%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU596^2 : 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 : n013.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 09:35:30 AM UTC 2026
% Result : Theorem 1.51s 1.21s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 601 ( 181 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 584 ( 90 ~; 64 |; 42 &; 349 @)
% ( 8 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 16 con; 0-2 aty)
% Number of variables : 138 ( 0 ^; 103 !; 35 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_11,type,
sK2: $i > $i ).
thf(f103,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f96,f102]) ).
thf(f102,plain,
~ spl10_4,
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl10_4 ),
inference(subsumption_resolution,[status(thm)],[f100,f80]) ).
thf(f80,plain,
( $true
= ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
= ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK0 ) )
| ( emptyset != emptyset ) ),
inference(superposition,[status(thm)],[f40,f74]) ).
thf(f74,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X0 @ X1 ) )
| ( ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X0 @ X1 ) )
| ( ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f59,f61]) ).
thf(f61,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) )
| ( emptyset = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) )
| ( emptyset = X0 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f38]) ).
thf(f38,plain,
emptyI = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( emptyset
!= ( binintersect @ sK1 @ sK0 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) )
& ( emptyI = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
=> ( ( emptyset
!= ( binintersect @ sK1 @ sK0 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
& ( emptyI = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( emptyI = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( emptyI = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X2: $i,X0: $i] :
( ~ ? [X1: $i] :
( ( in @ X1 @ X0 )
& ( in @ X1 @ X2 ) )
=> ( emptyset
= ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X2: $i,X0: $i] :
( ~ ? [X1: $i] :
( ( in @ X1 @ X0 )
& ( in @ X1 @ X2 ) )
=> ( emptyset
= ( binintersect @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',disjointsetsI1) ).
thf(f43,plain,
! [X0: $i] :
( ( emptyset = X0 )
| ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) )
| ( emptyI != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i] :
( ( emptyset = X0 )
| ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) ) )
| ( emptyI != $true ) )
& ( ( emptyI = $true )
| ( ( emptyset != sK3 )
& ! [X3: $i] :
( $true
!= ( in @ X3 @ sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f26,f25]) ).
thf(f25,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X2: $i] :
( ( emptyset != X2 )
& ! [X3: $i] :
( ( in @ X3 @ X2 )
!= $true ) )
=> ( ( emptyset != sK3 )
& ! [X3: $i] :
( $true
!= ( in @ X3 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ! [X0: $i] :
( ( emptyset = X0 )
| ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
| ( emptyI != $true ) )
& ( ( emptyI = $true )
| ? [X2: $i] :
( ( emptyset != X2 )
& ! [X3: $i] :
( ( in @ X3 @ X2 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i] :
( ( emptyset = X0 )
| ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
| ( emptyI != $true ) )
& ( ( emptyI = $true )
| ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i] :
( ( emptyset = X0 )
| ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
<=> ( emptyI = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
=> ( emptyset = X0 ) )
<=> ( emptyI = $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
=> ( emptyset = X0 ) )
<=> ( emptyI = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i] :
( ( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( emptyset = X0 ) )
= emptyI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( emptyset = X0 ) )
= emptyI ),
file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',emptyI) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f37]) ).
thf(f37,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( ( in @ sK5 @ ( binintersect @ sK6 @ sK4 ) )
= $true )
& ( $true
!= ( in @ sK5 @ sK4 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f29,f30]) ).
thf(f30,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
& ( ( in @ X4 @ X3 )
!= $true ) )
=> ( ( ( in @ sK5 @ ( binintersect @ sK6 @ sK4 ) )
= $true )
& ( $true
!= ( in @ sK5 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
& ( ( in @ X4 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( binintersectER = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X2 ) )
= binintersectER ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X1 @ X2 ) )
= binintersectER ),
file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',binintersectER) ).
thf(f40,plain,
( emptyset
!= ( binintersect @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f100,plain,
( ( $true
!= ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK0 ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true != $true )
| ( $true
!= ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK0 ) )
| ~ spl10_4 ),
inference(superposition,[status(thm)],[f39,f94]) ).
thf(f94,plain,
( ( ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK1 )
= $true )
| ~ spl10_4 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl10_4
<=> ( ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition]) ).
thf(f39,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f96,plain,
spl10_4,
inference(avatar_split_clause,[status(thm)],[f86,f92]) ).
thf(f86,plain,
( ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( in @ ( sK2 @ ( binintersect @ sK1 @ sK0 ) ) @ sK1 )
= $true )
| ( emptyset != emptyset ) ),
inference(superposition,[status(thm)],[f40,f76]) ).
thf(f76,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X0 @ X1 ) )
| ( $true
= ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( emptyset
= ( binintersect @ X0 @ X1 ) )
| ( $true
= ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f60,f61]) ).
thf(f60,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f36]) ).
thf(f36,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( binintersectEL = $true )
| ( ( $true
!= ( in @ sK7 @ sK8 ) )
& ( $true
= ( in @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f33,f34]) ).
thf(f34,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
=> ( ( $true
!= ( in @ sK7 @ sK8 ) )
& ( $true
= ( in @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true )
=> ( $true
= ( in @ X0 @ X1 ) ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersectEL
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',binintersectEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU596^2 : 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
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:27:53 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : SEU596^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.45 % Domain : Set Theory
% 0.28/0.45 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.28/0.45 % Version : Especial > Reduced > Especial.
% 0.28/0.45 % English : (! A:i.! B:i.~(? x:i.in x A & in x B) ->
% 0.28/0.45 % binintersect A B = emptyset)
% 0.28/0.45
% 0.28/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.45 % Source : [Bro08]
% 0.28/0.45 % Names : ZFC098l [Bro08]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.28/0.45 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.28/0.45 % Number of atoms : 18 ( 5 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 6 ( 4 avg)
% 0.28/0.45 % Number of connectives : 30 ( 2 ~; 0 |; 1 &; 20 @)
% 0.28/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 12 ( 4 avg)
% 0.28/0.45 % Number of types : 2 ( 0 usr)
% 0.28/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.28/0.45 % Number of variables : 11 ( 0 ^; 10 !; 1 ?; 11 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : http://mathgate.info/detsetitem.php?id=387
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 thf(in_type,type,
% 0.28/0.45 in: $i > $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyset_type,type,
% 0.28/0.45 emptyset: $i ).
% 0.28/0.45
% 0.28/0.45 thf(emptyI_type,type,
% 0.28/0.45 emptyI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyI,definition,
% 0.28/0.45 ( emptyI
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ~ ( in @ Xx @ A )
% 0.28/0.45 => ( A = emptyset ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binintersect_type,type,
% 0.28/0.45 binintersect: $i > $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(binintersectEL_type,type,
% 0.28/0.45 binintersectEL: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binintersectEL,definition,
% 0.28/0.45 ( binintersectEL
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binintersectER_type,type,
% 0.28/0.45 binintersectER: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binintersectER,definition,
% 0.28/0.45 ( binintersectER
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.45 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(disjointsetsI1,conjecture,
% 0.28/0.45 ( emptyI
% 0.28/0.45 => ( binintersectEL
% 0.28/0.45 => ( binintersectER
% 0.28/0.45 => ! [A: $i,B: $i] :
% 0.28/0.45 ( ~ ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ( in @ Xx @ B ) )
% 0.28/0.45 => ( ( binintersect @ A @ B )
% 0.28/0.45 = emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 1.37/1.18 ---- Embedded in THF ---
% 1.37/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.18 %%% Generated on Tue Feb 24 12:27:54 EST 2026
% 1.37/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.18 %%% Logic specification used:
% 1.37/1.18 %%% thf(spec, logic, $$dhol).
% 1.37/1.18
% 1.37/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2DTF19678.p
% See solution above
% 1.37/1.18 ------------------------
% 1.37/1.19 ---- Cleaned THF ---
% 1.37/1.19 thf(in_type,type,
% 1.37/1.19 in: $i > $i > $o ).
% 1.37/1.19
% 1.37/1.19 thf(emptyset_type,type,
% 1.37/1.19 emptyset: $i ).
% 1.37/1.19
% 1.37/1.19 thf(emptyI_type,type,
% 1.37/1.19 emptyI: $o ).
% 1.37/1.19
% 1.37/1.19 thf(emptyI,definition,
% 1.37/1.19 ( emptyI
% 1.37/1.19 = ( ! [A: $i] :
% 1.37/1.19 ( ! [Xx: $i] :
% 1.37/1.19 ~ ( in @ Xx @ A )
% 1.37/1.19 => ( A = emptyset ) ) ) ) ).
% 1.37/1.19
% 1.37/1.19 thf(binintersect_type,type,
% 1.37/1.19 binintersect: $i > $i > $i ).
% 1.37/1.19
% 1.37/1.19 thf(binintersectEL_type,type,
% 1.37/1.19 binintersectEL: $o ).
% 1.37/1.19
% 1.37/1.19 thf(binintersectEL,definition,
% 1.37/1.19 ( binintersectEL
% 1.37/1.19 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.37/1.19 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.37/1.19 => ( in @ Xx @ A ) ) ) ) ).
% 1.37/1.19
% 1.37/1.19 thf(binintersectER_type,type,
% 1.37/1.19 binintersectER: $o ).
% 1.37/1.19
% 1.37/1.19 thf(binintersectER,definition,
% 1.37/1.19 ( binintersectER
% 1.37/1.19 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.37/1.19 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.37/1.19 => ( in @ Xx @ B ) ) ) ) ).
% 1.37/1.19
% 1.37/1.19 thf(disjointsetsI1,conjecture,
% 1.37/1.19 ( emptyI
% 1.37/1.19 => ( binintersectEL
% 1.37/1.19 => ( binintersectER
% 1.37/1.19 => ! [A: $i,B: $i] :
% 1.37/1.19 ( ~ ? [Xx: $i] :
% 1.37/1.19 ( ( in @ Xx @ A )
% 1.37/1.19 & ( in @ Xx @ B ) )
% 1.37/1.19 => ( ( binintersect @ A @ B )
% 1.37/1.19 = emptyset ) ) ) ) ) ).
% 1.37/1.19 ------------------------
% 1.51/1.21 % (19960)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_19678 for (2999ds/2Mi)
% 1.51/1.21 % (19960)Instruction limit reached!
% 1.51/1.21 % (19960)------------------------------
% 1.51/1.21 % (19960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (19960)Termination reason: Unknown
% 1.51/1.21 % (19960)Termination phase: Property scanning
% 1.51/1.21
% 1.51/1.21 % (19960)Memory used [KB]: 895
% 1.51/1.21 % (19960)Time elapsed: 0.002 s
% 1.51/1.21 % (19960)Instructions burned: 2 (million)
% 1.51/1.21 % (19960)------------------------------
% 1.51/1.21 % (19960)------------------------------
% 1.51/1.21 % (19958)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_19678 for (2999ds/27Mi)
% 1.51/1.21 % (19962)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19678 for (2999ds/18Mi)
% 1.51/1.21 % (19962)First to succeed.
% 1.51/1.21 % (19958)Also succeeded, but the first one will report.
% 1.51/1.21 % (19962)Refutation found. Thanks to Tanya!
% 1.51/1.21 % SZS status Theorem for DTF2THF_19678
% 1.51/1.21 % SZS output start Proof for DTF2THF_19678
% 1.51/1.21 thf(func_def_0, type, in: $i > $i > $o).
% 1.51/1.21 thf(func_def_4, type, binintersect: $i > $i > $i).
% 1.51/1.21 thf(func_def_11, type, sK2: $i > $i).
% 1.51/1.21 thf(f103,plain,(
% 1.51/1.21 $false),
% 1.51/1.21 inference(avatar_sat_refutation,[status(thm)],[f96,f102])).
% 1.51/1.21 thf(f102,plain,(
% 1.51/1.21 ~spl10_4),
% 1.51/1.21 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.51/1.21 thf(f101,plain,(
% 1.51/1.21 $false | ~spl10_4),
% 1.51/1.21 inference(subsumption_resolution,[status(thm)],[f100,f80])).
% 1.51/1.21 thf(f80,plain,(
% 1.51/1.21 ($true = (in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK0))),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.51/1.21 thf(f77,plain,(
% 1.51/1.21 ($true = (in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK0)) | (emptyset != emptyset)),
% 1.51/1.21 inference(superposition,[status(thm)],[f40,f74])).
% 1.51/1.21 thf(f74,plain,(
% 1.51/1.21 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X0 @ X1)) | ((in @ (sK2 @ (binintersect @ X0 @ X1)) @ X1) = $true)) )),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.51/1.21 thf(f73,plain,(
% 1.51/1.21 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X0 @ X1)) | ((in @ (sK2 @ (binintersect @ X0 @ X1)) @ X1) = $true) | ($true != $true)) )),
% 1.51/1.21 inference(superposition,[status(thm)],[f59,f61])).
% 1.51/1.21 thf(f61,plain,(
% 1.51/1.21 ( ! [X0 : $i] : (($true = (in @ (sK2 @ X0) @ X0)) | (emptyset = X0)) )),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.51/1.21 thf(f50,plain,(
% 1.51/1.21 ( ! [X0 : $i] : (($true = (in @ (sK2 @ X0) @ X0)) | (emptyset = X0) | ($true != $true)) )),
% 1.51/1.21 inference(definition_unfolding,[status(thm)],[f43,f38])).
% 1.51/1.21 thf(f38,plain,(
% 1.51/1.21 (emptyI = $true)),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f22])).
% 1.51/1.21 thf(f22,plain,(
% 1.51/1.21 ((emptyset != (binintersect @ sK1 @ sK0)) & ! [X2 : $i] : (($true != (in @ X2 @ sK1)) | ($true != (in @ X2 @ sK0)))) & (emptyI = $true) & (binintersectER = $true) & (binintersectEL = $true)),
% 1.51/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f21])).
% 1.51/1.21 thf(f21,plain,(
% 1.51/1.21 ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0)))) => ((emptyset != (binintersect @ sK1 @ sK0)) & ! [X2 : $i] : (($true != (in @ X2 @ sK1)) | ($true != (in @ X2 @ sK0))))),
% 1.51/1.21 introduced(definition,[],[choice_axiom])).
% 1.51/1.21 thf(f18,plain,(
% 1.51/1.21 ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0)))) & (emptyI = $true) & (binintersectER = $true) & (binintersectEL = $true)),
% 1.51/1.21 inference(flattening,[status(thm)],[f17])).
% 1.51/1.21 thf(f17,plain,(
% 1.51/1.21 ((? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0)))) & (binintersectER = $true)) & (binintersectEL = $true)) & (emptyI = $true)),
% 1.51/1.21 inference(ennf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f12,plain,(
% 1.51/1.21 ~((emptyI = $true) => ((binintersectEL = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (~? [X2 : $i] : (($true = (in @ X2 @ X0)) & ((in @ X2 @ X1) = $true)) => (emptyset = (binintersect @ X1 @ X0))))))),
% 1.51/1.22 inference(fool_elimination,[status(thm)],[f11])).
% 1.51/1.22 thf(f11,plain,(
% 1.51/1.22 ~(emptyI => (binintersectEL => (binintersectER => ! [X0 : $i,X1 : $i] : (~? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (emptyset = (binintersect @ X1 @ X0))))))),
% 1.51/1.22 inference(rectify,[status(thm)],[f5])).
% 1.51/1.22 thf(f5,negated_conjecture,(
% 1.51/1.22 ~(emptyI => (binintersectEL => (binintersectER => ! [X2 : $i,X0 : $i] : (~? [X1 : $i] : ((in @ X1 @ X0) & (in @ X1 @ X2)) => (emptyset = (binintersect @ X0 @ X2))))))),
% 1.51/1.22 inference(negated_conjecture,[status(cth)],[f4])).
% 1.51/1.22 thf(f4,conjecture,(
% 1.51/1.22 emptyI => (binintersectEL => (binintersectER => ! [X2 : $i,X0 : $i] : (~? [X1 : $i] : ((in @ X1 @ X0) & (in @ X1 @ X2)) => (emptyset = (binintersect @ X0 @ X2)))))),
% 1.51/1.22 file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',disjointsetsI1)).
% 1.51/1.22 thf(f43,plain,(
% 1.51/1.22 ( ! [X0 : $i] : ((emptyset = X0) | ($true = (in @ (sK2 @ X0) @ X0)) | (emptyI != $true)) )),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f27])).
% 1.51/1.22 thf(f27,plain,(
% 1.51/1.22 (! [X0 : $i] : ((emptyset = X0) | ($true = (in @ (sK2 @ X0) @ X0))) | (emptyI != $true)) & ((emptyI = $true) | ((emptyset != sK3) & ! [X3 : $i] : ($true != (in @ X3 @ sK3))))),
% 1.51/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f26,f25])).
% 1.51/1.22 thf(f25,plain,(
% 1.51/1.22 ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) => ($true = (in @ (sK2 @ X0) @ X0)))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f26,plain,(
% 1.51/1.22 ? [X2 : $i] : ((emptyset != X2) & ! [X3 : $i] : ((in @ X3 @ X2) != $true)) => ((emptyset != sK3) & ! [X3 : $i] : ($true != (in @ X3 @ sK3)))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f24,plain,(
% 1.51/1.22 (! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : ((in @ X1 @ X0) = $true)) | (emptyI != $true)) & ((emptyI = $true) | ? [X2 : $i] : ((emptyset != X2) & ! [X3 : $i] : ((in @ X3 @ X2) != $true)))),
% 1.51/1.22 inference(rectify,[status(thm)],[f23])).
% 1.51/1.22 thf(f23,plain,(
% 1.51/1.22 (! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : ((in @ X1 @ X0) = $true)) | (emptyI != $true)) & ((emptyI = $true) | ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ((in @ X1 @ X0) != $true)))),
% 1.51/1.22 inference(nnf_transformation,[status(thm)],[f19])).
% 1.51/1.22 thf(f19,plain,(
% 1.51/1.22 ! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : ((in @ X1 @ X0) = $true)) <=> (emptyI = $true)),
% 1.51/1.22 inference(ennf_transformation,[status(thm)],[f15])).
% 1.51/1.22 thf(f15,plain,(
% 1.51/1.22 ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) != $true) => (emptyset = X0)) <=> (emptyI = $true)),
% 1.51/1.22 inference(flattening,[status(thm)],[f8])).
% 1.51/1.22 thf(f8,plain,(
% 1.51/1.22 ! [X0 : $i] : (! [X1 : $i] : ~((in @ X1 @ X0) = $true) => (emptyset = X0)) <=> (emptyI = $true)),
% 1.51/1.22 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.22 thf(f7,plain,(
% 1.51/1.22 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (emptyset = X0)) = emptyI)),
% 1.51/1.22 inference(rectify,[status(thm)],[f1])).
% 1.51/1.22 thf(f1,axiom,(
% 1.51/1.22 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (emptyset = X0)) = emptyI)),
% 1.51/1.22 file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',emptyI)).
% 1.51/1.22 thf(f59,plain,(
% 1.51/1.22 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ((in @ X1 @ X0) = $true)) )),
% 1.51/1.22 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.51/1.22 thf(f53,plain,(
% 1.51/1.22 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ($true != $true)) )),
% 1.51/1.22 inference(definition_unfolding,[status(thm)],[f46,f37])).
% 1.51/1.22 thf(f37,plain,(
% 1.51/1.22 (binintersectER = $true)),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.51/1.22 thf(f46,plain,(
% 1.51/1.22 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ((in @ X1 @ X0) = $true) | (binintersectER != $true)) )),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f31])).
% 1.51/1.22 thf(f31,plain,(
% 1.51/1.22 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ((in @ X1 @ X0) = $true)) | (binintersectER != $true)) & ((binintersectER = $true) | (((in @ sK5 @ (binintersect @ sK6 @ sK4)) = $true) & ($true != (in @ sK5 @ sK4))))),
% 1.51/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f29,f30])).
% 1.51/1.22 thf(f30,plain,(
% 1.51/1.22 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binintersect @ X5 @ X3)) = $true) & ((in @ X4 @ X3) != $true)) => (((in @ sK5 @ (binintersect @ sK6 @ sK4)) = $true) & ($true != (in @ sK5 @ sK4)))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f29,plain,(
% 1.51/1.22 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (binintersect @ X2 @ X0))) | ((in @ X1 @ X0) = $true)) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binintersect @ X5 @ X3)) = $true) & ((in @ X4 @ X3) != $true)))),
% 1.51/1.22 inference(rectify,[status(thm)],[f28])).
% 1.51/1.22 thf(f28,plain,(
% 1.51/1.22 (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true)) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X0 @ X2) != $true)))),
% 1.51/1.22 inference(nnf_transformation,[status(thm)],[f16])).
% 1.51/1.22 thf(f16,plain,(
% 1.51/1.22 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true)) <=> (binintersectER = $true)),
% 1.51/1.22 inference(ennf_transformation,[status(thm)],[f10])).
% 1.51/1.22 thf(f10,plain,(
% 1.51/1.22 (binintersectER = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) = $true) => ((in @ X0 @ X2) = $true))),
% 1.51/1.22 inference(fool_elimination,[status(thm)],[f9])).
% 1.51/1.22 thf(f9,plain,(
% 1.51/1.22 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X2)) = binintersectER)),
% 1.51/1.22 inference(rectify,[status(thm)],[f3])).
% 1.51/1.22 thf(f3,axiom,(
% 1.51/1.22 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X2)) = binintersectER)),
% 1.51/1.22 file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',binintersectER)).
% 1.51/1.22 thf(f40,plain,(
% 1.51/1.22 (emptyset != (binintersect @ sK1 @ sK0))),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.51/1.22 thf(f100,plain,(
% 1.51/1.22 ($true != (in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK0)) | ~spl10_4),
% 1.51/1.22 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.51/1.22 thf(f99,plain,(
% 1.51/1.22 ($true != $true) | ($true != (in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK0)) | ~spl10_4),
% 1.51/1.22 inference(superposition,[status(thm)],[f39,f94])).
% 1.51/1.22 thf(f94,plain,(
% 1.51/1.22 ((in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK1) = $true) | ~spl10_4),
% 1.51/1.22 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.51/1.22 thf(f92,definition,(
% 1.51/1.22 spl10_4 <=> ((in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK1) = $true)),
% 1.51/1.22 introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition])).
% 1.51/1.22 thf(f39,plain,(
% 1.51/1.22 ( ! [X2 : $i] : (($true != (in @ X2 @ sK1)) | ($true != (in @ X2 @ sK0))) )),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.51/1.22 thf(f96,plain,(
% 1.51/1.22 spl10_4),
% 1.51/1.22 inference(avatar_split_clause,[status(thm)],[f86,f92])).
% 1.51/1.22 thf(f86,plain,(
% 1.51/1.22 ((in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK1) = $true)),
% 1.51/1.22 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.51/1.22 thf(f83,plain,(
% 1.51/1.22 ((in @ (sK2 @ (binintersect @ sK1 @ sK0)) @ sK1) = $true) | (emptyset != emptyset)),
% 1.51/1.22 inference(superposition,[status(thm)],[f40,f76])).
% 1.51/1.22 thf(f76,plain,(
% 1.51/1.22 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X0 @ X1)) | ($true = (in @ (sK2 @ (binintersect @ X0 @ X1)) @ X0))) )),
% 1.51/1.22 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.51/1.22 thf(f75,plain,(
% 1.51/1.22 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (emptyset = (binintersect @ X0 @ X1)) | ($true = (in @ (sK2 @ (binintersect @ X0 @ X1)) @ X0))) )),
% 1.51/1.22 inference(superposition,[status(thm)],[f60,f61])).
% 1.51/1.22 thf(f60,plain,(
% 1.51/1.22 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true)) )),
% 1.51/1.22 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.51/1.22 thf(f58,plain,(
% 1.51/1.22 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true) | ($true != $true)) )),
% 1.51/1.22 inference(definition_unfolding,[status(thm)],[f47,f36])).
% 1.51/1.22 thf(f36,plain,(
% 1.51/1.22 (binintersectEL = $true)),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.51/1.22 thf(f47,plain,(
% 1.51/1.22 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | (binintersectEL != $true)) )),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f35])).
% 1.51/1.22 thf(f35,plain,(
% 1.51/1.22 ((binintersectEL = $true) | (($true != (in @ sK7 @ sK8)) & ($true = (in @ sK7 @ (binintersect @ sK8 @ sK9))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ (binintersect @ X4 @ X5)) != $true)) | (binintersectEL != $true))),
% 1.51/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f33,f34])).
% 1.51/1.22 thf(f34,plain,(
% 1.51/1.22 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X1 @ X2)) = $true)) => (($true != (in @ sK7 @ sK8)) & ($true = (in @ sK7 @ (binintersect @ sK8 @ sK9))))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f33,plain,(
% 1.51/1.22 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X1 @ X2)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ (binintersect @ X4 @ X5)) != $true)) | (binintersectEL != $true))),
% 1.51/1.22 inference(rectify,[status(thm)],[f32])).
% 1.51/1.22 thf(f32,plain,(
% 1.51/1.22 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X1 @ X2)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) | ((in @ X0 @ (binintersect @ X1 @ X2)) != $true)) | (binintersectEL != $true))),
% 1.51/1.22 inference(nnf_transformation,[status(thm)],[f20])).
% 1.51/1.22 thf(f20,plain,(
% 1.51/1.22 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) | ((in @ X0 @ (binintersect @ X1 @ X2)) != $true))),
% 1.51/1.22 inference(ennf_transformation,[status(thm)],[f14])).
% 1.51/1.22 thf(f14,plain,(
% 1.51/1.22 ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X1 @ X2)) = $true) => ($true = (in @ X0 @ X1))) <=> (binintersectEL = $true)),
% 1.51/1.22 inference(fool_elimination,[status(thm)],[f13])).
% 1.51/1.22 thf(f13,plain,(
% 1.51/1.22 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X1)))),
% 1.51/1.22 inference(rectify,[status(thm)],[f2])).
% 1.51/1.22 thf(f2,axiom,(
% 1.51/1.22 (binintersectEL = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X0)))),
% 1.51/1.22 file('/export/starexec/sandbox/tmp/tmp.xUpvOtbuo7/DTF2THF_19678.p',binintersectEL)).
% 1.51/1.22 % SZS output end Proof for DTF2THF_19678
% 1.51/1.22 % (19962)------------------------------
% 1.51/1.22 % (19962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (19962)Termination reason: Refutation
% 1.51/1.22
% 1.51/1.22 % (19962)Memory used [KB]: 5500
% 1.51/1.22 % (19962)Time elapsed: 0.005 s
% 1.51/1.22 % (19962)Instructions burned: 7 (million)
% 1.51/1.22 % (19962)------------------------------
% 1.51/1.22 % (19962)------------------------------
% 1.51/1.22 % (19955)Success in time 0.016 s
%------------------------------------------------------------------------------