%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU762^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:31:12 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 161 ( 51 unt; 0 typ; 19 def)
% Number of atoms : 1809 ( 438 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 2188 ( 360 ~; 336 |; 97 &;1280 @)
% ( 30 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 45 con; 0-2 aty)
% Number of variables : 241 ( 0 sgn 196 !; 45 ?; 241 :)
% 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,
subset: $i > $i > $o ).
thf(func_def_3,type,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
binintersectT_lem: $o ).
thf(func_def_6,type,
woz13rule1: $o ).
thf(func_def_7,type,
woz13rule2: $o ).
thf(func_def_8,type,
woz13rule3: $o ).
thf(f1,axiom,
( binintersectT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(f2,axiom,
( woz13rule1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1) ).
thf(f3,axiom,
( woz13rule2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2) ).
thf(f4,axiom,
( woz13rule3
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X2 )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3) ).
thf(f5,conjecture,
( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule4) ).
thf(f6,negated_conjecture,
~ ( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( woz13rule3
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ X2 )
=> ( ( subset @ X0 @ X3 )
=> ( subset @ X0 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
=> ( ( $true
= ( subset @ X0 @ X2 ) )
=> ( ( ( subset @ X0 @ X3 )
= $true )
=> ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true ) ) ) ) ) )
<=> ( woz13rule3 = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f10,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $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 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X1 @ X3 )
= $true )
=> ( ( ( subset @ X2 @ X4 )
= $true )
=> ( ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
= $true ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( woz13rule2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X2 @ X3 )
= $true )
=> ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true ) ) ) ) )
<=> ( woz13rule2 = $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( woz13rule1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X1 @ X3 )
= $true )
=> ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true ) ) ) ) )
<=> ( woz13rule1 = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ( binintersectT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( subset @ X1 @ X3 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( woz13rule1 = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f19,plain,
( ( woz13rule1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X3 )
!= $true )
| ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( subset @ X2 @ X4 )
= $true )
& ( ( subset @ X1 @ X3 )
= $true )
& ( ( in @ X4 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f21,plain,
( ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X3 )
= $true )
& ( ( subset @ X2 @ X4 )
= $true )
& ( ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( binintersectT_lem = $true )
& ( woz13rule1 = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( woz13rule3 = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( woz13rule3 = $true ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( woz13rule2 = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f25,plain,
( ( woz13rule2 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X2 @ X3 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ( ( woz13rule2 = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X2 @ X3 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X2 @ X3 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( woz13rule2 != $true ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f27,plain,
( ( ( woz13rule2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
& ( ( subset @ X2 @ X3 )
= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ! [X7: $i] :
( ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( subset @ X6 @ X7 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( woz13rule2 != $true ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ( woz13rule2 = $true )
| ( ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ( $true
!= ( subset @ ( binintersect @ sK0 @ sK2 ) @ sK3 ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
& ( $true
= ( subset @ sK2 @ sK3 ) )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ! [X7: $i] :
( ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( subset @ X6 @ X7 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( woz13rule2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f27]) ).
thf(f29,plain,
( ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X1 ) ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( ( subset @ X2 @ X4 )
= $true )
& ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) ) )
& ( binintersectT_lem = $true )
& ( woz13rule1 = $true ) ),
inference(rectify,[],[f21]) ).
thf(f30,plain,
( ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) )
& ( $true
= ( subset @ sK4 @ sK7 ) )
& ( ( subset @ sK6 @ sK8 )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) )
& ( binintersectT_lem = $true )
& ( woz13rule1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8)],[f29]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[],[f17]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) )
& ( $true
!= ( in @ ( binintersect @ X3 @ X5 ) @ ( powerset @ X4 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ( ( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) )
& ( ( in @ ( binintersect @ sK9 @ sK11 ) @ ( powerset @ sK10 ) )
!= $true )
& ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X3,sK9),skolemize(X4,sK10),skolemize(X5,sK11)],[f32]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( woz13rule3 != $true ) )
& ( ( woz13rule3 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( woz13rule3 != $true ) )
& ( ( woz13rule3 = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( subset @ X4 @ X6 ) )
& ( ( subset @ X4 @ X7 )
= $true )
& ( $true
!= ( subset @ X4 @ ( binintersect @ X6 @ X7 ) ) )
& ( $true
= ( in @ X7 @ ( powerset @ X5 ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) ) ) ),
inference(rectify,[],[f34]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( woz13rule3 != $true ) )
& ( ( woz13rule3 = $true )
| ( ( $true
= ( subset @ sK12 @ sK14 ) )
& ( $true
= ( subset @ sK12 @ sK15 ) )
& ( $true
!= ( subset @ sK12 @ ( binintersect @ sK14 @ sK15 ) ) )
& ( $true
= ( in @ sK15 @ ( powerset @ sK13 ) ) )
& ( $true
= ( in @ sK14 @ ( powerset @ sK13 ) ) )
& ( $true
= ( in @ sK12 @ ( powerset @ sK13 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X4,sK12),skolemize(X5,sK13),skolemize(X6,sK14),skolemize(X7,sK15)],[f35]) ).
thf(f37,plain,
( ( ( woz13rule1 = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X3 )
!= $true )
| ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( woz13rule1 != $true ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f38,plain,
( ( ( woz13rule1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( ( subset @ X4 @ X7 )
!= $true )
| ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( woz13rule1 != $true ) ) ),
inference(rectify,[],[f37]) ).
thf(f39,plain,
( ( ( woz13rule1 = $true )
| ( ( $true
= ( in @ sK18 @ ( powerset @ sK17 ) ) )
& ( $true
= ( in @ sK19 @ ( powerset @ sK17 ) ) )
& ( $true
= ( subset @ sK16 @ sK19 ) )
& ( $true
!= ( subset @ ( binintersect @ sK16 @ sK18 ) @ sK19 ) )
& ( $true
= ( in @ sK16 @ ( powerset @ sK17 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( ( subset @ X4 @ X7 )
!= $true )
| ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( woz13rule1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18),skolemize(X3,sK19)],[f38]) ).
thf(f40,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X6 @ X7 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( woz13rule2 != $true )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f46,plain,
woz13rule1 = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f47,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f48,plain,
( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f49,plain,
( $true
!= ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f50,plain,
( ( subset @ sK6 @ sK8 )
= $true ),
inference(cnf_transformation,[],[f30]) ).
thf(f51,plain,
( $true
= ( subset @ sK4 @ sK7 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f52,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f53,plain,
( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f54,plain,
( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f55,plain,
woz13rule2 = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f56,plain,
woz13rule3 = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( binintersectT_lem != $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( woz13rule3 != $true ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f68,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X7 )
!= $true )
| ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( woz13rule1 != $true )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f76,definition,
( spl20_1
<=> ( binintersectT_lem = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f80,definition,
( spl20_2
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f81,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f82,plain,
( ~ spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f60,f80,f76]) ).
thf(f83,plain,
spl20_1,
inference(avatar_split_clause,[],[f47,f76]) ).
thf(f85,definition,
( spl20_3
<=> ( woz13rule3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
thf(f94,definition,
( spl20_5
<=> ( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition]) ).
thf(f96,plain,
( ( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,plain,
spl20_5,
inference(avatar_split_clause,[],[f52,f94]) ).
thf(f99,definition,
( spl20_6
<=> ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
thf(f101,plain,
( ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f99]) ).
thf(f102,plain,
spl20_6,
inference(avatar_split_clause,[],[f53,f99]) ).
thf(f104,definition,
( spl20_7
<=> ( ( subset @ sK6 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f106,plain,
( ( ( subset @ sK6 @ sK8 )
= $true )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f107,plain,
spl20_7,
inference(avatar_split_clause,[],[f50,f104]) ).
thf(f114,definition,
( spl20_9
<=> ( woz13rule1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
thf(f117,plain,
spl20_9,
inference(avatar_split_clause,[],[f46,f114]) ).
thf(f124,definition,
( spl20_11
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition]) ).
thf(f125,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( subset @ X0 @ X3 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f126,plain,
( ~ spl20_3
| spl20_11 ),
inference(avatar_split_clause,[],[f67,f124,f85]) ).
thf(f143,definition,
( spl20_15
<=> ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
thf(f145,plain,
( ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) )
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f146,plain,
spl20_15,
inference(avatar_split_clause,[],[f48,f143]) ).
thf(f158,definition,
( spl20_18
<=> ( woz13rule2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_18])],[avatar_definition]) ).
thf(f161,plain,
spl20_18,
inference(avatar_split_clause,[],[f55,f158]) ).
thf(f178,definition,
( spl20_22
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( $true
!= ( subset @ X6 @ X7 ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_22])],[avatar_definition]) ).
thf(f179,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( subset @ X6 @ X7 ) ) )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f178]) ).
thf(f180,plain,
( ~ spl20_18
| spl20_22 ),
inference(avatar_split_clause,[],[f40,f178,f158]) ).
thf(f187,definition,
( spl20_24
<=> ( $true
= ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_24])],[avatar_definition]) ).
thf(f189,plain,
( ( $true
!= ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) ) )
| spl20_24 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f190,plain,
~ spl20_24,
inference(avatar_split_clause,[],[f49,f187]) ).
thf(f197,definition,
( spl20_26
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( subset @ X4 @ X7 )
!= $true )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_26])],[avatar_definition]) ).
thf(f198,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ ( binintersect @ X4 @ X6 ) @ X7 ) )
| ( ( subset @ X4 @ X7 )
!= $true )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) )
| ~ spl20_26 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f199,plain,
( spl20_26
| ~ spl20_9 ),
inference(avatar_split_clause,[],[f68,f114,f197]) ).
thf(f211,definition,
( spl20_29
<=> ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_29])],[avatar_definition]) ).
thf(f213,plain,
( ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f214,plain,
spl20_29,
inference(avatar_split_clause,[],[f54,f211]) ).
thf(f221,definition,
( spl20_31
<=> ( $true
= ( subset @ sK4 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_31])],[avatar_definition]) ).
thf(f223,plain,
( ( $true
= ( subset @ sK4 @ sK7 ) )
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f224,plain,
spl20_31,
inference(avatar_split_clause,[],[f51,f221]) ).
thf(f230,plain,
spl20_3,
inference(avatar_split_clause,[],[f56,f85]) ).
thf(f262,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
!= $true )
| ( $true
!= ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) ) ) )
| ~ spl20_11
| spl20_24 ),
inference(superposition,[],[f189,f125]) ).
thf(f263,plain,
( ! [X0: $i] :
( ( $true
!= ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
!= $true )
| ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) ) ) )
| ~ spl20_11
| spl20_24 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f265,definition,
( spl20_38
<=> ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_38])],[avatar_definition]) ).
thf(f267,plain,
( ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
!= $true )
| spl20_38 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f269,definition,
( spl20_39
<=> ! [X0: $i] :
( ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_39])],[avatar_definition]) ).
thf(f270,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl20_39 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,definition,
( spl20_40
<=> ( $true
= ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_40])],[avatar_definition]) ).
thf(f274,plain,
( ( $true
!= ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 ) )
| spl20_40 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,plain,
( ~ spl20_38
| spl20_39
| ~ spl20_40
| ~ spl20_11
| spl20_24 ),
inference(avatar_split_clause,[],[f263,f187,f124,f272,f269,f265]) ).
thf(f299,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ sK6 @ sK8 )
!= $true ) )
| ~ spl20_22
| spl20_38 ),
inference(superposition,[],[f267,f179]) ).
thf(f301,plain,
( ! [X0: $i] :
( ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ sK6 @ sK8 )
!= $true )
| ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) )
| ~ spl20_22
| spl20_38 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f303,definition,
( spl20_45
<=> ! [X0: $i] :
( ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_45])],[avatar_definition]) ).
thf(f304,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) )
| ~ spl20_45 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl20_7
| ~ spl20_22
| spl20_38 ),
inference(forward_subsumption_resolution,[],[f301,f106]) ).
thf(f307,plain,
( spl20_45
| ~ spl20_7
| ~ spl20_22
| spl20_38 ),
inference(avatar_split_clause,[],[f306,f265,f178,f104,f303]) ).
thf(f308,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( $true
!= ( subset @ sK4 @ sK7 ) ) )
| ~ spl20_26
| spl20_40 ),
inference(superposition,[],[f274,f198]) ).
thf(f311,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( $true
!= ( subset @ sK4 @ sK7 ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) )
| ~ spl20_26
| spl20_40 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f312,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) ) )
| ~ spl20_26
| ~ spl20_31
| spl20_40 ),
inference(forward_subsumption_resolution,[],[f311,f223]) ).
thf(f313,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_15
| ~ spl20_26
| ~ spl20_31
| spl20_40 ),
inference(superposition,[],[f312,f145]) ).
thf(f314,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_15
| ~ spl20_26
| ~ spl20_31
| spl20_40 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f315,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_6
| ~ spl20_15
| ~ spl20_26
| ~ spl20_31
| spl20_40 ),
inference(forward_subsumption_resolution,[],[f314,f101]) ).
thf(f316,plain,
( $false
| ~ spl20_6
| ~ spl20_15
| ~ spl20_26
| ~ spl20_29
| ~ spl20_31
| spl20_40 ),
inference(forward_subsumption_resolution,[],[f315,f213]) ).
thf(f317,plain,
( ~ spl20_6
| ~ spl20_15
| ~ spl20_26
| ~ spl20_29
| ~ spl20_31
| spl20_40 ),
inference(avatar_contradiction_clause,[],[f316]) ).
thf(f318,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) ) )
| ~ spl20_2
| ~ spl20_39 ),
inference(superposition,[],[f270,f81]) ).
thf(f319,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK7 @ ( powerset @ X0 ) ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK6 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) )
| ~ spl20_2
| ~ spl20_39 ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f320,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_2
| ~ spl20_15
| ~ spl20_39 ),
inference(superposition,[],[f319,f145]) ).
thf(f321,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ~ spl20_2
| ~ spl20_15
| ~ spl20_39 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f322,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ~ spl20_2
| ~ spl20_15
| ~ spl20_29
| ~ spl20_39 ),
inference(forward_subsumption_resolution,[],[f321,f213]) ).
thf(f323,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ~ spl20_2
| ~ spl20_6
| ~ spl20_15
| ~ spl20_29
| ~ spl20_39 ),
inference(forward_subsumption_resolution,[],[f322,f101]) ).
thf(f324,plain,
( $false
| ~ spl20_2
| ~ spl20_5
| ~ spl20_6
| ~ spl20_15
| ~ spl20_29
| ~ spl20_39 ),
inference(forward_subsumption_resolution,[],[f323,f96]) ).
thf(f325,plain,
( ~ spl20_2
| ~ spl20_5
| ~ spl20_6
| ~ spl20_15
| ~ spl20_29
| ~ spl20_39 ),
inference(avatar_contradiction_clause,[],[f324]) ).
thf(f331,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ( $true != $true )
| ~ spl20_6
| ~ spl20_45 ),
inference(superposition,[],[f304,f101]) ).
thf(f332,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_6
| ~ spl20_45 ),
inference(trivial_inequality_removal,[],[f331]) ).
thf(f333,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ sK5 ) ) )
| ~ spl20_5
| ~ spl20_6
| ~ spl20_45 ),
inference(forward_subsumption_resolution,[],[f332,f96]) ).
thf(f334,plain,
( $false
| ~ spl20_5
| ~ spl20_6
| ~ spl20_29
| ~ spl20_45 ),
inference(forward_subsumption_resolution,[],[f333,f213]) ).
thf(f335,plain,
( ~ spl20_5
| ~ spl20_6
| ~ spl20_29
| ~ spl20_45 ),
inference(avatar_contradiction_clause,[],[f334]) ).
cnf(s1,plain,
( ~ spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
spl20_1,
inference(sat_conversion,[],[f83]) ).
cnf(s4,plain,
spl20_5,
inference(sat_conversion,[],[f97]) ).
cnf(s5,plain,
spl20_6,
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
spl20_7,
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
spl20_9,
inference(sat_conversion,[],[f117]) ).
cnf(s10,plain,
( ~ spl20_3
| spl20_11 ),
inference(sat_conversion,[],[f126]) ).
cnf(s14,plain,
spl20_15,
inference(sat_conversion,[],[f146]) ).
cnf(s17,plain,
spl20_18,
inference(sat_conversion,[],[f161]) ).
cnf(s21,plain,
( ~ spl20_18
| spl20_22 ),
inference(sat_conversion,[],[f180]) ).
cnf(s23,plain,
~ spl20_24,
inference(sat_conversion,[],[f190]) ).
cnf(s25,plain,
( ~ spl20_9
| spl20_26 ),
inference(sat_conversion,[],[f199]) ).
cnf(s28,plain,
spl20_29,
inference(sat_conversion,[],[f214]) ).
cnf(s30,plain,
spl20_31,
inference(sat_conversion,[],[f224]) ).
cnf(s32,plain,
spl20_3,
inference(sat_conversion,[],[f230]) ).
cnf(s37,plain,
( ~ spl20_11
| spl20_24
| ~ spl20_38
| spl20_39
| ~ spl20_40 ),
inference(sat_conversion,[],[f275]) ).
cnf(s41,plain,
( ~ spl20_7
| ~ spl20_22
| spl20_38
| spl20_45 ),
inference(sat_conversion,[],[f307]) ).
cnf(s42,plain,
( ~ spl20_6
| ~ spl20_15
| ~ spl20_26
| ~ spl20_29
| ~ spl20_31
| spl20_40 ),
inference(sat_conversion,[],[f317]) ).
cnf(s43,plain,
( ~ spl20_2
| ~ spl20_5
| ~ spl20_6
| ~ spl20_15
| ~ spl20_29
| ~ spl20_39 ),
inference(sat_conversion,[],[f325]) ).
cnf(s45,plain,
( ~ spl20_5
| ~ spl20_6
| ~ spl20_29
| ~ spl20_45 ),
inference(sat_conversion,[],[f335]) ).
cnf(s46,plain,
spl20_22,
inference(rat,[],[s21,s17]) ).
cnf(s47,plain,
spl20_11,
inference(rat,[],[s10,s32]) ).
cnf(s48,plain,
spl20_26,
inference(rat,[],[s25,s8]) ).
cnf(s49,plain,
spl20_40,
inference(rat,[],[s42,s48,s30,s28,s14,s5]) ).
cnf(s50,plain,
~ spl20_45,
inference(rat,[],[s45,s5,s28,s4]) ).
cnf(s51,plain,
spl20_38,
inference(rat,[],[s41,s6,s46,s50]) ).
cnf(s52,plain,
spl20_39,
inference(rat,[],[s37,s49,s47,s23,s51]) ).
cnf(s53,plain,
~ spl20_2,
inference(rat,[],[s43,s4,s28,s14,s5,s52]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s1,s53,s2]) ).
thf(f336,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU762^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:25:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.32 % (153643)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (153650)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=335883758:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (153648)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2588943130:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (153649)lrs+10_16_si=on:nwc=1.5:random_seed=3587009776:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (153650)Instruction limit reached!
% 0.22/0.32 % (153650)------------------------------
% 0.22/0.32 % (153650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (153650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (153650)CaDiCaL version: 2.1.3
% 0.22/0.32 % (153650)Termination reason: Instruction limit
% 0.22/0.32 % (153650)Termination phase: Saturation
% 0.22/0.32 % (153650)Time elapsed: 0.002 s
% 0.22/0.32 % (153650)Peak memory usage: 11 MB
% 0.22/0.32 % (153650)Instructions burned: 4 (million)
% 0.22/0.32 % (153653)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1572453742:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (153649)Instruction limit reached!
% 0.22/0.32 % (153649)------------------------------
% 0.22/0.32 % (153649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (153649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (153649)CaDiCaL version: 2.1.3
% 0.22/0.32 % (153649)Termination reason: Instruction limit
% 0.22/0.32 % (153649)Termination phase: Saturation
% 0.22/0.32 % (153649)Time elapsed: 0.010 s
% 0.22/0.32 % (153649)Peak memory usage: 12 MB
% 0.22/0.32 % (153649)Instructions burned: 18 (million)
% 0.22/0.32 % (153651)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=760705822: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)
% 0.22/0.32 % (153654)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (153654)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
% 0.22/0.32 % (153651) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-153643-153651"...
% 0.22/0.32 % (153651)...printing done.
% 0.22/0.32 % (153652)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2132795940:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (153658)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3843658983:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (153651)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (153651)------------------------------
% 0.22/0.32 % (153651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (153651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (153651)CaDiCaL version: 2.1.3
% 0.22/0.32 % (153651)Termination reason: Refutation
% 0.22/0.32 % (153651)Time elapsed: 0.013 s
% 0.22/0.32 % (153651)Peak memory usage: 13 MB
% 0.22/0.32 % (153651)Instructions burned: 24 (million)
% 0.22/0.32 % (153643)Success in time 0.063 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------