%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU742^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:04 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 65 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1139 ( 306 equ; 0 cnn)
% Maximal formula atoms : 14 ( 17 avg)
% Number of connectives : 1407 ( 160 ~; 147 |; 69 &; 954 @)
% ( 9 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 23 con; 0-2 aty)
% Number of variables : 194 ( 0 ^; 158 !; 36 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
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_3,type,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
binintersectI: $o ).
thf(func_def_6,type,
inIntersectImpInUnion: $o ).
thf(func_def_7,type,
inIntersectImpInUnion2: $o ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X1 @ X3 ) ) ) ) ) ) )
= inIntersectImpInUnion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(f3,axiom,
( inIntersectImpInUnion2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(f4,conjecture,
( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(f5,negated_conjecture,
~ ( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
= binintersectI ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) )
<=> ( binintersectI = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [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 ) ) ) ) ) ) )
= inIntersectImpInUnion ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
=> ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) ) ) ) )
<=> ( inIntersectImpInUnion = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [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 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( binintersectI = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
=> ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( inIntersectImpInUnion2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
=> ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) ) ) ) ) )
<=> ( inIntersectImpInUnion2 = $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( inIntersectImpInUnion2 = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( inIntersectImpInUnion2 = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( inIntersectImpInUnion = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
<=> ( inIntersectImpInUnion = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f19,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( binintersectI = $true ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f21,plain,
( ( binintersectI = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
| ( inIntersectImpInUnion2 != $true ) )
& ( ( inIntersectImpInUnion2 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
!= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) )
| ( inIntersectImpInUnion2 != $true ) )
& ( ( inIntersectImpInUnion2 = $true )
| ? [X5: $i,X6: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ ( powerset @ X6 ) )
= $true )
& ? [X8: $i] :
( ( $true
= ( in @ X8 @ ( powerset @ X6 ) ) )
& ? [X9: $i] :
( ( ( in @ X9 @ ( binunion @ X7 @ X8 ) )
!= $true )
& ( $true
= ( in @ X9 @ X6 ) )
& ( $true
= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) )
| ( inIntersectImpInUnion2 != $true ) )
& ( ( inIntersectImpInUnion2 = $true )
| ( ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
& ( $true
!= ( in @ sK4 @ ( binunion @ sK2 @ sK3 ) ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
= ( in @ sK4 @ ( binintersect @ sK0 @ sK2 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X5,sK0),skolemize(X6,sK1),skolemize(X7,sK2),skolemize(X8,sK3),skolemize(X9,sK4)],[f23]) ).
thf(f25,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
& ( ( in @ X4 @ ( binintersect @ X5 @ X3 ) )
!= $true )
& ( $true
= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ( ( $true
= ( in @ sK6 @ sK5 ) )
& ( $true
!= ( in @ sK6 @ ( binintersect @ sK7 @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ sK7 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7)],[f26]) ).
thf(f28,plain,
( ( binintersectI = $true )
& ( $true
= ( in @ sK8 @ ( powerset @ sK9 ) ) )
& ( $true
= ( in @ sK10 @ ( powerset @ sK9 ) ) )
& ( $true
= ( in @ sK11 @ ( powerset @ sK9 ) ) )
& ( ( in @ sK12 @ sK9 )
= $true )
& ( ( in @ sK12 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
!= ( in @ sK12 @ ( binintersect @ ( binunion @ sK8 @ sK11 ) @ ( binunion @ sK10 @ sK11 ) ) ) )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12)],[f21]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( inIntersectImpInUnion != $true ) )
& ( ( inIntersectImpInUnion = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f17]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( inIntersectImpInUnion != $true ) )
& ( ( inIntersectImpInUnion = $true )
| ? [X5: $i,X6: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
& ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ X6 ) )
& ( $true
= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
& ( $true
!= ( in @ X9 @ ( binunion @ X5 @ X8 ) ) ) )
& ( $true
= ( in @ X8 @ ( powerset @ X6 ) ) ) )
& ( ( in @ X7 @ ( powerset @ X6 ) )
= $true ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( inIntersectImpInUnion != $true ) )
& ( ( inIntersectImpInUnion = $true )
| ( ( $true
= ( in @ sK13 @ ( powerset @ sK14 ) ) )
& ( $true
= ( in @ sK17 @ sK14 ) )
& ( $true
= ( in @ sK17 @ ( binintersect @ sK13 @ sK15 ) ) )
& ( $true
!= ( in @ sK17 @ ( binunion @ sK13 @ sK16 ) ) )
& ( ( in @ sK16 @ ( powerset @ sK14 ) )
= $true )
& ( $true
= ( in @ sK15 @ ( powerset @ sK14 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X5,sK13),skolemize(X6,sK14),skolemize(X7,sK15),skolemize(X8,sK16),skolemize(X9,sK17)],[f30]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( inIntersectImpInUnion2 != $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersectI != $true )
| ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f43,plain,
inIntersectImpInUnion = $true,
inference(cnf_transformation,[],[f28]) ).
thf(f44,plain,
inIntersectImpInUnion2 = $true,
inference(cnf_transformation,[],[f28]) ).
thf(f45,plain,
( $true
!= ( in @ sK12 @ ( binintersect @ ( binunion @ sK8 @ sK11 ) @ ( binunion @ sK10 @ sK11 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f46,plain,
( ( in @ sK12 @ ( binintersect @ sK8 @ sK10 ) )
= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f47,plain,
( ( in @ sK12 @ sK9 )
= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f48,plain,
( $true
= ( in @ sK11 @ ( powerset @ sK9 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f49,plain,
( $true
= ( in @ sK10 @ ( powerset @ sK9 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f50,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK9 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f51,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f28]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( inIntersectImpInUnion != $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ),
inference(forward_subsumption_resolution,[],[f42,f51]) ).
thf(f64,plain,
( ( $true
!= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) ) ),
inference(superposition,[],[f45,f63]) ).
thf(f65,plain,
( ( $true
!= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) )
| ( $true
!= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ X1 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f38,f44]) ).
thf(f68,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK10 @ ( powerset @ X1 ) ) )
| ( ( in @ sK8 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ sK12 @ X1 ) )
| ( ( in @ sK12 @ ( binunion @ sK10 @ X0 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(superposition,[],[f66,f46]) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ sK12 @ X1 ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X1 ) ) )
| ( ( in @ sK12 @ ( binunion @ sK10 @ X0 ) )
= $true )
| ( ( in @ sK8 @ ( powerset @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f73,plain,
( ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) )
| ( $true
= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) )
| ( $true != $true )
| ( ( in @ sK12 @ sK9 )
!= $true ) ),
inference(superposition,[],[f69,f48]) ).
thf(f78,plain,
( ( $true
= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) )
| ( ( in @ sK12 @ sK9 )
!= $true )
| ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f81,plain,
( ( $true
= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) ) ),
inference(forward_subsumption_resolution,[],[f78,f47]) ).
thf(f84,plain,
( ( $true
= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) ) ),
inference(forward_subsumption_resolution,[],[f81,f49]) ).
thf(f85,plain,
( $true
= ( in @ sK12 @ ( binunion @ sK10 @ sK11 ) ) ),
inference(forward_subsumption_resolution,[],[f84,f50]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(forward_subsumption_resolution,[],[f58,f43]) ).
thf(f87,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) ) ),
inference(superposition,[],[f65,f85]) ).
thf(f88,plain,
( $true
!= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f90,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ sK12 @ ( binunion @ sK8 @ X1 ) ) )
| ( $true
!= ( in @ sK12 @ X0 ) )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) ) ),
inference(superposition,[],[f86,f46]) ).
thf(f91,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK12 @ X0 ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK12 @ ( binunion @ sK8 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f95,plain,
( ( $true
= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) )
| ( ( in @ sK12 @ sK9 )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f91,f48]) ).
thf(f100,plain,
( ( ( in @ sK12 @ sK9 )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) )
| ( $true
= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) ) ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f103,plain,
( ( $true
= ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) ) ),
inference(forward_subsumption_resolution,[],[f100,f47]) ).
thf(f106,plain,
( ( $true
!= ( in @ sK10 @ ( powerset @ sK9 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) ) ),
inference(forward_subsumption_resolution,[],[f103,f88]) ).
thf(f107,plain,
( $true
!= ( in @ sK8 @ ( powerset @ sK9 ) ) ),
inference(forward_subsumption_resolution,[],[f106,f49]) ).
thf(f108,plain,
$false,
inference(forward_subsumption_resolution,[],[f107,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU742^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:19:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.30 % (2732710)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (2732717)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4100820120:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (2732717)Instruction limit reached!
% 0.23/0.30 % (2732717)------------------------------
% 0.23/0.30 % (2732717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2732717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2732717)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2732717)Termination reason: Instruction limit
% 0.23/0.30 % (2732717)Termination phase: Saturation
% 0.23/0.30 % (2732717)Time elapsed: 0.001 s
% 0.23/0.30 % (2732717)Peak memory usage: 12 MB
% 0.23/0.30 % (2732717)Instructions burned: 4 (million)
% 0.23/0.30 % (2732721)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (2732721)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.30 % (2732715)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1371436438:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (2732716)lrs+10_16_si=on:nwc=1.5:random_seed=47339307:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (2732720)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3962867352:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (2732719)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3295165737:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (2732718)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=952111946:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.30 % (2732721)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2367665155:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (2732723)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2752489380:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.30 % (2732723)Instruction limit reached!
% 0.23/0.30 % (2732723)------------------------------
% 0.23/0.30 % (2732723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2732723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2732723)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2732723)Termination reason: Instruction limit
% 0.23/0.30 % (2732723)Termination phase: Property scanning
% 0.23/0.30 % (2732723)Time elapsed: 0.001 s
% 0.23/0.30 % (2732723)Peak memory usage: 10 MB
% 0.23/0.30 % (2732723)Instructions burned: 3 (million)
% 0.23/0.30 % (2732719) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2732710-2732719"...
% 0.23/0.30 % (2732718) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2732710-2732718"...
% 0.23/0.30 % (2732719)...printing done.
% 0.23/0.30 % (2732716)Instruction limit reached!
% 0.23/0.30 % (2732716)------------------------------
% 0.23/0.30 % (2732716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2732716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2732716)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2732716)Termination reason: Instruction limit
% 0.23/0.30 % (2732716)Termination phase: Saturation
% 0.23/0.30 % (2732716)Time elapsed: 0.010 s
% 0.23/0.30 % (2732716)Peak memory usage: 12 MB
% 0.23/0.30 % (2732716)Instructions burned: 19 (million)
% 0.23/0.30 % (2732719)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (2732719)------------------------------
% 0.23/0.31 % (2732719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (2732719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (2732719)CaDiCaL version: 2.1.3
% 0.23/0.31 % (2732719)Termination reason: Refutation
% 0.23/0.31 % (2732719)Time elapsed: 0.008 s
% 0.23/0.31 % (2732719)Peak memory usage: 12 MB
% 0.23/0.31 % (2732719)Instructions burned: 16 (million)
% 0.23/0.31 % (2732710)Success in time 0.052 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------