%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU753^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 08:33:16 AM UTC 2026
% Result : Theorem 2.54s 0.64s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 10
% Syntax : Number of formulae : 198 ( 71 unt; 0 typ; 3 def)
% Number of atoms : 2551 ( 711 equ; 0 cnn)
% Maximal formula atoms : 16 ( 12 avg)
% Number of connectives : 6146 ( 31 ~; 498 |; 24 &;5130 @)
% ( 3 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 33 ( 29 usr; 15 con; 0-4 aty)
% ( 136 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 576 ( 0 sgn 409 !; 6 ?; 576 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_5,type,
binintersectT_lem: $o ).
thf(func_def_7,type,
binunionT_lem: $o ).
thf(func_def_8,type,
complementT_lem: $o ).
thf(func_def_9,type,
setextT: $o ).
thf(func_def_10,type,
demorgan1a: $o ).
thf(func_def_11,type,
demorgan1b: $o ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
sK3: $i > $i > $i > $i ).
thf(func_def_27,type,
sK4: $i > $i > $i > $i ).
thf(f1,axiom,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(f2,axiom,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(f3,axiom,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(f4,axiom,
( setextT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(f5,axiom,
( demorgan1a
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a) ).
thf(f6,axiom,
( demorgan1b
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).
thf(f7,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).
thf(f8,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( binintersectT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( binunionT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( setextT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( demorgan1a
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( demorgan1a
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( demorgan1b
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( demorgan1b
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
!= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
!= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) )
!= ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f24]) ).
thf(f26,plain,
( binintersectT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f27,plain,
( binunionT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f28,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( demorgan1a
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f31,plain,
( demorgan1b
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f33,plain,
binunionT_lem = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
complementT_lem = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f35,plain,
setextT = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f36,plain,
demorgan1a = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f37,plain,
demorgan1b = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f38,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f39,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f40,plain,
( ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) )
!= ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f32]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f33]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f34]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f29,f35]) ).
thf(f47,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f30,f36]) ).
thf(f48,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f37]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( binunion @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( binunion @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) )
=> ( in @ Y1 @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) )
=> ( in @ Y1 @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) )
=> ( in @ Y1 @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
=> ( in @ Y0 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
=> ( in @ Y0 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
=> ( in @ Y0 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( in @ X4 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $true
= ( ( in @ X4 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) ) )
=> ( in @ Y2 @ ( binunion @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) ) )
=> ( in @ Y2 @ ( binunion @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
=> ( in @ Y0 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
=> ( in @ Y0 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
=> ( in @ Y0 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $true
= ( ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f74,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ X1 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ X1 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ X1 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ X1 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
=> ( X1 = Y0 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) ) )
| ( $true
= ( X1 = X3 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( X1 = X3 ) ) ),
inference(sigma_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) ) ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f103,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f104,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f109,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ X1 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ X1 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ Y0 ) @ ( powerset @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ X3 ) @ ( powerset @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( binunion @ X1 @ X3 ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f117,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ X1 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ X1 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ Y0 ) @ ( powerset @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X4 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(constrained_superposition,[],[f72,f91]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X4 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $true
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X4 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(constrained_superposition,[],[f60,f96]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $true
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X4 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f215,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(constrained_superposition,[],[f72,f97]) ).
thf(f216,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $true
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X0 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(constrained_superposition,[],[f60,f98]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $true
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X0 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X0 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(constrained_superposition,[],[f72,f101]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X0 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f305,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f92,f152]) ).
thf(f317,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f305]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f435,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f100,f177]) ).
thf(f456,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f435]) ).
thf(f457,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X3 ) )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f456]) ).
thf(f646,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f90,f318]) ).
thf(f649,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f646]) ).
thf(f650,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f649]) ).
thf(f1024,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f102,f260]) ).
thf(f1072,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f1024]) ).
thf(f1073,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1072]) ).
thf(f1158,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(constrained_superposition,[],[f60,f216]) ).
thf(f1159,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(duplicate_literal_removal,[],[f1158]) ).
thf(f1160,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK3 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f1159]) ).
thf(f1518,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f235,f1160]) ).
thf(f1546,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1518]) ).
thf(f1547,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1546]) ).
thf(f1626,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) ) ),
inference(constrained_superposition,[],[f1073,f1547]) ).
thf(f1627,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1626]) ).
thf(f1628,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1627]) ).
thf(f1653,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) ) ),
inference(constrained_superposition,[],[f457,f1628]) ).
thf(f1659,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f1653]) ).
thf(f1660,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1659]) ).
thf(f1675,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f650,f1660]) ).
thf(f1681,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f1675]) ).
thf(f1682,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1681]) ).
thf(f1691,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) ) )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f115,f1682]) ).
thf(f1692,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1691]) ).
thf(f1697,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f107,f1692]) ).
thf(f1698,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) ) )
| ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1697]) ).
thf(f1737,plain,
( ( ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) )
!= ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f40,f1698]) ).
thf(f1871,plain,
( ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1737]) ).
thf(f1872,plain,
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f1871,f38]) ).
thf(f1873,plain,
( ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1872]) ).
thf(f1874,plain,
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f1873,f39]) ).
thf(f1875,plain,
( ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f1874]) ).
thf(f1877,definition,
( spl5_1
<=> ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f1879,plain,
( ( $false
= ( in @ ( binintersect @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f1877]) ).
thf(f1881,definition,
( spl5_2
<=> ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f1883,plain,
( ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f1881]) ).
thf(f1885,definition,
( spl5_3
<=> ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f1887,plain,
( ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f1885]) ).
thf(f1888,plain,
( spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f1875,f1885,f1881,f1877]) ).
thf(f1977,plain,
( ( $true = $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f107,f1883]) ).
thf(f1978,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f1977]) ).
thf(f2039,plain,
( ( $true = $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f1978,f39]) ).
thf(f2045,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f2039]) ).
thf(f2046,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f2045]) ).
thf(f2051,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f107,f1887]) ).
thf(f2052,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f2051]) ).
thf(f2153,plain,
( ( $true = $false )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f2052,f38]) ).
thf(f2159,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f2153]) ).
thf(f2160,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f2159]) ).
thf(f2163,plain,
( ( $true = $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f123,f1879]) ).
thf(f2164,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f2163]) ).
thf(f2167,plain,
( ( $true = $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f2164,f38]) ).
thf(f2168,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f2167]) ).
thf(f2171,plain,
( ( $true = $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f2168,f39]) ).
thf(f2177,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f2171]) ).
thf(f2178,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f2177]) ).
cnf(s1,plain,
( spl5_1
| spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f1888]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f2046]) ).
cnf(s5,plain,
~ spl5_3,
inference(sat_conversion,[],[f2160]) ).
cnf(s7,plain,
~ spl5_1,
inference(sat_conversion,[],[f2178]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s5,s3,s7]) ).
thf(f2179,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU753^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n026.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 14:24:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.54/0.63 % (669678)Will run a generic schedule for satisfiability detection.
% 2.54/0.63 % (669684)% WARNING: option uhcvi not known.
% 2.54/0.63 % (669683)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1083860508_2999 on theBenchmark for (2999ds/0Mi)
% 2.54/0.63 % (669687)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3177944878:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.54/0.63 % (669684)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=746318150:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.54/0.63 % (669685)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3372866886:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.54/0.63 % (669686)dis+10_1_sil=32000:sp=arity:random_seed=2497601549:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.54/0.63 % (669687)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.63 % (669684)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.63 % (669684)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.54/0.63 % Exception at run slice level
% 2.54/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.63 % (669689)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3739318207:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.54/0.63 % (669688)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2847764857:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.54/0.63 % (669695)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3418080342:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.54/0.63 % Exception at run slice level
% 2.54/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.63 % (669699)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3138523715:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.54/0.63 % (669686)Instruction limit reached!
% 2.54/0.63 % (669686)------------------------------
% 2.54/0.63 % (669686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.63 % (669686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.63 % (669686)CaDiCaL version: 2.1.3
% 2.54/0.63 % (669686)Termination reason: Instruction limit
% 2.54/0.63 % (669686)Termination phase: Saturation
% 2.54/0.63 % (669686)Time elapsed: 0.050 s
% 2.54/0.63 % (669686)Peak memory usage: 12 MB
% 2.54/0.63 % (669686)Instructions burned: 103 (million)
% 2.54/0.63 % (669687)Instruction limit reached!
% 2.54/0.63 % (669687)------------------------------
% 2.54/0.63 % (669687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.63 % (669687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.63 % (669687)CaDiCaL version: 2.1.3
% 2.54/0.63 % (669687)Termination reason: Instruction limit
% 2.54/0.63 % (669687)Termination phase: Saturation
% 2.54/0.63 % (669687)Time elapsed: 0.058 s
% 2.54/0.63 % (669687)Peak memory usage: 12 MB
% 2.54/0.63 % (669687)Instructions burned: 117 (million)
% 2.54/0.63 % (669701)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3557896603:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.54/0.63 % (669701)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.63 % (669701)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.54/0.63 % (669702)ott-21_1_sil=16000:fs=off:random_seed=403413355:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.54/0.63 % (669688)Instruction limit reached!
% 2.54/0.63 % (669688)------------------------------
% 2.54/0.63 % (669688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.63 % (669688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.63 % (669688)CaDiCaL version: 2.1.3
% 2.54/0.63 % (669688)Termination reason: Instruction limit
% 2.54/0.63 % (669688)Termination phase: Saturation
% 2.54/0.63 % (669688)Time elapsed: 0.067 s
% 2.54/0.63 % (669688)Peak memory usage: 12 MB
% 2.54/0.63 % (669688)Instructions burned: 133 (million)
% 2.54/0.63 % (669689)Instruction limit reached!
% 2.54/0.63 % (669689)------------------------------
% 2.54/0.63 % (669689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.63 % (669689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.63 % (669689)CaDiCaL version: 2.1.3
% 2.54/0.63 % (669689)Termination reason: Instruction limit
% 2.54/0.63 % (669689)Termination phase: Saturation
% 2.54/0.63 % (669689)Time elapsed: 0.079 s
% 2.54/0.63 % (669689)Peak memory usage: 13 MB
% 2.54/0.63 % (669689)Instructions burned: 161 (million)
% 2.54/0.63 % (669705)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4240677596:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.54/0.63 % (669699)Instruction limit reached!
% 2.54/0.63 % (669699)------------------------------
% 2.54/0.63 % (669699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.63 % (669699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.63 % (669699)CaDiCaL version: 2.1.3
% 2.54/0.63 % (669699)Termination reason: Instruction limit
% 2.54/0.63 % (669699)Termination phase: Saturation
% 2.54/0.63 % (669699)Time elapsed: 0.063 s
% 2.54/0.63 % (669699)Peak memory usage: 12 MB
% 2.54/0.63 % (669699)Instructions burned: 132 (million)
% 2.54/0.63 % (669706)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=583950544:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.54/0.63 % Exception at run slice level
% 2.54/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.63 % (669708)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=921371570:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.54/0.63 % (669710)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=617835125:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.54/0.63 % Exception at run slice level
% 2.54/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.63 % (669713)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=631735327:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.54/0.63 % (669713)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.63 % (669702)Instruction limit reached!
% 2.54/0.63 % (669702)------------------------------
% 2.54/0.63 % (669702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.63 % (669702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.63 % (669702)CaDiCaL version: 2.1.3
% 2.54/0.63 % (669702)Termination reason: Instruction limit
% 2.54/0.63 % (669702)Termination phase: Saturation
% 2.54/0.63 % (669702)Time elapsed: 0.088 s
% 2.54/0.63 % (669702)Peak memory usage: 12 MB
% 2.54/0.63 % (669702)Instructions burned: 181 (million)
% 2.54/0.63 % (669715)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2914403362:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.54/0.63 % (669715)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.63 % (669684) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-669678-669684"...
% 2.54/0.63 % (669705)Instruction limit reached!
% 2.54/0.63 % (669705)------------------------------
% 2.54/0.63 % (669705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.64 % (669705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.64 % (669705)CaDiCaL version: 2.1.3
% 2.54/0.64 % (669705)Termination reason: Instruction limit
% 2.54/0.64 % (669705)Termination phase: Saturation
% 2.54/0.64 % (669705)Time elapsed: 0.250 s
% 2.54/0.64 % (669705)Peak memory usage: 13 MB
% 2.54/0.64 % (669705)Instructions burned: 477 (million)
% 2.54/0.64 % (669684)...printing done.
% 2.54/0.64 % (669684)Refutation found. Thanks to Tanya!
% 2.54/0.64 % SZS status Theorem for theBenchmark
% 2.54/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.64 % (669684)------------------------------
% 2.54/0.64 % (669684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.64 % (669684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.64 % (669684)CaDiCaL version: 2.1.3
% 2.54/0.64 % (669684)Termination reason: Refutation
% 2.54/0.64 % (669684)Time elapsed: 0.358 s
% 2.54/0.64 % (669684)Peak memory usage: 14 MB
% 2.54/0.64 % (669684)Instructions burned: 771 (million)
% 2.54/0.64 % (669678)Success in time 0.391 s
% 2.54/0.64 % Vampire exiting
%------------------------------------------------------------------------------