%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU741^2 : 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 : n026.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 09:36:49 AM UTC 2026
% Result : Theorem 1.74s 1.33s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 584 ( 155 equ; 0 cnn)
% Maximal formula atoms : 12 ( 13 avg)
% Number of connectives : 642 ( 52 ~; 32 |; 65 &; 449 @)
% ( 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 : 127 ( 0 ^; 82 !; 45 ?; 127 :)
% 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(f79,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
$true != $true,
inference(superposition,[status(thm)],[f39,f76]) ).
thf(f76,plain,
! [X0: $i] :
( $true
= ( in @ sK10 @ ( binunion @ sK8 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: $i] :
( ( $true
= ( in @ sK10 @ ( binunion @ sK8 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f49,f74]) ).
thf(f74,plain,
( $true
= ( in @ sK10 @ sK8 ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true != $true )
| ( $true
= ( in @ sK10 @ sK8 ) ) ),
inference(superposition,[status(thm)],[f50,f38]) ).
thf(f38,plain,
( $true
= ( in @ sK10 @ ( binintersect @ sK6 @ sK8 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( binintersectER = $true )
& ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ( $true
= ( in @ sK10 @ sK7 ) )
& ( $true
!= ( in @ sK10 @ ( binunion @ sK8 @ sK9 ) ) )
& ( $true
= ( in @ sK10 @ ( binintersect @ sK6 @ sK8 ) ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK7 ) ) )
& ( binunionIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f14,f27,f26,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK7 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ sK6 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK7 ) ) ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK7 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ sK6 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK7 ) ) ) ) )
=> ( ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK7 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ sK6 @ sK8 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK7 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK7 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ sK6 @ sK8 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ sK7 ) ) ) )
=> ( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK7 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ sK9 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ sK6 @ sK8 ) ) ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK7 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ sK9 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ sK6 @ sK8 ) ) ) )
=> ( ( $true
= ( in @ sK10 @ sK7 ) )
& ( $true
!= ( in @ sK10 @ ( binunion @ sK8 @ sK9 ) ) )
& ( $true
= ( in @ sK10 @ ( binintersect @ sK6 @ sK8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( binintersectER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionIL = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binunion @ X2 @ X3 ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binintersectER = $true )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( binunionIL = $true )
=> ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
=> ( $true
= ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( binunionIL
=> ( binintersectER
=> ! [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 @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( binunionIL
=> ( binintersectER
=> ! [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 @ X4 @ X5 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( binunionIL
=> ( binintersectER
=> ! [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 @ X4 @ X5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2THF_20547.p',inIntersectImpInUnion2) ).
thf(f50,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( $true
= ( in @ X5 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f42]) ).
thf(f42,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f32,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( binintersectER = $true )
| ( ( $true
= ( in @ sK5 @ ( binintersect @ sK3 @ sK4 ) ) )
& ( $true
!= ( in @ sK5 @ sK4 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( $true
= ( in @ X5 @ X4 ) ) )
| ( binintersectER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( in @ sK5 @ ( binintersect @ sK3 @ sK4 ) ) )
& ( $true
!= ( in @ sK5 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( $true
= ( in @ X5 @ X4 ) ) )
| ( binintersectER != $true ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( binintersectER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( binintersectER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( binintersectER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( $true
= ( in @ X0 @ X2 ) ) )
<=> ( binintersectER = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X2 ) )
= binintersectER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
file('/export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2THF_20547.p',binintersectER) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f31,f35]) ).
thf(f35,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( $true
!= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK0 @ sK1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).
thf(f18,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( $true
= ( in @ X3 @ X4 ) ) )
=> ( ( $true
!= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( $true
= ( in @ X3 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( binunionIL = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
= binunionIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2THF_20547.p',binunionIL) ).
thf(f39,plain,
( $true
!= ( in @ sK10 @ ( binunion @ sK8 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU741^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:32:55 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU741^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.19/0.45 % Version : Especial > Reduced > Especial.
% 0.19/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.45 % (! Z:i.in Z (powerset A) -> (! x:i.in x A ->
% 0.19/0.45 % in x (binintersect X Y) -> in x (binunion Y Z)))))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC243l [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.19/0.45 % Number of atoms : 16 ( 2 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 8 ( 5 avg)
% 0.19/0.45 % Number of connectives : 40 ( 0 ~; 0 |; 0 &; 31 @)
% 0.19/0.45 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 16 ( 6 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=303
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(in_type,type,
% 0.19/0.45 in: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(powerset_type,type,
% 0.19/0.45 powerset: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(binunion_type,type,
% 0.19/0.45 binunion: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(binunionIL_type,type,
% 0.19/0.45 binunionIL: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binunionIL,definition,
% 0.19/0.45 ( binunionIL
% 0.19/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binintersect_type,type,
% 0.19/0.45 binintersect: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectER_type,type,
% 0.19/0.45 binintersectER: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectER,definition,
% 0.19/0.45 ( binintersectER
% 0.19/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.45 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(inIntersectImpInUnion2,conjecture,
% 0.19/0.45 ( binunionIL
% 0.19/0.45 => ( binintersectER
% 0.19/0.45 => ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ! [Z: $i] :
% 0.19/0.45 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.19/0.45 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.56/1.30 ---- Embedded in THF ---
% 1.74/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.30 %%% Generated on Tue Feb 24 12:32:56 EST 2026
% 1.74/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.30 %%% Logic specification used:
% 1.74/1.30 %%% thf(spec, logic, $$dhol).
% 1.74/1.30
% 1.74/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2DTF20547.p
% See solution above
% 1.74/1.30 ------------------------
% 1.74/1.31 ---- Cleaned THF ---
% 1.74/1.31 thf(in_type,type,
% 1.74/1.31 in: $i > $i > $o ).
% 1.74/1.31
% 1.74/1.31 thf(powerset_type,type,
% 1.74/1.31 powerset: $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(binunion_type,type,
% 1.74/1.31 binunion: $i > $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(binunionIL_type,type,
% 1.74/1.31 binunionIL: $o ).
% 1.74/1.31
% 1.74/1.31 thf(binunionIL,definition,
% 1.74/1.31 ( binunionIL
% 1.74/1.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.74/1.31 ( ( in @ Xx @ A )
% 1.74/1.31 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.74/1.31
% 1.74/1.31 thf(binintersect_type,type,
% 1.74/1.31 binintersect: $i > $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(binintersectER_type,type,
% 1.74/1.31 binintersectER: $o ).
% 1.74/1.31
% 1.74/1.31 thf(binintersectER,definition,
% 1.74/1.31 ( binintersectER
% 1.74/1.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.74/1.31 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.74/1.31 => ( in @ Xx @ B ) ) ) ) ).
% 1.74/1.31
% 1.74/1.31 thf(inIntersectImpInUnion2,conjecture,
% 1.74/1.31 ( binunionIL
% 1.74/1.31 => ( binintersectER
% 1.74/1.31 => ! [A: $i,X: $i] :
% 1.74/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.31 => ! [Y: $i] :
% 1.74/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.31 => ! [Z: $i] :
% 1.74/1.31 ( ( in @ Z @ ( powerset @ A ) )
% 1.74/1.31 => ! [Xx: $i] :
% 1.74/1.31 ( ( in @ Xx @ A )
% 1.74/1.31 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.74/1.31 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 1.74/1.31 ------------------------
% 1.74/1.32 % (20741)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20547 for (3000ds/18Mi)
% 1.74/1.32 % (20736)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_20547 for (3000ds/4Mi)
% 1.74/1.32 % (20736)Instruction limit reached!
% 1.74/1.32 % (20736)------------------------------
% 1.74/1.32 % (20736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.32 % (20736)Termination reason: Unknown
% 1.74/1.32 % (20736)Termination phase: Saturation
% 1.74/1.32
% 1.74/1.32 % (20736)Memory used [KB]: 5500
% 1.74/1.32 % (20736)Time elapsed: 0.003 s
% 1.74/1.32 % (20736)Instructions burned: 5 (million)
% 1.74/1.32 % (20736)------------------------------
% 1.74/1.32 % (20736)------------------------------
% 1.74/1.32 % (20741)First to succeed.
% 1.74/1.33 % (20741)Refutation found. Thanks to Tanya!
% 1.74/1.33 % SZS status Theorem for DTF2THF_20547
% 1.74/1.33 % SZS output start Proof for DTF2THF_20547
% 1.74/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.74/1.33 thf(func_def_1, type, powerset: $i > $i).
% 1.74/1.33 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.74/1.33 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.74/1.33 thf(f79,plain,(
% 1.74/1.33 $false),
% 1.74/1.33 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.74/1.33 thf(f77,plain,(
% 1.74/1.33 ($true != $true)),
% 1.74/1.33 inference(superposition,[status(thm)],[f39,f76])).
% 1.74/1.33 thf(f76,plain,(
% 1.74/1.33 ( ! [X0 : $i] : (($true = (in @ sK10 @ (binunion @ sK8 @ X0)))) )),
% 1.74/1.33 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.74/1.33 thf(f75,plain,(
% 1.74/1.33 ( ! [X0 : $i] : (($true = (in @ sK10 @ (binunion @ sK8 @ X0))) | ($true != $true)) )),
% 1.74/1.33 inference(superposition,[status(thm)],[f49,f74])).
% 1.74/1.33 thf(f74,plain,(
% 1.74/1.33 ($true = (in @ sK10 @ sK8))),
% 1.74/1.33 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.74/1.33 thf(f73,plain,(
% 1.74/1.33 ($true != $true) | ($true = (in @ sK10 @ sK8))),
% 1.74/1.33 inference(superposition,[status(thm)],[f50,f38])).
% 1.74/1.33 thf(f38,plain,(
% 1.74/1.33 ($true = (in @ sK10 @ (binintersect @ sK6 @ sK8)))),
% 1.74/1.33 inference(cnf_transformation,[status(thm)],[f28])).
% 1.74/1.33 thf(f28,plain,(
% 1.74/1.33 (binintersectER = $true) & ((($true = (in @ sK8 @ (powerset @ sK7))) & ((($true = (in @ sK10 @ sK7)) & ($true != (in @ sK10 @ (binunion @ sK8 @ sK9))) & ($true = (in @ sK10 @ (binintersect @ sK6 @ sK8)))) & ($true = (in @ sK9 @ (powerset @ sK7))))) & ($true = (in @ sK6 @ (powerset @ sK7)))) & (binunionIL = $true)),
% 1.74/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f14,f27,f26,f25,f24])).
% 1.74/1.33 thf(f24,plain,(
% 1.74/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X1)) & ($true != (in @ X4 @ (binunion @ X2 @ X3))) & ($true = (in @ X4 @ (binintersect @ X0 @ X2)))) & ($true = (in @ X3 @ (powerset @ X1))))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK7))) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK7)) & ($true != (in @ X4 @ (binunion @ X2 @ X3))) & ($true = (in @ X4 @ (binintersect @ sK6 @ X2)))) & ($true = (in @ X3 @ (powerset @ sK7))))) & ($true = (in @ sK6 @ (powerset @ sK7))))),
% 1.74/1.33 introduced(definition,[],[choice_axiom])).
% 1.74/1.33 thf(f25,plain,(
% 1.74/1.33 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK7))) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK7)) & ($true != (in @ X4 @ (binunion @ X2 @ X3))) & ($true = (in @ X4 @ (binintersect @ sK6 @ X2)))) & ($true = (in @ X3 @ (powerset @ sK7))))) => (($true = (in @ sK8 @ (powerset @ sK7))) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK7)) & ($true != (in @ X4 @ (binunion @ sK8 @ X3))) & ($true = (in @ X4 @ (binintersect @ sK6 @ sK8)))) & ($true = (in @ X3 @ (powerset @ sK7)))))),
% 1.74/1.33 introduced(definition,[],[choice_axiom])).
% 1.74/1.33 thf(f26,plain,(
% 1.74/1.33 ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK7)) & ($true != (in @ X4 @ (binunion @ sK8 @ X3))) & ($true = (in @ X4 @ (binintersect @ sK6 @ sK8)))) & ($true = (in @ X3 @ (powerset @ sK7)))) => (? [X4 : $i] : (($true = (in @ X4 @ sK7)) & ($true != (in @ X4 @ (binunion @ sK8 @ sK9))) & ($true = (in @ X4 @ (binintersect @ sK6 @ sK8)))) & ($true = (in @ sK9 @ (powerset @ sK7))))),
% 1.74/1.33 introduced(definition,[],[choice_axiom])).
% 1.74/1.33 thf(f27,plain,(
% 1.74/1.33 ? [X4 : $i] : (($true = (in @ X4 @ sK7)) & ($true != (in @ X4 @ (binunion @ sK8 @ sK9))) & ($true = (in @ X4 @ (binintersect @ sK6 @ sK8)))) => (($true = (in @ sK10 @ sK7)) & ($true != (in @ sK10 @ (binunion @ sK8 @ sK9))) & ($true = (in @ sK10 @ (binintersect @ sK6 @ sK8))))),
% 1.74/1.33 introduced(definition,[],[choice_axiom])).
% 1.74/1.33 thf(f14,plain,(
% 1.74/1.33 (binintersectER = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X1)) & ($true != (in @ X4 @ (binunion @ X2 @ X3))) & ($true = (in @ X4 @ (binintersect @ X0 @ X2)))) & ($true = (in @ X3 @ (powerset @ X1))))) & ($true = (in @ X0 @ (powerset @ X1)))) & (binunionIL = $true)),
% 1.74/1.33 inference(flattening,[status(thm)],[f13])).
% 1.74/1.33 thf(f13,plain,(
% 1.74/1.33 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((($true != (in @ X4 @ (binunion @ X2 @ X3))) & ($true = (in @ X4 @ (binintersect @ X0 @ X2)))) & ($true = (in @ X4 @ X1))) & ($true = (in @ X3 @ (powerset @ X1)))) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (binintersectER = $true)) & (binunionIL = $true)),
% 1.74/1.33 inference(ennf_transformation,[status(thm)],[f7])).
% 1.74/1.33 thf(f7,plain,(
% 1.74/1.33 ~((binunionIL = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (($true = (in @ X3 @ (powerset @ X1))) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => (($true = (in @ X4 @ (binintersect @ X0 @ X2))) => ($true = (in @ X4 @ (binunion @ X2 @ X3))))))))))),
% 1.74/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 1.74/1.33 thf(f6,plain,(
% 1.74/1.33 ~(binunionIL => (binintersectER => ! [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 @ X2 @ X3)))))))))),
% 1.74/1.33 inference(rectify,[status(thm)],[f4])).
% 1.74/1.33 thf(f4,negated_conjecture,(
% 1.74/1.33 ~(binunionIL => (binintersectER => ! [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 @ X4 @ X5)))))))))),
% 1.74/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 1.74/1.33 thf(f3,conjecture,(
% 1.74/1.33 binunionIL => (binintersectER => ! [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 @ X4 @ X5))))))))),
% 1.74/1.33 file('/export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2THF_20547.p',inIntersectImpInUnion2)).
% 1.74/1.33 thf(f50,plain,(
% 1.74/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X3 @ X4))) | ($true = (in @ X5 @ X4))) )),
% 1.74/1.33 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.74/1.33 thf(f48,plain,(
% 1.74/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ X4)) | ($true != (in @ X5 @ (binintersect @ X3 @ X4))) | ($true != $true)) )),
% 1.74/1.33 inference(definition_unfolding,[status(thm)],[f32,f42])).
% 1.74/1.33 thf(f42,plain,(
% 1.74/1.33 (binintersectER = $true)),
% 1.74/1.33 inference(cnf_transformation,[status(thm)],[f28])).
% 1.74/1.33 thf(f32,plain,(
% 1.74/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X3 @ X4))) | ($true = (in @ X5 @ X4)) | (binintersectER != $true)) )),
% 1.74/1.33 inference(cnf_transformation,[status(thm)],[f23])).
% 1.74/1.33 thf(f23,plain,(
% 1.74/1.33 ((binintersectER = $true) | (($true = (in @ sK5 @ (binintersect @ sK3 @ sK4))) & ($true != (in @ sK5 @ sK4)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X3 @ X4))) | ($true = (in @ X5 @ X4))) | (binintersectER != $true))),
% 1.74/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f21,f22])).
% 1.74/1.33 thf(f22,plain,(
% 1.74/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) & ((in @ X2 @ X1) != $true)) => (($true = (in @ sK5 @ (binintersect @ sK3 @ sK4))) & ($true != (in @ sK5 @ sK4)))),
% 1.74/1.33 introduced(definition,[],[choice_axiom])).
% 1.74/1.33 thf(f21,plain,(
% 1.74/1.33 ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) & ((in @ X2 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X3 @ X4))) | ($true = (in @ X5 @ X4))) | (binintersectER != $true))),
% 1.74/1.33 inference(rectify,[status(thm)],[f20])).
% 1.74/1.33 thf(f20,plain,(
% 1.74/1.33 ((binintersectER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) & ($true != (in @ X0 @ X2)))) & (! [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X0 @ (binintersect @ X1 @ X2))) | ($true = (in @ X0 @ X2))) | (binintersectER != $true))),
% 1.74/1.33 inference(nnf_transformation,[status(thm)],[f15])).
% 1.74/1.33 thf(f15,plain,(
% 1.74/1.33 (binintersectER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X0 @ (binintersect @ X1 @ X2))) | ($true = (in @ X0 @ X2)))),
% 1.74/1.33 inference(ennf_transformation,[status(thm)],[f9])).
% 1.74/1.33 thf(f9,plain,(
% 1.74/1.33 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) => ($true = (in @ X0 @ X2))) <=> (binintersectER = $true)),
% 1.74/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.74/1.33 thf(f8,plain,(
% 1.74/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X2)) = binintersectER)),
% 1.74/1.33 inference(rectify,[status(thm)],[f2])).
% 1.74/1.33 thf(f2,axiom,(
% 1.74/1.33 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 1.74/1.33 file('/export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2THF_20547.p',binintersectER)).
% 1.74/1.33 thf(f49,plain,(
% 1.74/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (binunion @ X1 @ X2)))) )),
% 1.74/1.33 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.74/1.33 thf(f43,plain,(
% 1.74/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (binunion @ X1 @ X2))) | ($true != (in @ X0 @ X1)) | ($true != $true)) )),
% 1.74/1.33 inference(definition_unfolding,[status(thm)],[f31,f35])).
% 1.74/1.33 thf(f35,plain,(
% 1.74/1.33 (binunionIL = $true)),
% 1.74/1.33 inference(cnf_transformation,[status(thm)],[f28])).
% 1.74/1.33 thf(f31,plain,(
% 1.74/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (binunion @ X1 @ X2))) | ($true != (in @ X0 @ X1)) | (binunionIL != $true)) )),
% 1.74/1.33 inference(cnf_transformation,[status(thm)],[f19])).
% 1.74/1.33 thf(f19,plain,(
% 1.74/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binunion @ X1 @ X2))) | ($true != (in @ X0 @ X1))) | (binunionIL != $true)) & ((binunionIL = $true) | (($true != (in @ sK0 @ (binunion @ sK1 @ sK2))) & ($true = (in @ sK0 @ sK1))))),
% 1.74/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18])).
% 1.74/1.33 thf(f18,plain,(
% 1.74/1.33 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binunion @ X4 @ X5))) & ($true = (in @ X3 @ X4))) => (($true != (in @ sK0 @ (binunion @ sK1 @ sK2))) & ($true = (in @ sK0 @ sK1)))),
% 1.74/1.33 introduced(definition,[],[choice_axiom])).
% 1.74/1.33 thf(f17,plain,(
% 1.74/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binunion @ X1 @ X2))) | ($true != (in @ X0 @ X1))) | (binunionIL != $true)) & ((binunionIL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binunion @ X4 @ X5))) & ($true = (in @ X3 @ X4))))),
% 1.74/1.33 inference(rectify,[status(thm)],[f16])).
% 1.74/1.33 thf(f16,plain,(
% 1.74/1.33 (! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X1 @ (binunion @ X2 @ X0))) | ($true != (in @ X1 @ X2))) | (binunionIL != $true)) & ((binunionIL = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X1 @ (binunion @ X2 @ X0))) & ($true = (in @ X1 @ X2))))),
% 1.74/1.33 inference(nnf_transformation,[status(thm)],[f12])).
% 1.74/1.33 thf(f12,plain,(
% 1.74/1.33 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X1 @ (binunion @ X2 @ X0))) | ($true != (in @ X1 @ X2))) <=> (binunionIL = $true)),
% 1.74/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.74/1.33 thf(f11,plain,(
% 1.74/1.33 (binunionIL = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X1 @ X2)) => ($true = (in @ X1 @ (binunion @ X2 @ X0))))),
% 1.74/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.74/1.33 thf(f10,plain,(
% 1.74/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X2 @ X0))) = binunionIL)),
% 1.74/1.33 inference(rectify,[status(thm)],[f1])).
% 1.74/1.33 thf(f1,axiom,(
% 1.74/1.33 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 1.74/1.33 file('/export/starexec/sandbox/tmp/tmp.THP8iuCWQq/DTF2THF_20547.p',binunionIL)).
% 1.74/1.33 thf(f39,plain,(
% 1.74/1.33 ($true != (in @ sK10 @ (binunion @ sK8 @ sK9)))),
% 1.74/1.33 inference(cnf_transformation,[status(thm)],[f28])).
% 1.74/1.33 % SZS output end Proof for DTF2THF_20547
% 1.74/1.33 % (20741)------------------------------
% 1.74/1.33 % (20741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.33 % (20741)Termination reason: Refutation
% 1.74/1.33
% 1.74/1.33 % (20741)Memory used [KB]: 5628
% 1.74/1.33 % (20741)Time elapsed: 0.006 s
% 1.74/1.33 % (20741)Instructions burned: 10 (million)
% 1.74/1.33 % (20741)------------------------------
% 1.74/1.33 % (20741)------------------------------
% 1.74/1.33 % (20734)Success in time 0.004 s
%------------------------------------------------------------------------------