%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU740^2 : 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 : 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 09:36:48 AM UTC 2026
% Result : Theorem 1.45s 1.27s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 583 ( 154 equ; 0 cnn)
% Maximal formula atoms : 12 ( 13 avg)
% Number of connectives : 639 ( 53 ~; 32 |; 65 &; 445 @)
% ( 4 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 125 ( 0 ^; 80 !; 45 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(f55,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f54,f52]) ).
thf(f52,plain,
( $true
!= ( in @ sK7 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK7 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f36,f49]) ).
thf(f49,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( $true != $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f39]) ).
thf(f39,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( binunionIL = $true )
& ( binintersectEL = $true )
& ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ sK7 @ ( binunion @ sK3 @ sK6 ) )
!= $true )
& ( ( in @ sK7 @ sK4 )
= $true )
& ( ( in @ sK7 @ ( binintersect @ sK3 @ sK5 ) )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f15,f23,f22,f21,f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X0 @ X3 ) )
!= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
=> ( ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ sK3 @ X3 ) )
!= $true )
& ( ( in @ X4 @ sK4 )
= $true )
& ( ( in @ X4 @ ( binintersect @ sK3 @ X2 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK4 ) ) ) )
& ( ( in @ X2 @ ( powerset @ sK4 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ sK3 @ X3 ) )
!= $true )
& ( ( in @ X4 @ sK4 )
= $true )
& ( ( in @ X4 @ ( binintersect @ sK3 @ X2 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK4 ) ) ) )
& ( ( in @ X2 @ ( powerset @ sK4 ) )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ sK3 @ X3 ) )
!= $true )
& ( ( in @ X4 @ sK4 )
= $true )
& ( ( in @ X4 @ ( binintersect @ sK3 @ sK5 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK4 ) ) ) )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ sK3 @ X3 ) )
!= $true )
& ( ( in @ X4 @ sK4 )
= $true )
& ( ( in @ X4 @ ( binintersect @ sK3 @ sK5 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK4 ) ) ) )
=> ( ? [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binunion @ sK3 @ sK6 ) ) )
& ( ( in @ X4 @ sK4 )
= $true )
& ( ( in @ X4 @ ( binintersect @ sK3 @ sK5 ) )
= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binunion @ sK3 @ sK6 ) ) )
& ( ( in @ X4 @ sK4 )
= $true )
& ( ( in @ X4 @ ( binintersect @ sK3 @ sK5 ) )
= $true ) )
=> ( ( ( in @ sK7 @ ( binunion @ sK3 @ sK6 ) )
!= $true )
& ( ( in @ sK7 @ sK4 )
= $true )
& ( ( in @ sK7 @ ( binintersect @ sK3 @ sK5 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( binunionIL = $true )
& ( binintersectEL = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X0 @ X3 ) )
!= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X0 @ X3 ) )
!= $true )
& ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binintersectEL = $true )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( binunionIL = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
=> ( ( in @ X4 @ ( binunion @ X0 @ X3 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( binunionIL
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( binunionIL
=> ( binintersectEL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ ( binunion @ X3 @ X5 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( binunionIL
=> ( binintersectEL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ ( binunion @ X3 @ X5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2THF_5082.p',inIntersectImpInUnion) ).
thf(f29,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( binunionIL = $true )
| ( ( ( in @ sK1 @ sK2 )
= $true )
& ( ( in @ sK1 @ ( binunion @ sK2 @ sK0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) )
=> ( ( ( in @ sK1 @ sK2 )
= $true )
& ( ( in @ sK1 @ ( binunion @ sK2 @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( binunionIL = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( binunionIL = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( binunionIL = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
= binunionIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2THF_5082.p',binunionIL) ).
thf(f36,plain,
( ( in @ sK7 @ ( binunion @ sK3 @ sK6 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f54,plain,
( $true
= ( in @ sK7 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true
= ( in @ sK7 @ sK3 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f50,f34]) ).
thf(f34,plain,
( ( in @ sK7 @ ( binintersect @ sK3 @ sK5 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f50,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f40,f38]) ).
thf(f38,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f40,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK10 @ ( binintersect @ sK9 @ sK8 ) )
= $true )
& ( $true
!= ( in @ sK10 @ sK9 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f26,f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( ( in @ sK10 @ ( binintersect @ sK9 @ sK8 ) )
= $true )
& ( $true
!= ( in @ sK10 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersectEL
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2THF_5082.p',binintersectEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU740^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:32:25 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 ---- Original DTF file ---
% 0.07/0.34 thf(spec,logic,$$dhol).
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 % File : SEU740^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.34 % Domain : Set Theory
% 0.07/0.34 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.07/0.34 % Version : Especial > Reduced > Especial.
% 0.07/0.34 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.07/0.34 % (! Z:i.in Z (powerset A) -> (! x:i.in x A ->
% 0.07/0.34 % in x (binintersect X Y) -> in x (binunion X Z)))))
% 0.07/0.34
% 0.07/0.34 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.34 % Source : [Bro08]
% 0.07/0.34 % Names : ZFC242l [Bro08]
% 0.07/0.34
% 0.07/0.34 % Status : Theorem
% 0.07/0.34 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.07/0.34 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.07/0.34 % Number of atoms : 16 ( 2 equ; 0 cnn)
% 0.07/0.34 % Maximal formula atoms : 8 ( 5 avg)
% 0.07/0.34 % Number of connectives : 40 ( 0 ~; 0 |; 0 &; 31 @)
% 0.07/0.34 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.07/0.34 % Maximal formula depth : 16 ( 6 avg)
% 0.07/0.34 % Number of types : 2 ( 0 usr)
% 0.07/0.34 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.07/0.34 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.07/0.34 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.07/0.34 % SPC : TH0_THM_EQU_NAR
% 0.07/0.34
% 0.07/0.34 % Comments : http://mathgate.info/detsetitem.php?id=302
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 thf(in_type,type,
% 0.07/0.34 in: $i > $i > $o ).
% 0.07/0.34
% 0.07/0.34 thf(powerset_type,type,
% 0.07/0.34 powerset: $i > $i ).
% 0.07/0.34
% 0.07/0.34 thf(binunion_type,type,
% 0.07/0.34 binunion: $i > $i > $i ).
% 0.07/0.34
% 0.07/0.34 thf(binunionIL_type,type,
% 0.07/0.34 binunionIL: $o ).
% 0.07/0.34
% 0.07/0.34 thf(binunionIL,definition,
% 0.07/0.34 ( binunionIL
% 0.07/0.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.07/0.34 ( ( in @ Xx @ A )
% 0.07/0.34 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(binintersect_type,type,
% 0.07/0.34 binintersect: $i > $i > $i ).
% 0.07/0.34
% 0.07/0.34 thf(binintersectEL_type,type,
% 0.07/0.34 binintersectEL: $o ).
% 0.07/0.34
% 0.07/0.34 thf(binintersectEL,definition,
% 0.07/0.34 ( binintersectEL
% 0.07/0.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.07/0.34 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.07/0.34 => ( in @ Xx @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(inIntersectImpInUnion,conjecture,
% 0.07/0.34 ( binunionIL
% 0.07/0.34 => ( binintersectEL
% 0.07/0.34 => ! [A: $i,X: $i] :
% 0.07/0.34 ( ( in @ X @ ( powerset @ A ) )
% 0.07/0.34 => ! [Y: $i] :
% 0.07/0.34 ( ( in @ Y @ ( powerset @ A ) )
% 0.07/0.34 => ! [Z: $i] :
% 0.07/0.34 ( ( in @ Z @ ( powerset @ A ) )
% 0.07/0.34 => ! [Xx: $i] :
% 0.07/0.34 ( ( in @ Xx @ A )
% 0.07/0.34 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.07/0.34 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 ------------------------
% 1.45/1.23 ---- Embedded in THF ---
% 1.45/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.24 %%% Generated on Tue Feb 24 07:32:26 EST 2026
% 1.45/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.24 %%% Logic specification used:
% 1.45/1.24 %%% thf(spec, logic, $$dhol).
% 1.45/1.24
% 1.45/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2DTF5082.p
% See solution above
% 1.45/1.24 ------------------------
% 1.45/1.24 ---- Cleaned THF ---
% 1.45/1.24 thf(in_type,type,
% 1.45/1.24 in: $i > $i > $o ).
% 1.45/1.24
% 1.45/1.24 thf(powerset_type,type,
% 1.45/1.24 powerset: $i > $i ).
% 1.45/1.24
% 1.45/1.24 thf(binunion_type,type,
% 1.45/1.24 binunion: $i > $i > $i ).
% 1.45/1.24
% 1.45/1.24 thf(binunionIL_type,type,
% 1.45/1.24 binunionIL: $o ).
% 1.45/1.24
% 1.45/1.24 thf(binunionIL,definition,
% 1.45/1.24 ( binunionIL
% 1.45/1.24 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.45/1.24 ( ( in @ Xx @ A )
% 1.45/1.24 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(binintersect_type,type,
% 1.45/1.24 binintersect: $i > $i > $i ).
% 1.45/1.24
% 1.45/1.24 thf(binintersectEL_type,type,
% 1.45/1.24 binintersectEL: $o ).
% 1.45/1.24
% 1.45/1.24 thf(binintersectEL,definition,
% 1.45/1.24 ( binintersectEL
% 1.45/1.24 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.45/1.24 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.45/1.24 => ( in @ Xx @ A ) ) ) ) ).
% 1.45/1.24
% 1.45/1.24 thf(inIntersectImpInUnion,conjecture,
% 1.45/1.24 ( binunionIL
% 1.45/1.24 => ( binintersectEL
% 1.45/1.24 => ! [A: $i,X: $i] :
% 1.45/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.45/1.24 => ! [Y: $i] :
% 1.45/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.45/1.24 => ! [Z: $i] :
% 1.45/1.24 ( ( in @ Z @ ( powerset @ A ) )
% 1.45/1.24 => ! [Xx: $i] :
% 1.45/1.24 ( ( in @ Xx @ A )
% 1.45/1.24 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.45/1.24 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 1.45/1.24 ------------------------
% 1.45/1.26 % (5179)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5082 for (2999ds/183Mi)
% 1.45/1.26 % (5180)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_5082 for (2999ds/4Mi)
% 1.45/1.26 % (5182)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5082 for (2999ds/2Mi)
% 1.45/1.26 % (5181)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_5082 for (2999ds/27Mi)
% 1.45/1.26 % (5183)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_5082 for (2999ds/2Mi)
% 1.45/1.26 % (5185)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5082 for (2999ds/18Mi)
% 1.45/1.26 % (5184)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_5082 for (2999ds/275Mi)
% 1.45/1.27 % (5182)Instruction limit reached!
% 1.45/1.27 % (5182)------------------------------
% 1.45/1.27 % (5182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (5182)Termination reason: Unknown
% 1.45/1.27 % (5183)Instruction limit reached!
% 1.45/1.27 % (5183)------------------------------
% 1.45/1.27 % (5183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (5182)Termination phase: Saturation
% 1.45/1.27
% 1.45/1.27 % (5182)Memory used [KB]: 5500
% 1.45/1.27 % (5182)Time elapsed: 0.003 s
% 1.45/1.27 % (5182)Instructions burned: 3 (million)
% 1.45/1.27 % (5182)------------------------------
% 1.45/1.27 % (5182)------------------------------
% 1.45/1.27 % (5183)Termination reason: Unknown
% 1.45/1.27 % (5183)Termination phase: Saturation
% 1.45/1.27
% 1.45/1.27 % (5183)Memory used [KB]: 5500
% 1.45/1.27 % (5183)Time elapsed: 0.003 s
% 1.45/1.27 % (5183)Instructions burned: 3 (million)
% 1.45/1.27 % (5183)------------------------------
% 1.45/1.27 % (5183)------------------------------
% 1.45/1.27 % (5180)Instruction limit reached!
% 1.45/1.27 % (5180)------------------------------
% 1.45/1.27 % (5180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (5180)Termination reason: Unknown
% 1.45/1.27 % (5180)Termination phase: Saturation
% 1.45/1.27
% 1.45/1.27 % (5180)Memory used [KB]: 5500
% 1.45/1.27 % (5180)Time elapsed: 0.004 s
% 1.45/1.27 % (5180)Instructions burned: 4 (million)
% 1.45/1.27 % (5180)------------------------------
% 1.45/1.27 % (5180)------------------------------
% 1.45/1.27 % (5184)First to succeed.
% 1.45/1.27 % (5181)Also succeeded, but the first one will report.
% 1.45/1.27 % (5184)Refutation found. Thanks to Tanya!
% 1.45/1.27 % SZS status Theorem for DTF2THF_5082
% 1.45/1.27 % SZS output start Proof for DTF2THF_5082
% 1.45/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.45/1.27 thf(func_def_1, type, powerset: $i > $i).
% 1.45/1.27 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.45/1.27 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.45/1.27 thf(f55,plain,(
% 1.45/1.27 $false),
% 1.45/1.27 inference(subsumption_resolution,[status(thm)],[f54,f52])).
% 1.45/1.27 thf(f52,plain,(
% 1.45/1.27 ($true != (in @ sK7 @ sK3))),
% 1.45/1.27 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.45/1.27 thf(f51,plain,(
% 1.45/1.27 ($true != $true) | ($true != (in @ sK7 @ sK3))),
% 1.45/1.27 inference(superposition,[status(thm)],[f36,f49])).
% 1.45/1.27 thf(f49,plain,(
% 1.45/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binunion @ X5 @ X3)) = $true) | ((in @ X4 @ X5) != $true)) )),
% 1.45/1.27 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.45/1.27 thf(f45,plain,(
% 1.45/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ($true != $true) | ((in @ X4 @ (binunion @ X5 @ X3)) = $true)) )),
% 1.45/1.27 inference(definition_unfolding,[status(thm)],[f29,f39])).
% 1.45/1.27 thf(f39,plain,(
% 1.45/1.27 (binunionIL = $true)),
% 1.45/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 1.45/1.27 thf(f24,plain,(
% 1.45/1.27 (binunionIL = $true) & (binintersectEL = $true) & (((in @ sK3 @ (powerset @ sK4)) = $true) & (((((in @ sK7 @ (binunion @ sK3 @ sK6)) != $true) & ((in @ sK7 @ sK4) = $true) & ((in @ sK7 @ (binintersect @ sK3 @ sK5)) = $true)) & ((in @ sK6 @ (powerset @ sK4)) = $true)) & ((in @ sK5 @ (powerset @ sK4)) = $true)))),
% 1.45/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f15,f23,f22,f21,f20])).
% 1.45/1.27 thf(f20,plain,(
% 1.45/1.27 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binunion @ X0 @ X3)) != $true) & ($true = (in @ X4 @ X1)) & ((in @ X4 @ (binintersect @ X0 @ X2)) = $true)) & ((in @ X3 @ (powerset @ X1)) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true))) => (((in @ sK3 @ (powerset @ sK4)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binunion @ sK3 @ X3)) != $true) & ((in @ X4 @ sK4) = $true) & ((in @ X4 @ (binintersect @ sK3 @ X2)) = $true)) & ($true = (in @ X3 @ (powerset @ sK4)))) & ((in @ X2 @ (powerset @ sK4)) = $true)))),
% 1.45/1.27 introduced(definition,[],[choice_axiom])).
% 1.45/1.27 thf(f21,plain,(
% 1.45/1.27 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binunion @ sK3 @ X3)) != $true) & ((in @ X4 @ sK4) = $true) & ((in @ X4 @ (binintersect @ sK3 @ X2)) = $true)) & ($true = (in @ X3 @ (powerset @ sK4)))) & ((in @ X2 @ (powerset @ sK4)) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binunion @ sK3 @ X3)) != $true) & ((in @ X4 @ sK4) = $true) & ((in @ X4 @ (binintersect @ sK3 @ sK5)) = $true)) & ($true = (in @ X3 @ (powerset @ sK4)))) & ((in @ sK5 @ (powerset @ sK4)) = $true))),
% 1.45/1.27 introduced(definition,[],[choice_axiom])).
% 1.45/1.27 thf(f22,plain,(
% 1.45/1.27 ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binunion @ sK3 @ X3)) != $true) & ((in @ X4 @ sK4) = $true) & ((in @ X4 @ (binintersect @ sK3 @ sK5)) = $true)) & ($true = (in @ X3 @ (powerset @ sK4)))) => (? [X4 : $i] : (($true != (in @ X4 @ (binunion @ sK3 @ sK6))) & ((in @ X4 @ sK4) = $true) & ((in @ X4 @ (binintersect @ sK3 @ sK5)) = $true)) & ((in @ sK6 @ (powerset @ sK4)) = $true))),
% 1.45/1.27 introduced(definition,[],[choice_axiom])).
% 1.45/1.27 thf(f23,plain,(
% 1.45/1.27 ? [X4 : $i] : (($true != (in @ X4 @ (binunion @ sK3 @ sK6))) & ((in @ X4 @ sK4) = $true) & ((in @ X4 @ (binintersect @ sK3 @ sK5)) = $true)) => (((in @ sK7 @ (binunion @ sK3 @ sK6)) != $true) & ((in @ sK7 @ sK4) = $true) & ((in @ sK7 @ (binintersect @ sK3 @ sK5)) = $true))),
% 1.45/1.27 introduced(definition,[],[choice_axiom])).
% 1.45/1.27 thf(f15,plain,(
% 1.45/1.27 (binunionIL = $true) & (binintersectEL = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binunion @ X0 @ X3)) != $true) & ($true = (in @ X4 @ X1)) & ((in @ X4 @ (binintersect @ X0 @ X2)) = $true)) & ((in @ X3 @ (powerset @ X1)) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)))),
% 1.45/1.27 inference(flattening,[status(thm)],[f14])).
% 1.45/1.27 thf(f14,plain,(
% 1.45/1.27 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ (binunion @ X0 @ X3)) != $true) & ((in @ X4 @ (binintersect @ X0 @ X2)) = $true)) & ($true = (in @ X4 @ X1))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binintersectEL = $true)) & (binunionIL = $true)),
% 1.45/1.27 inference(ennf_transformation,[status(thm)],[f7])).
% 1.45/1.27 thf(f7,plain,(
% 1.45/1.27 ~((binunionIL = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) => ((in @ X4 @ (binunion @ X0 @ X3)) = $true))))))))),
% 1.45/1.27 inference(fool_elimination,[status(thm)],[f6])).
% 1.45/1.27 thf(f6,plain,(
% 1.45/1.27 ~(binunionIL => (binintersectEL => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ (binintersect @ X0 @ X2)) => (in @ X4 @ (binunion @ X0 @ X3)))))))))),
% 1.45/1.27 inference(rectify,[status(thm)],[f4])).
% 1.45/1.27 thf(f4,negated_conjecture,(
% 1.45/1.27 ~(binunionIL => (binintersectEL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binunion @ X3 @ X5)))))))))),
% 1.45/1.27 inference(negated_conjecture,[status(cth)],[f3])).
% 1.45/1.27 thf(f3,conjecture,(
% 1.45/1.27 binunionIL => (binintersectEL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binunion @ X3 @ X5))))))))),
% 1.45/1.27 file('/export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2THF_5082.p',inIntersectImpInUnion)).
% 1.45/1.27 thf(f29,plain,(
% 1.45/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ (binunion @ X5 @ X3)) = $true) | (binunionIL != $true)) )),
% 1.45/1.27 inference(cnf_transformation,[status(thm)],[f19])).
% 1.45/1.27 thf(f19,plain,(
% 1.45/1.27 ((binunionIL = $true) | (((in @ sK1 @ sK2) = $true) & ((in @ sK1 @ (binunion @ sK2 @ sK0)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ (binunion @ X5 @ X3)) = $true)) | (binunionIL != $true))),
% 1.45/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18])).
% 1.45/1.27 thf(f18,plain,(
% 1.45/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (binunion @ X2 @ X0)) != $true)) => (((in @ sK1 @ sK2) = $true) & ((in @ sK1 @ (binunion @ sK2 @ sK0)) != $true))),
% 1.45/1.27 introduced(definition,[],[choice_axiom])).
% 1.45/1.27 thf(f17,plain,(
% 1.45/1.27 ((binunionIL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (binunion @ X2 @ X0)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ (binunion @ X5 @ X3)) = $true)) | (binunionIL != $true))),
% 1.45/1.27 inference(rectify,[status(thm)],[f16])).
% 1.45/1.27 thf(f16,plain,(
% 1.45/1.27 ((binunionIL = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X1 @ (binunion @ X0 @ X2)) != $true))) & (! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (binunion @ X0 @ X2)) = $true)) | (binunionIL != $true))),
% 1.45/1.27 inference(nnf_transformation,[status(thm)],[f13])).
% 1.45/1.27 thf(f13,plain,(
% 1.45/1.27 (binunionIL = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (binunion @ X0 @ X2)) = $true))),
% 1.45/1.27 inference(ennf_transformation,[status(thm)],[f9])).
% 1.45/1.27 thf(f9,plain,(
% 1.45/1.27 (binunionIL = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) => ((in @ X1 @ (binunion @ X0 @ X2)) = $true))),
% 1.45/1.27 inference(fool_elimination,[status(thm)],[f8])).
% 1.45/1.27 thf(f8,plain,(
% 1.45/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (binunion @ X0 @ X2))) = binunionIL)),
% 1.45/1.27 inference(rectify,[status(thm)],[f1])).
% 1.45/1.27 thf(f1,axiom,(
% 1.45/1.27 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 1.45/1.27 file('/export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2THF_5082.p',binunionIL)).
% 1.45/1.27 thf(f36,plain,(
% 1.45/1.27 ((in @ sK7 @ (binunion @ sK3 @ sK6)) != $true)),
% 1.45/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 1.45/1.27 thf(f54,plain,(
% 1.45/1.27 ($true = (in @ sK7 @ sK3))),
% 1.45/1.27 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.45/1.27 thf(f53,plain,(
% 1.45/1.27 ($true = (in @ sK7 @ sK3)) | ($true != $true)),
% 1.45/1.27 inference(superposition,[status(thm)],[f50,f34])).
% 1.45/1.27 thf(f34,plain,(
% 1.45/1.27 ((in @ sK7 @ (binintersect @ sK3 @ sK5)) = $true)),
% 1.45/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 1.45/1.27 thf(f50,plain,(
% 1.45/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | ((in @ X5 @ X4) = $true)) )),
% 1.45/1.27 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.45/1.27 thf(f48,plain,(
% 1.45/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | ($true != $true)) )),
% 1.45/1.27 inference(definition_unfolding,[status(thm)],[f40,f38])).
% 1.45/1.27 thf(f38,plain,(
% 1.45/1.27 (binintersectEL = $true)),
% 1.45/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 1.45/1.27 thf(f40,plain,(
% 1.45/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | ((in @ X5 @ X4) = $true) | (binintersectEL != $true)) )),
% 1.45/1.27 inference(cnf_transformation,[status(thm)],[f28])).
% 1.45/1.27 thf(f28,plain,(
% 1.45/1.27 ((binintersectEL = $true) | (((in @ sK10 @ (binintersect @ sK9 @ sK8)) = $true) & ($true != (in @ sK10 @ sK9)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | ((in @ X5 @ X4) = $true)) | (binintersectEL != $true))),
% 1.45/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f26,f27])).
% 1.45/1.27 thf(f27,plain,(
% 1.45/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true)) => (((in @ sK10 @ (binintersect @ sK9 @ sK8)) = $true) & ($true != (in @ sK10 @ sK9)))),
% 1.45/1.27 introduced(definition,[],[choice_axiom])).
% 1.45/1.27 thf(f26,plain,(
% 1.45/1.27 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) | ((in @ X5 @ X4) = $true)) | (binintersectEL != $true))),
% 1.45/1.27 inference(rectify,[status(thm)],[f25])).
% 1.45/1.27 thf(f25,plain,(
% 1.45/1.27 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) != $true) | ((in @ X2 @ X1) = $true)) | (binintersectEL != $true))),
% 1.45/1.27 inference(nnf_transformation,[status(thm)],[f12])).
% 1.45/1.27 thf(f12,plain,(
% 1.45/1.27 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) != $true) | ((in @ X2 @ X1) = $true))),
% 1.45/1.27 inference(ennf_transformation,[status(thm)],[f11])).
% 1.45/1.27 thf(f11,plain,(
% 1.45/1.27 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) => ((in @ X2 @ X1) = $true)) <=> (binintersectEL = $true)),
% 1.45/1.27 inference(fool_elimination,[status(thm)],[f10])).
% 1.45/1.27 thf(f10,plain,(
% 1.45/1.27 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X1)))),
% 1.45/1.27 inference(rectify,[status(thm)],[f2])).
% 1.45/1.27 thf(f2,axiom,(
% 1.45/1.27 (binintersectEL = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.45/1.27 file('/export/starexec/sandbox/tmp/tmp.WY8DKEFrdT/DTF2THF_5082.p',binintersectEL)).
% 1.45/1.27 % SZS output end Proof for DTF2THF_5082
% 1.45/1.27 % (5184)------------------------------
% 1.45/1.27 % (5184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (5184)Termination reason: Refutation
% 1.45/1.27
% 1.45/1.27 % (5184)Memory used [KB]: 5500
% 1.45/1.27 % (5184)Time elapsed: 0.006 s
% 1.45/1.27 % (5184)Instructions burned: 4 (million)
% 1.45/1.27 % (5184)------------------------------
% 1.45/1.27 % (5184)------------------------------
% 1.45/1.27 % (5178)Success in time 0.02 s
%------------------------------------------------------------------------------