%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU786^2 : 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 : n017.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 09:37:11 AM UTC 2026
% Result : Theorem 0.25s 1.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 565 ( 141 equ; 0 cnn)
% Maximal formula atoms : 14 ( 18 avg)
% Number of connectives : 658 ( 51 ~; 34 |; 70 &; 468 @)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 89 ( 0 ^; 53 !; 36 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(f42,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f33]) ).
thf(f33,plain,
( ( in @ ( kpair @ sK6 @ sK7 ) @ sK5 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK5 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ sK7 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
& ( ( in @ sK7 @ sK4 )
= $true )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( ( breln1 @ sK4 @ sK5 )
= $true )
& ( ( breln1 @ sK4 @ sK3 )
= $true )
& ( binunionE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f10,f20,f19,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK3 @ X2 ) )
= $true )
& ( ( in @ X4 @ sK4 )
= $true ) )
& ( ( in @ X3 @ sK4 )
= $true ) )
& ( ( breln1 @ sK4 @ X2 )
= $true ) )
& ( ( breln1 @ sK4 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK3 @ X2 ) )
= $true )
& ( ( in @ X4 @ sK4 )
= $true ) )
& ( ( in @ X3 @ sK4 )
= $true ) )
& ( ( breln1 @ sK4 @ X2 )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK5 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
& ( ( in @ X4 @ sK4 )
= $true ) )
& ( ( in @ X3 @ sK4 )
= $true ) )
& ( ( breln1 @ sK4 @ sK5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK5 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
& ( ( in @ X4 @ sK4 )
= $true ) )
& ( ( in @ X3 @ sK4 )
= $true ) )
=> ( ? [X4: $i] :
( ( ( in @ ( kpair @ sK6 @ X4 ) @ sK5 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ X4 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ X4 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
& ( ( in @ X4 @ sK4 )
= $true ) )
& ( ( in @ sK6 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X4: $i] :
( ( ( in @ ( kpair @ sK6 @ X4 ) @ sK5 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ X4 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ X4 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
& ( ( in @ X4 @ sK4 )
= $true ) )
=> ( ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK5 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK3 )
!= $true )
& ( ( in @ ( kpair @ sK6 @ sK7 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
& ( ( in @ sK7 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( binunionE = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( binunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( binunionE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
| ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binunionE
=> ! [X3: $i,X0: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ ( binunion @ X3 @ X4 ) )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ X3 )
| ( in @ ( kpair @ X2 @ X5 ) @ X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binunionE
=> ! [X3: $i,X0: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ ( binunion @ X3 @ X4 ) )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ X3 )
| ( in @ ( kpair @ X2 @ X5 ) @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qutryyItS4/DTF2THF_345.p',breln1unionE) ).
thf(f41,plain,
( ( in @ ( kpair @ sK6 @ sK7 ) @ sK5 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f40,f32]) ).
thf(f32,plain,
( ( in @ ( kpair @ sK6 @ sK7 ) @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f40,plain,
( ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK3 )
= $true )
| ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true != $true )
| ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK5 )
= $true )
| ( ( in @ ( kpair @ sK6 @ sK7 ) @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f38,f31]) ).
thf(f31,plain,
( ( in @ ( kpair @ sK6 @ sK7 ) @ ( binunion @ sK3 @ sK5 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f38,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X4 @ X5 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f22,f26]) ).
thf(f26,plain,
binunionE = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f22,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( binunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( binunionE = $true )
| ( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ sK2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
= $true ) )
| ( binunionE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true ) )
=> ( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( ( binunionE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
= $true ) )
| ( binunionE != $true ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( binunionE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binunionE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
=> ( ( in @ X1 @ X0 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binunionE
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qutryyItS4/DTF2THF_345.p',binunionE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU786^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n017.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:32:26 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SEU786^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.39 % Domain : Set Theory
% 0.18/0.39 % Problem : Binary Relations on a Set
% 0.18/0.39 % Version : Especial > Reduced > Especial.
% 0.18/0.39 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.18/0.39 % (! y:i.in y A -> in (kpair x y) (binunion R S) ->
% 0.18/0.39 % in (kpair x y) R | in (kpair x y) S))))
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.39 % Source : [Bro08]
% 0.18/0.39 % Names : ZFC288l [Bro08]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 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 v3.7.0
% 0.18/0.39 % Syntax : Number of formulae : 7 ( 1 unt; 5 typ; 1 def)
% 0.18/0.39 % Number of atoms : 13 ( 1 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 8 ( 6 avg)
% 0.18/0.39 % Number of connectives : 39 ( 0 ~; 2 |; 0 &; 30 @)
% 0.18/0.39 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 17 ( 9 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 6 ( 5 usr; 1 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : http://mathgate.info/detsetitem.php?id=351
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(in_type,type,
% 0.18/0.39 in: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunion_type,type,
% 0.18/0.39 binunion: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(binunionE_type,type,
% 0.18/0.39 binunionE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionE,definition,
% 0.18/0.39 ( binunionE
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.39 => ( ( in @ Xx @ A )
% 0.18/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(kpair_type,type,
% 0.18/0.39 kpair: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(breln1_type,type,
% 0.18/0.39 breln1: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(breln1unionE,conjecture,
% 0.18/0.39 ( binunionE
% 0.18/0.39 => ! [A: $i,R: $i] :
% 0.18/0.39 ( ( breln1 @ A @ R )
% 0.18/0.39 => ! [S: $i] :
% 0.18/0.39 ( ( breln1 @ A @ S )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.18/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.39 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 0.25/1.30 ---- Embedded in THF ---
% 0.25/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.25/1.30 %%% Generated on Tue Feb 24 12:32:26 EST 2026
% 0.25/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.25/1.30 %%% Logic specification used:
% 0.25/1.30 %%% thf(spec, logic, $$dhol).
% 0.25/1.30
% 0.25/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qutryyItS4/DTF2DTF345.p
% See solution above
% 0.25/1.30 ------------------------
% 0.25/1.31 ---- Cleaned THF ---
% 0.25/1.31 thf(in_type,type,
% 0.25/1.31 in: $i > $i > $o ).
% 0.25/1.31
% 0.25/1.31 thf(binunion_type,type,
% 0.25/1.31 binunion: $i > $i > $i ).
% 0.25/1.31
% 0.25/1.31 thf(binunionE_type,type,
% 0.25/1.31 binunionE: $o ).
% 0.25/1.31
% 0.25/1.31 thf(binunionE,definition,
% 0.25/1.31 ( binunionE
% 0.25/1.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.25/1.31 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.25/1.31 => ( ( in @ Xx @ A )
% 0.25/1.31 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.25/1.31
% 0.25/1.31 thf(kpair_type,type,
% 0.25/1.31 kpair: $i > $i > $i ).
% 0.25/1.31
% 0.25/1.31 thf(breln1_type,type,
% 0.25/1.31 breln1: $i > $i > $o ).
% 0.25/1.31
% 0.25/1.31 thf(breln1unionE,conjecture,
% 0.25/1.31 ( binunionE
% 0.25/1.31 => ! [A: $i,R: $i] :
% 0.25/1.31 ( ( breln1 @ A @ R )
% 0.25/1.31 => ! [S: $i] :
% 0.25/1.31 ( ( breln1 @ A @ S )
% 0.25/1.31 => ! [Xx: $i] :
% 0.25/1.31 ( ( in @ Xx @ A )
% 0.25/1.31 => ! [Xy: $i] :
% 0.25/1.31 ( ( in @ Xy @ A )
% 0.25/1.31 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.25/1.31 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.25/1.31 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ).
% 0.25/1.31 ------------------------
% 0.25/1.33 % (445)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_345 for (2999ds/27Mi)
% 0.25/1.33 % (449)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_345 for (2999ds/18Mi)
% 0.25/1.33 % (447)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_345 for (2999ds/2Mi)
% 0.25/1.33 % (444)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_345 for (2999ds/4Mi)
% 0.25/1.33 % (448)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_345 for (2999ds/275Mi)
% 0.25/1.33 % (446)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_345 for (2999ds/2Mi)
% 0.25/1.33 % (443)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_345 for (2999ds/183Mi)
% 0.25/1.33 % (446)Instruction limit reached!
% 0.25/1.33 % (446)------------------------------
% 0.25/1.33 % (446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (446)Termination reason: Unknown
% 0.25/1.33 % (447)Instruction limit reached!
% 0.25/1.33 % (447)------------------------------
% 0.25/1.33 % (447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (446)Termination phase: Preprocessing 3
% 0.25/1.33
% 0.25/1.33 % (446)Memory used [KB]: 1023
% 0.25/1.33 % (446)Time elapsed: 0.003 s
% 0.25/1.33 % (446)Instructions burned: 2 (million)
% 0.25/1.33 % (446)------------------------------
% 0.25/1.33 % (446)------------------------------
% 0.25/1.33 % (447)Termination reason: Unknown
% 0.25/1.33 % (447)Termination phase: shuffling
% 0.25/1.33
% 0.25/1.33 % (447)Memory used [KB]: 895
% 0.25/1.33 % (447)Time elapsed: 0.003 s
% 0.25/1.33 % (447)Instructions burned: 2 (million)
% 0.25/1.33 % (447)------------------------------
% 0.25/1.33 % (447)------------------------------
% 0.25/1.33 % (448)First to succeed.
% 0.25/1.33 % (444)Instruction limit reached!
% 0.25/1.33 % (444)------------------------------
% 0.25/1.33 % (444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (444)Termination reason: Unknown
% 0.25/1.33 % (444)Termination phase: Saturation
% 0.25/1.33
% 0.25/1.33 % (444)Memory used [KB]: 5500
% 0.25/1.33 % (444)Time elapsed: 0.005 s
% 0.25/1.33 % (444)Instructions burned: 5 (million)
% 0.25/1.33 % (444)------------------------------
% 0.25/1.33 % (444)------------------------------
% 0.25/1.34 % (443)Also succeeded, but the first one will report.
% 0.25/1.34 % (449)Also succeeded, but the first one will report.
% 0.25/1.34 % (448)Refutation found. Thanks to Tanya!
% 0.25/1.34 % SZS status Theorem for DTF2THF_345
% 0.25/1.34 % SZS output start Proof for DTF2THF_345
% 0.25/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 0.25/1.34 thf(func_def_1, type, binunion: $i > $i > $i).
% 0.25/1.34 thf(func_def_4, type, kpair: $i > $i > $i).
% 0.25/1.34 thf(func_def_5, type, breln1: $i > $i > $o).
% 0.25/1.34 thf(f42,plain,(
% 0.25/1.34 $false),
% 0.25/1.34 inference(subsumption_resolution,[status(thm)],[f41,f33])).
% 0.25/1.34 thf(f33,plain,(
% 0.25/1.34 ((in @ (kpair @ sK6 @ sK7) @ sK5) != $true)),
% 0.25/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 0.25/1.34 thf(f21,plain,(
% 0.25/1.34 ((((((in @ (kpair @ sK6 @ sK7) @ sK5) != $true) & ((in @ (kpair @ sK6 @ sK7) @ sK3) != $true) & ((in @ (kpair @ sK6 @ sK7) @ (binunion @ sK3 @ sK5)) = $true) & ((in @ sK7 @ sK4) = $true)) & ((in @ sK6 @ sK4) = $true)) & ((breln1 @ sK4 @ sK5) = $true)) & ((breln1 @ sK4 @ sK3) = $true)) & (binunionE = $true)),
% 0.25/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f10,f20,f19,f18,f17])).
% 0.25/1.34 thf(f17,plain,(
% 0.25/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) & ((in @ (kpair @ X3 @ X4) @ X0) != $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) & ((in @ X4 @ X1) = $true)) & ($true = (in @ X3 @ X1))) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) & ((in @ (kpair @ X3 @ X4) @ sK3) != $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK3 @ X2)) = $true) & ((in @ X4 @ sK4) = $true)) & ((in @ X3 @ sK4) = $true)) & ((breln1 @ sK4 @ X2) = $true)) & ((breln1 @ sK4 @ sK3) = $true))),
% 0.25/1.34 introduced(definition,[],[choice_axiom])).
% 0.25/1.34 thf(f18,plain,(
% 0.25/1.34 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) & ((in @ (kpair @ X3 @ X4) @ sK3) != $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK3 @ X2)) = $true) & ((in @ X4 @ sK4) = $true)) & ((in @ X3 @ sK4) = $true)) & ((breln1 @ sK4 @ X2) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK5) != $true) & ((in @ (kpair @ X3 @ X4) @ sK3) != $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK3 @ sK5)) = $true) & ((in @ X4 @ sK4) = $true)) & ((in @ X3 @ sK4) = $true)) & ((breln1 @ sK4 @ sK5) = $true))),
% 0.25/1.34 introduced(definition,[],[choice_axiom])).
% 0.25/1.34 thf(f19,plain,(
% 0.25/1.34 ? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK5) != $true) & ((in @ (kpair @ X3 @ X4) @ sK3) != $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK3 @ sK5)) = $true) & ((in @ X4 @ sK4) = $true)) & ((in @ X3 @ sK4) = $true)) => (? [X4 : $i] : (((in @ (kpair @ sK6 @ X4) @ sK5) != $true) & ((in @ (kpair @ sK6 @ X4) @ sK3) != $true) & ((in @ (kpair @ sK6 @ X4) @ (binunion @ sK3 @ sK5)) = $true) & ((in @ X4 @ sK4) = $true)) & ((in @ sK6 @ sK4) = $true))),
% 0.25/1.34 introduced(definition,[],[choice_axiom])).
% 0.25/1.34 thf(f20,plain,(
% 0.25/1.34 ? [X4 : $i] : (((in @ (kpair @ sK6 @ X4) @ sK5) != $true) & ((in @ (kpair @ sK6 @ X4) @ sK3) != $true) & ((in @ (kpair @ sK6 @ X4) @ (binunion @ sK3 @ sK5)) = $true) & ((in @ X4 @ sK4) = $true)) => (((in @ (kpair @ sK6 @ sK7) @ sK5) != $true) & ((in @ (kpair @ sK6 @ sK7) @ sK3) != $true) & ((in @ (kpair @ sK6 @ sK7) @ (binunion @ sK3 @ sK5)) = $true) & ((in @ sK7 @ sK4) = $true))),
% 0.25/1.34 introduced(definition,[],[choice_axiom])).
% 0.25/1.34 thf(f10,plain,(
% 0.25/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) & ((in @ (kpair @ X3 @ X4) @ X0) != $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) & ((in @ X4 @ X1) = $true)) & ($true = (in @ X3 @ X1))) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) & (binunionE = $true)),
% 0.25/1.34 inference(flattening,[status(thm)],[f9])).
% 0.25/1.34 thf(f9,plain,(
% 0.25/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((((in @ (kpair @ X3 @ X4) @ X0) != $true) & ((in @ (kpair @ X3 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true)) & ((in @ X4 @ X1) = $true)) & ($true = (in @ X3 @ X1))) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) & (binunionE = $true)),
% 0.25/1.34 inference(ennf_transformation,[status(thm)],[f6])).
% 0.25/1.34 thf(f6,plain,(
% 0.25/1.34 ~((binunionE = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) => ! [X2 : $i] : (((breln1 @ X1 @ X2) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) => (((in @ (kpair @ X3 @ X4) @ X0) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))))))))),
% 0.25/1.34 inference(fool_elimination,[status(thm)],[f5])).
% 0.25/1.34 thf(f5,plain,(
% 0.25/1.34 ~(binunionE => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) => ((in @ (kpair @ X3 @ X4) @ X0) | (in @ (kpair @ X3 @ X4) @ X2))))))))),
% 0.25/1.34 inference(rectify,[status(thm)],[f3])).
% 0.25/1.34 thf(f3,negated_conjecture,(
% 0.25/1.34 ~(binunionE => ! [X3 : $i,X0 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X2 @ X5) @ (binunion @ X3 @ X4)) => ((in @ (kpair @ X2 @ X5) @ X3) | (in @ (kpair @ X2 @ X5) @ X4))))))))),
% 0.25/1.34 inference(negated_conjecture,[status(cth)],[f2])).
% 0.25/1.34 thf(f2,conjecture,(
% 0.25/1.34 binunionE => ! [X3 : $i,X0 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X2 @ X5) @ (binunion @ X3 @ X4)) => ((in @ (kpair @ X2 @ X5) @ X3) | (in @ (kpair @ X2 @ X5) @ X4)))))))),
% 0.25/1.34 file('/export/starexec/sandbox/tmp/tmp.qutryyItS4/DTF2THF_345.p',breln1unionE)).
% 0.25/1.34 thf(f41,plain,(
% 0.25/1.34 ((in @ (kpair @ sK6 @ sK7) @ sK5) = $true)),
% 0.25/1.34 inference(subsumption_resolution,[status(thm)],[f40,f32])).
% 0.25/1.34 thf(f32,plain,(
% 0.25/1.34 ((in @ (kpair @ sK6 @ sK7) @ sK3) != $true)),
% 0.25/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 0.25/1.34 thf(f40,plain,(
% 0.25/1.34 ((in @ (kpair @ sK6 @ sK7) @ sK3) = $true) | ((in @ (kpair @ sK6 @ sK7) @ sK5) = $true)),
% 0.25/1.34 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 0.25/1.34 thf(f39,plain,(
% 0.25/1.34 ($true != $true) | ((in @ (kpair @ sK6 @ sK7) @ sK5) = $true) | ((in @ (kpair @ sK6 @ sK7) @ sK3) = $true)),
% 0.25/1.34 inference(superposition,[status(thm)],[f38,f31])).
% 0.25/1.34 thf(f31,plain,(
% 0.25/1.34 ((in @ (kpair @ sK6 @ sK7) @ (binunion @ sK3 @ sK5)) = $true)),
% 0.25/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 0.25/1.34 thf(f38,plain,(
% 0.25/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true) | ((in @ X3 @ X5) = $true)) )),
% 0.25/1.34 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 0.25/1.34 thf(f37,plain,(
% 0.25/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X4 @ X5)) != $true) | ($true != $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) = $true)) )),
% 0.25/1.34 inference(definition_unfolding,[status(thm)],[f22,f26])).
% 0.25/1.34 thf(f26,plain,(
% 0.25/1.34 (binunionE = $true)),
% 0.25/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 0.25/1.34 thf(f22,plain,(
% 0.25/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true) | ((in @ X3 @ X5) = $true) | (binunionE != $true)) )),
% 0.25/1.34 inference(cnf_transformation,[status(thm)],[f16])).
% 0.25/1.34 thf(f16,plain,(
% 0.25/1.34 ((binunionE = $true) | (((in @ sK0 @ (binunion @ sK1 @ sK2)) = $true) & ((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ sK2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true) | ((in @ X3 @ X5) = $true)) | (binunionE != $true))),
% 0.25/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 0.25/1.34 thf(f15,plain,(
% 0.25/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binunion @ X1 @ X2))) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) != $true)) => (((in @ sK0 @ (binunion @ sK1 @ sK2)) = $true) & ((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ sK2) != $true))),
% 0.25/1.34 introduced(definition,[],[choice_axiom])).
% 0.25/1.34 thf(f14,plain,(
% 0.25/1.34 ((binunionE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binunion @ X1 @ X2))) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true) | ((in @ X3 @ X5) = $true)) | (binunionE != $true))),
% 0.25/1.34 inference(rectify,[status(thm)],[f13])).
% 0.25/1.34 thf(f13,plain,(
% 0.25/1.34 ((binunionE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) = $true) & ((in @ X1 @ X2) != $true) & ((in @ X1 @ X0) != $true))) & (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) != $true) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) = $true)) | (binunionE != $true))),
% 0.25/1.34 inference(nnf_transformation,[status(thm)],[f12])).
% 0.25/1.34 thf(f12,plain,(
% 0.25/1.34 (binunionE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) != $true) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) = $true))),
% 0.25/1.34 inference(flattening,[status(thm)],[f11])).
% 0.25/1.34 thf(f11,plain,(
% 0.25/1.34 (binunionE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) = $true)) | ((in @ X1 @ (binunion @ X2 @ X0)) != $true))),
% 0.25/1.34 inference(ennf_transformation,[status(thm)],[f8])).
% 0.25/1.34 thf(f8,plain,(
% 0.25/1.34 (binunionE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) = $true) => (((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) = $true)))),
% 0.25/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 0.25/1.34 thf(f7,plain,(
% 0.25/1.34 (binunionE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binunion @ X2 @ X0)) => ((in @ X1 @ X0) | (in @ X1 @ X2))))),
% 0.25/1.34 inference(rectify,[status(thm)],[f1])).
% 0.25/1.34 thf(f1,axiom,(
% 0.25/1.34 (binunionE = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X1) | (in @ X2 @ X0))))),
% 0.25/1.34 file('/export/starexec/sandbox/tmp/tmp.qutryyItS4/DTF2THF_345.p',binunionE)).
% 0.25/1.34 % SZS output end Proof for DTF2THF_345
% 0.25/1.34 % (448)------------------------------
% 0.25/1.34 % (448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.34 % (448)Termination reason: Refutation
% 0.25/1.34
% 0.25/1.34 % (448)Memory used [KB]: 5500
% 0.25/1.34 % (448)Time elapsed: 0.006 s
% 0.25/1.34 % (448)Instructions burned: 4 (million)
% 0.25/1.34 % (448)------------------------------
% 0.25/1.34 % (448)------------------------------
% 0.25/1.34 % (442)Success in time 0.02 s
%------------------------------------------------------------------------------