 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X6 @ Y0 @ Y1)))))))) => (((sK1 @ sK0 @ sK2) != $true) & ($true = (in @ (kpair @ sK0 @ sK2) @ (dpsetconstr @ sK4 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))))),
% 1.56/1.26 introduced(definition,[],[choice_axiom])).
% 1.56/1.26 thf(f21,plain,(
% 1.56/1.26 (! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : (((X1 @ X0 @ X2) = $true) | ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X5 : $i,X6 : $i > $i > $o,X7 : $i,X8 : $i,X9 : $i] : (($true != (X6 @ X5 @ X7)) & ($true = (in @ (kpair @ X5 @ X7) @ (dpsetconstr @ X9 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X6 @ Y0 @ Y1)))))))))),
% 1.56/1.26 inference(rectify,[status(thm)],[f20])).
% 1.56/1.26 thf(f20,plain,(
% 1.56/1.26 (! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : (((X1 @ X0 @ X2) = $true) | ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : (((X1 @ X0 @ X2) != $true) & ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true)))),
% 1.56/1.26 inference(nnf_transformation,[status(thm)],[f19])).
% 1.56/1.26 thf(f19,plain,(
% 1.56/1.26 ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : (((X1 @ X0 @ X2) = $true) | ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) != $true)) <=> (dpsetconstrER = $true)),
% 1.56/1.26 inference(ennf_transformation,[status(thm)],[f12])).
% 1.56/1.26 thf(f12,plain,(
% 1.56/1.26 ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : (((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true) => ((X1 @ X0 @ X2) = $true)) <=> (dpsetconstrER = $true)),
% 1.56/1.26 inference(fool_elimination,[status(thm)],[f11])).
% 1.56/1.26 thf(f11,plain,(
% 1.56/1.26 (! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i,X4 : $i] : ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X0 @ X2)) = dpsetconstrER)),
% 1.56/1.26 inference(rectify,[status(thm)],[f2])).
% 1.56/1.26 thf(f2,axiom,(
% 1.56/1.26 (! [X4 : $i,X3 : $i > $i > $o,X5 : $i,X1 : $i,X0 : $i] : ((in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7)))) => (X3 @ X4 @ X5)) = dpsetconstrER)),
% 1.56/1.26 file('/export/starexec/sandbox2/tmp/tmp.5lNrHcfRk2/DTF2THF_13031.p',dpsetconstrER)).
% 1.56/1.26 % SZS output end Proof for DTF2THF_13031
% 1.56/1.26 % (13184)------------------------------
% 1.56/1.26 % (13184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.26 % (13184)Termination reason: Refutation
% 1.56/1.26
% 1.56/1.26 % (13184)Memory used [KB]: 5500
% 1.56/1.26 % (13184)Time elapsed: 0.004 s
% 1.56/1.26 % (13184)Instructions burned: 5 (million)
% 1.56/1.26 % (13184)------------------------------
% 1.56/1.26 % (13184)------------------------------
% 1.56/1.26 % (13177)Success in time 0.014 s
%------------------------------------------------------------------------------