%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU743^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:05 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 46
% Syntax : Number of formulae : 320 ( 95 unt; 0 typ; 41 def)
% Number of atoms : 2798 ( 541 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 3761 ( 352 ~; 634 |; 21 &;2343 @)
% ( 27 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 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 : 67 ( 63 usr; 52 con; 0-4 aty)
% ( 139 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 402 ( 0 sgn 240 !; 8 ?; 402 :)
% 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,
binintersectT_lem: $o ).
thf(func_def_6,type,
binunionT_lem: $o ).
thf(func_def_7,type,
powersetTI1: $o ).
thf(func_def_8,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vIMP: $o > $o > $o ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sF4: $o ).
thf(func_def_25,type,
sF6: $o ).
thf(func_def_26,type,
sF7: $o ).
thf(func_def_32,type,
sF13: $o ).
thf(func_def_33,type,
sF14: $o ).
thf(func_def_34,type,
sF15: $o ).
thf(func_def_35,type,
sF16: $o ).
thf(func_def_36,type,
sF17: $o ).
thf(func_def_48,type,
sK29: $i > $i > $i > $i ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binintersectT_lem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(f2,axiom,
( binunionT_lem
= ( ! [X1: $i,X0: $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,
( powersetTI1
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(f4,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) )
= inIntersectImpInIntersectUnions ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(f5,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(f6,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( powersetTI1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X0 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
( powersetTI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) )
= inIntersectImpInIntersectUnions ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
( inIntersectImpInIntersectUnions
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binintersectT_lem ),
inference(rectify,[],[f1]) ).
thf(f12,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,[],[f11]) ).
thf(f13,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetTI1 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( binunionT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) ) )
& ( inIntersectImpInIntersectUnions = $true )
& ( powersetTI1 = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f18,plain,
( ( binunionT_lem = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) ) )
& ( inIntersectImpInIntersectUnions = $true )
& ( powersetTI1 = $true )
& ( binintersectT_lem = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( binunionT_lem = $true )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
& ( inIntersectImpInIntersectUnions = $true )
& ( powersetTI1 = $true )
& ( binintersectT_lem = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f18]) ).
thf(f20,plain,
( binunionT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f22,plain,
powersetTI1 = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f23,plain,
inIntersectImpInIntersectUnions = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f25,plain,
( $true
!= ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
binunionT_lem = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f29,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,[],[f12]) ).
thf(f30,plain,
( inIntersectImpInIntersectUnions
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f31,plain,
( powersetTI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f20,f28]) ).
thf(f35,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f29,f21]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f30,f23]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f31,f22]) ).
thf(f38,definition,
( sF4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) )
= sF4 ),
inference(reorient_equations,[],[f38]) ).
thf(f40,plain,
$true = sF4,
inference(definition_folding,[],[f34,f39]) ).
thf(f41,definition,
( sF5
= ( powerset @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f42,plain,
( ( powerset @ sK1 )
= sF5 ),
inference(reorient_equations,[],[f41]) ).
thf(f43,definition,
( sF6
= ( in @ sK0 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f44,plain,
( ( in @ sK0 @ sF5 )
= sF6 ),
inference(reorient_equations,[],[f43]) ).
thf(f45,plain,
$true = sF6,
inference(definition_folding,[],[f27,f44,f42]) ).
thf(f46,definition,
( sF7
= ( in @ sK2 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f47,plain,
( ( in @ sK2 @ sF5 )
= sF7 ),
inference(reorient_equations,[],[f46]) ).
thf(f48,plain,
$true = sF7,
inference(definition_folding,[],[f26,f47,f42]) ).
thf(f49,definition,
( sF8
= ( binintersect @ sK0 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f50,plain,
( ( binintersect @ sK0 @ sK2 )
= sF8 ),
inference(reorient_equations,[],[f49]) ).
thf(f51,definition,
( sF9
= ( binunion @ sK0 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f52,plain,
( ( binunion @ sK0 @ sK3 )
= sF9 ),
inference(reorient_equations,[],[f51]) ).
thf(f53,definition,
( sF10
= ( binunion @ sK2 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f54,plain,
( ( binunion @ sK2 @ sK3 )
= sF10 ),
inference(reorient_equations,[],[f53]) ).
thf(f55,definition,
( sF11
= ( binintersect @ sF9 @ sF10 ) ),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
thf(f56,definition,
( sF12
= ( powerset @ sF11 ) ),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
thf(f57,definition,
( sF13
= ( in @ sF8 @ sF12 ) ),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
thf(f58,plain,
$true != sF13,
inference(definition_folding,[],[f25,f57,f56,f55,f54,f52,f50]) ).
thf(f59,definition,
( sF14
= ( in @ sK3 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
thf(f60,plain,
$true = sF14,
inference(definition_folding,[],[f24,f59,f42]) ).
thf(f61,definition,
( sF15
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
thf(f62,plain,
$true = sF15,
inference(definition_folding,[],[f35,f61]) ).
thf(f63,definition,
( sF16
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
thf(f64,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= sF16 ),
inference(reorient_equations,[],[f63]) ).
thf(f65,plain,
$true = sF16,
inference(definition_folding,[],[f36,f64]) ).
thf(f66,definition,
( sF17
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
thf(f67,plain,
$true = sF17,
inference(definition_folding,[],[f37,f66]) ).
thf(f68,plain,
( ( $true = sF13 )
| ( $false
= ( in @ sF8 @ sF12 ) ) ),
inference(iff_proxy_clausification,[],[f57]) ).
thf(f70,plain,
( ( $true
= ( in @ sK2 @ sF5 ) )
| ( $false = sF7 ) ),
inference(iff_proxy_clausification,[],[f47]) ).
thf(f73,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binintersect @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) )
| ( sF15 = $false ) ),
inference(iff_proxy_clausification,[],[f61]) ).
thf(f74,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 ) )
| ( sF15 = $false ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X1: $i] :
( ( sF15 = $false )
| ( $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,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( sF15 = $false )
| ( $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,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) )
| ( sF15 = $false ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( sF15 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF15 = $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ Y0 ) @ ( powerset @ X2 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF15 = $false )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF15 = $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f92,plain,
( ( sF6 = $false )
| ( $true
= ( in @ sK0 @ sF5 ) ) ),
inference(iff_proxy_clausification,[],[f44]) ).
thf(f94,plain,
( ( $false = sF16 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f64]) ).
thf(f116,plain,
! [X1: $i] :
( ( $false = sF16 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y4 @ ( binintersect @ Y1 @ Y2 ) )
=> ( in @ Y4 @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f117,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( in @ Y3 @ ( binintersect @ Y0 @ Y1 ) )
=> ( in @ Y3 @ ( binintersect @ ( binunion @ Y0 @ Y2 ) @ ( binunion @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false = sF16 ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( $false = sF16 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( in @ Y3 @ ( binintersect @ Y0 @ Y1 ) )
=> ( in @ Y3 @ ( binintersect @ ( binunion @ Y0 @ Y2 ) @ ( binunion @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( $false = sF16 )
| ( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ ( binintersect @ X2 @ Y0 ) )
=> ( in @ Y2 @ ( binintersect @ ( binunion @ X2 @ Y1 ) @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ ( binintersect @ X2 @ Y0 ) )
=> ( in @ Y2 @ ( binintersect @ ( binunion @ X2 @ Y1 ) @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $false = sF16 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ ( binintersect @ X2 @ Y0 ) )
=> ( in @ Y2 @ ( binintersect @ ( binunion @ X2 @ Y1 ) @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ Y1 @ ( binintersect @ ( binunion @ X2 @ Y0 ) @ ( binunion @ X3 @ Y0 ) ) ) ) ) ) ) ) ) )
| ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF16 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ Y1 @ ( binintersect @ ( binunion @ X2 @ Y0 ) @ ( binunion @ X3 @ Y0 ) ) ) ) ) ) ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ Y1 @ ( binintersect @ ( binunion @ X2 @ Y0 ) @ ( binunion @ X3 @ Y0 ) ) ) ) ) ) )
@ X4 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ Y0 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ Y0 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) )
| ( ( in @ X4 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ Y0 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) )
@ X5 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X4 @ ( powerset @ X1 ) )
= $false )
| ( $false = sF16 ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $false )
| ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X5 @ X1 )
= $false )
| ( $false = sF16 )
| ( $true
= ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
=> ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X1 )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) )
= $true )
| ( $false = sF16 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $false
= ( in @ X5 @ ( binintersect @ X2 @ X3 ) ) )
| ( ( in @ X4 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( sF4 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f143,plain,
! [X1: $i] :
( ( sF4 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f144,plain,
! [X1: $i] :
( ( sF4 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ Y0 @ Y1 ) @ ( powerset @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ Y0 @ Y1 ) @ ( powerset @ X1 ) ) ) ) )
@ X2 ) )
| ( sF4 = $false ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X1: $i] :
( ( sF4 = $false )
| ( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ Y0 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ Y0 ) @ ( powerset @ X1 ) ) ) ) )
| ( sF4 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ Y0 ) @ ( powerset @ X1 ) ) )
@ X3 ) )
| ( sF4 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( sF4 = $false ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( sF4 = $false ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f152,plain,
( ( sF17 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f66]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) )
@ X1 ) )
| ( sF17 = $false ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ) ) )
| ( sF17 = $false ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) )
@ X2 ) )
| ( sF17 = $false ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( sF17 = $false )
| ( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( in @ X2 @ ( powerset @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( sF17 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( in @ X2 @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( in @ X2 @ ( powerset @ Y0 ) ) ) )
@ X3 ) )
| ( sF17 = $false ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( in @ X2 @ ( powerset @ X3 ) ) ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( sF17 = $false ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( in @ X2 @ ( powerset @ X3 ) ) ) )
| ( sF17 = $false ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( sF17 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK29 @ X3 @ X1 @ X2 ) )
= $false )
| ( sF17 = $false ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X3 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( sF17 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( sF17 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( sF17 = $false )
| ( $true
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( sF17 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( sF17 = $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f185,plain,
( ( sF14 = $false )
| ( $true
= ( in @ sK3 @ sF5 ) ) ),
inference(iff_proxy_clausification,[],[f59]) ).
thf(f191,definition,
( spl33_2
<=> ( $true
= ( in @ sF8 @ sF12 ) ) ),
introduced(definition,[new_symbols(definition,[spl33_2])],[avatar_definition]) ).
thf(f192,plain,
( ( $true
!= ( in @ sF8 @ sF12 ) )
| spl33_2 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f193,plain,
( ( $true
= ( in @ sF8 @ sF12 ) )
| ~ spl33_2 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f196,definition,
( spl33_3
<=> ( $false
= ( in @ sF8 @ sF12 ) ) ),
introduced(definition,[new_symbols(definition,[spl33_3])],[avatar_definition]) ).
thf(f198,plain,
( ( $false
= ( in @ sF8 @ sF12 ) )
| ~ spl33_3 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f200,definition,
( spl33_4
<=> ( $true = sF13 ) ),
introduced(definition,[new_symbols(definition,[spl33_4])],[avatar_definition]) ).
thf(f203,plain,
( spl33_3
| spl33_4 ),
inference(avatar_split_clause,[],[f68,f200,f196]) ).
thf(f209,definition,
( spl33_6
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl33_6])],[avatar_definition]) ).
thf(f211,plain,
( ( $true = sF7 )
| ~ spl33_6 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f214,definition,
( spl33_7
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl33_7])],[avatar_definition]) ).
thf(f216,plain,
( ( $false = sF7 )
| ~ spl33_7 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f218,definition,
( spl33_8
<=> ( $true
= ( in @ sK2 @ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl33_8])],[avatar_definition]) ).
thf(f220,plain,
( ( $true
= ( in @ sK2 @ sF5 ) )
| ~ spl33_8 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
( spl33_7
| spl33_8 ),
inference(avatar_split_clause,[],[f70,f218,f214]) ).
thf(f222,plain,
spl33_6,
inference(avatar_split_clause,[],[f48,f209]) ).
thf(f223,plain,
~ spl33_4,
inference(avatar_split_clause,[],[f58,f200]) ).
thf(f225,definition,
( spl33_9
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl33_9])],[avatar_definition]) ).
thf(f226,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) )
| ~ spl33_9 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f228,definition,
( spl33_10
<=> ( sF15 = $false ) ),
introduced(definition,[new_symbols(definition,[spl33_10])],[avatar_definition]) ).
thf(f230,plain,
( ( sF15 = $false )
| ~ spl33_10 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl33_9
| spl33_10 ),
inference(avatar_split_clause,[],[f81,f228,f225]) ).
thf(f233,definition,
( spl33_11
<=> ( $true = sF15 ) ),
introduced(definition,[new_symbols(definition,[spl33_11])],[avatar_definition]) ).
thf(f235,plain,
( ( $true = sF15 )
| ~ spl33_11 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f252,definition,
( spl33_15
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl33_15])],[avatar_definition]) ).
thf(f254,plain,
( ( $true = sF6 )
| ~ spl33_15 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f261,definition,
( spl33_17
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(definition,[spl33_17])],[avatar_definition]) ).
thf(f263,plain,
( ( sF6 = $false )
| ~ spl33_17 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f265,definition,
( spl33_18
<=> ( $true
= ( in @ sK0 @ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl33_18])],[avatar_definition]) ).
thf(f267,plain,
( ( $true
= ( in @ sK0 @ sF5 ) )
| ~ spl33_18 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl33_17
| spl33_18 ),
inference(avatar_split_clause,[],[f92,f265,f261]) ).
thf(f269,plain,
spl33_15,
inference(avatar_split_clause,[],[f45,f252]) ).
thf(f271,definition,
( spl33_19
<=> ( $true = sF16 ) ),
introduced(definition,[new_symbols(definition,[spl33_19])],[avatar_definition]) ).
thf(f273,plain,
( ( $true = sF16 )
| ~ spl33_19 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f305,definition,
( spl33_26
<=> ! [X2: $i,X3: $i,X4: $i,X5: $i,X1: $i] :
( ( ( in @ X5 @ X1 )
= $false )
| ( ( in @ X4 @ ( powerset @ X1 ) )
= $false )
| ( $false
= ( in @ X5 @ ( binintersect @ X2 @ X3 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl33_26])],[avatar_definition]) ).
thf(f306,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X5 @ X1 )
= $false )
| ( $false
= ( in @ X5 @ ( binintersect @ X2 @ X3 ) ) )
| ( ( in @ X4 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl33_26 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f308,definition,
( spl33_27
<=> ( $false = sF16 ) ),
introduced(definition,[new_symbols(definition,[spl33_27])],[avatar_definition]) ).
thf(f310,plain,
( ( $false = sF16 )
| ~ spl33_27 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f311,plain,
( spl33_26
| spl33_27 ),
inference(avatar_split_clause,[],[f130,f308,f305]) ).
thf(f313,definition,
( spl33_28
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl33_28])],[avatar_definition]) ).
thf(f315,plain,
( ( $true = sF4 )
| ~ spl33_28 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f332,definition,
( spl33_32
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl33_32])],[avatar_definition]) ).
thf(f334,plain,
( ( sF4 = $false )
| ~ spl33_32 ),
inference(avatar_component_clause,[],[f332]) ).
thf(f336,definition,
( spl33_33
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl33_33])],[avatar_definition]) ).
thf(f337,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl33_33 ),
inference(avatar_component_clause,[],[f336]) ).
thf(f338,plain,
( spl33_32
| spl33_33 ),
inference(avatar_split_clause,[],[f150,f336,f332]) ).
thf(f339,plain,
spl33_28,
inference(avatar_split_clause,[],[f40,f313]) ).
thf(f341,definition,
( spl33_34
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl33_34])],[avatar_definition]) ).
thf(f342,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) )
| ~ spl33_34 ),
inference(avatar_component_clause,[],[f341]) ).
thf(f344,definition,
( spl33_35
<=> ( sF17 = $false ) ),
introduced(definition,[new_symbols(definition,[spl33_35])],[avatar_definition]) ).
thf(f346,plain,
( ( sF17 = $false )
| ~ spl33_35 ),
inference(avatar_component_clause,[],[f344]) ).
thf(f347,plain,
( spl33_34
| spl33_35 ),
inference(avatar_split_clause,[],[f165,f344,f341]) ).
thf(f349,definition,
( spl33_36
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl33_36])],[avatar_definition]) ).
thf(f350,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) )
| ~ spl33_36 ),
inference(avatar_component_clause,[],[f349]) ).
thf(f351,plain,
( spl33_35
| spl33_36 ),
inference(avatar_split_clause,[],[f167,f349,f344]) ).
thf(f353,definition,
( spl33_37
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl33_37])],[avatar_definition]) ).
thf(f354,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK29 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl33_37 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f355,plain,
( spl33_35
| spl33_37 ),
inference(avatar_split_clause,[],[f166,f353,f344]) ).
thf(f361,definition,
( spl33_39
<=> ( $true = sF17 ) ),
introduced(definition,[new_symbols(definition,[spl33_39])],[avatar_definition]) ).
thf(f363,plain,
( ( $true = sF17 )
| ~ spl33_39 ),
inference(avatar_component_clause,[],[f361]) ).
thf(f380,definition,
( spl33_43
<=> ( $true
= ( in @ sK3 @ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl33_43])],[avatar_definition]) ).
thf(f382,plain,
( ( $true
= ( in @ sK3 @ sF5 ) )
| ~ spl33_43 ),
inference(avatar_component_clause,[],[f380]) ).
thf(f384,definition,
( spl33_44
<=> ( sF14 = $false ) ),
introduced(definition,[new_symbols(definition,[spl33_44])],[avatar_definition]) ).
thf(f386,plain,
( ( sF14 = $false )
| ~ spl33_44 ),
inference(avatar_component_clause,[],[f384]) ).
thf(f387,plain,
( spl33_43
| spl33_44 ),
inference(avatar_split_clause,[],[f185,f384,f380]) ).
thf(f393,definition,
( spl33_46
<=> ( $true = sF14 ) ),
introduced(definition,[new_symbols(definition,[spl33_46])],[avatar_definition]) ).
thf(f395,plain,
( ( $true = sF14 )
| ~ spl33_46 ),
inference(avatar_component_clause,[],[f393]) ).
thf(f397,plain,
spl33_46,
inference(avatar_split_clause,[],[f60,f393]) ).
thf(f398,plain,
spl33_11,
inference(avatar_split_clause,[],[f62,f233]) ).
thf(f399,plain,
spl33_19,
inference(avatar_split_clause,[],[f65,f271]) ).
thf(f400,plain,
spl33_39,
inference(avatar_split_clause,[],[f67,f361]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl33_6
| ~ spl33_7 ),
inference(forward_demodulation,[],[f216,f211]) ).
thf(f402,plain,
( $false
| ~ spl33_6
| ~ spl33_7 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f403,plain,
( ~ spl33_6
| ~ spl33_7 ),
inference(avatar_contradiction_clause,[],[f402]) ).
thf(f405,plain,
( ( $true = $false )
| ~ spl33_15
| ~ spl33_17 ),
inference(forward_demodulation,[],[f263,f254]) ).
thf(f406,plain,
( $false
| ~ spl33_15
| ~ spl33_17 ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f407,plain,
( ~ spl33_15
| ~ spl33_17 ),
inference(avatar_contradiction_clause,[],[f406]) ).
thf(f424,plain,
( ( $true = $false )
| ~ spl33_28
| ~ spl33_32 ),
inference(forward_demodulation,[],[f315,f334]) ).
thf(f425,plain,
( $false
| ~ spl33_28
| ~ spl33_32 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f426,plain,
( ~ spl33_28
| ~ spl33_32 ),
inference(avatar_contradiction_clause,[],[f425]) ).
thf(f431,plain,
( ( $true = $false )
| ~ spl33_35
| ~ spl33_39 ),
inference(forward_demodulation,[],[f363,f346]) ).
thf(f432,plain,
( $false
| ~ spl33_35
| ~ spl33_39 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f433,plain,
( ~ spl33_35
| ~ spl33_39 ),
inference(avatar_contradiction_clause,[],[f432]) ).
thf(f436,plain,
( ( $true = $false )
| ~ spl33_2
| ~ spl33_3 ),
inference(forward_demodulation,[],[f198,f193]) ).
thf(f437,plain,
( $false
| ~ spl33_2
| ~ spl33_3 ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f438,plain,
( ~ spl33_2
| ~ spl33_3 ),
inference(avatar_contradiction_clause,[],[f437]) ).
thf(f448,plain,
( ( $true = $false )
| ~ spl33_44
| ~ spl33_46 ),
inference(forward_demodulation,[],[f386,f395]) ).
thf(f449,plain,
( $false
| ~ spl33_44
| ~ spl33_46 ),
inference(trivial_inequality_removal,[],[f448]) ).
thf(f450,plain,
( ~ spl33_44
| ~ spl33_46 ),
inference(avatar_contradiction_clause,[],[f449]) ).
thf(f453,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X0 @ X1 ) @ sF5 ) )
| ( $false
= ( in @ X1 @ sF5 ) )
| ( $false
= ( in @ X0 @ sF5 ) ) )
| ~ spl33_9 ),
inference(constrained_superposition,[],[f226,f42]) ).
thf(f456,plain,
( ! [X0: $i] :
( ( $true
= ( in @ sF11 @ ( powerset @ X0 ) ) )
| ( ( in @ sF10 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sF9 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl33_9 ),
inference(constrained_superposition,[],[f226,f55]) ).
thf(f457,plain,
( ( $false
= ( in @ sK2 @ sF5 ) )
| ( ( in @ sF8 @ sF5 )
= $true )
| ( ( in @ sK0 @ sF5 )
= $false )
| ~ spl33_9 ),
inference(constrained_superposition,[],[f453,f50]) ).
thf(f460,definition,
( spl33_47
<=> ( $true
= ( in @ sF11 @ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl33_47])],[avatar_definition]) ).
thf(f462,plain,
( ( $true
= ( in @ sF11 @ sF5 ) )
| ~ spl33_47 ),
inference(avatar_component_clause,[],[f460]) ).
thf(f472,plain,
( ( ( in @ sK0 @ sF5 )
= $false )
| ( $true = $false )
| ( ( in @ sF8 @ sF5 )
= $true )
| ~ spl33_8
| ~ spl33_9 ),
inference(forward_demodulation,[],[f457,f220]) ).
thf(f473,plain,
( ( ( in @ sF8 @ sF5 )
= $true )
| ( ( in @ sK0 @ sF5 )
= $false )
| ~ spl33_8
| ~ spl33_9 ),
inference(trivial_inequality_removal,[],[f472]) ).
thf(f474,plain,
( ( $true = $false )
| ( ( in @ sF8 @ sF5 )
= $true )
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18 ),
inference(forward_demodulation,[],[f473,f267]) ).
thf(f475,plain,
( ( ( in @ sF8 @ sF5 )
= $true )
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18 ),
inference(trivial_inequality_removal,[],[f474]) ).
thf(f505,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( binunion @ X0 @ X1 ) @ sF5 ) )
| ( $false
= ( in @ X0 @ sF5 ) )
| ( $false
= ( in @ X1 @ sF5 ) ) )
| ~ spl33_33 ),
inference(constrained_superposition,[],[f337,f42]) ).
thf(f509,plain,
( ( $true
= ( in @ sF9 @ sF5 ) )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ( ( in @ sK0 @ sF5 )
= $false )
| ~ spl33_33 ),
inference(constrained_superposition,[],[f505,f52]) ).
thf(f510,plain,
( ( $false
= ( in @ sK2 @ sF5 ) )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ( $true
= ( in @ sF10 @ sF5 ) )
| ~ spl33_33 ),
inference(constrained_superposition,[],[f505,f54]) ).
thf(f511,plain,
( ( $true
= ( in @ sF9 @ sF5 ) )
| ( ( in @ sK0 @ sF5 )
= $false )
| ( $true = $false )
| ~ spl33_33
| ~ spl33_43 ),
inference(forward_demodulation,[],[f509,f382]) ).
thf(f512,plain,
( ( $true
= ( in @ sF9 @ sF5 ) )
| ( ( in @ sK0 @ sF5 )
= $false )
| ~ spl33_33
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f511]) ).
thf(f513,plain,
( ( $true
= ( in @ sF10 @ sF5 ) )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ( $true = $false )
| ~ spl33_8
| ~ spl33_33 ),
inference(forward_demodulation,[],[f510,f220]) ).
thf(f514,plain,
( ( $true
= ( in @ sF10 @ sF5 ) )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ~ spl33_8
| ~ spl33_33 ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f515,plain,
( ( $true
= ( in @ sF9 @ sF5 ) )
| ( $true = $false )
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(forward_demodulation,[],[f512,f267]) ).
thf(f516,plain,
( ( $true
= ( in @ sF9 @ sF5 ) )
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f515]) ).
thf(f517,plain,
( ( $true
= ( in @ sF10 @ sF5 ) )
| ( $true = $false )
| ~ spl33_8
| ~ spl33_33
| ~ spl33_43 ),
inference(forward_demodulation,[],[f514,f382]) ).
thf(f518,plain,
( ( $true
= ( in @ sF10 @ sF5 ) )
| ~ spl33_8
| ~ spl33_33
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f517]) ).
thf(f545,plain,
( ( $false
= ( in @ sF9 @ sF5 ) )
| ( ( in @ sF10 @ sF5 )
= $false )
| ( $true
= ( in @ sF11 @ sF5 ) )
| ~ spl33_9 ),
inference(constrained_superposition,[],[f456,f42]) ).
thf(f628,plain,
( ( $true = $false )
| ~ spl33_19
| ~ spl33_27 ),
inference(forward_demodulation,[],[f310,f273]) ).
thf(f629,plain,
( $false
| ~ spl33_19
| ~ spl33_27 ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f630,plain,
( ~ spl33_19
| ~ spl33_27 ),
inference(avatar_contradiction_clause,[],[f629]) ).
thf(f660,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ ( binunion @ X1 @ sK3 ) @ sF10 ) ) )
| ( ( in @ sK3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X0 @ X2 )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X0 @ ( binintersect @ X1 @ sK2 ) )
= $false )
| ( $false
= ( in @ sK2 @ ( powerset @ X2 ) ) ) )
| ~ spl33_26 ),
inference(constrained_superposition,[],[f306,f54]) ).
thf(f693,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ sK2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( ( in @ sK3 @ ( powerset @ X1 ) )
= $false )
| ( $false
= ( in @ X0 @ ( binintersect @ sK0 @ sK2 ) ) )
| ( $false
= ( in @ sK0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ X0 @ ( binintersect @ sF9 @ sF10 ) ) ) )
| ~ spl33_26 ),
inference(constrained_superposition,[],[f660,f52]) ).
thf(f701,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ sK0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ sF8 ) )
| ( ( in @ sK3 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( in @ X0 @ ( binintersect @ sF9 @ sF10 ) ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X1 ) ) ) )
| ~ spl33_26 ),
inference(forward_demodulation,[],[f693,f50]) ).
thf(f702,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ sK2 @ ( powerset @ X1 ) ) )
| ( ( in @ sK3 @ ( powerset @ X1 ) )
= $false )
| ( $false
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ sF11 ) )
| ( $false
= ( in @ sK0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ sF8 ) ) )
| ~ spl33_26 ),
inference(forward_demodulation,[],[f701,f55]) ).
thf(f703,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK2 @ sF5 ) )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ( ( in @ sK0 @ sF5 )
= $false )
| ( $true
= ( in @ X0 @ sF11 ) )
| ( $false
= ( in @ X0 @ sF8 ) )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl33_26 ),
inference(constrained_superposition,[],[f702,f42]) ).
thf(f711,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( in @ X0 @ sK1 )
= $false )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ( $true
= ( in @ X0 @ sF11 ) )
| ( $false
= ( in @ X0 @ sF8 ) )
| ( ( in @ sK0 @ sF5 )
= $false ) )
| ~ spl33_8
| ~ spl33_26 ),
inference(forward_demodulation,[],[f703,f220]) ).
thf(f712,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sF11 ) )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ sK0 @ sF5 )
= $false )
| ( $false
= ( in @ X0 @ sF8 ) )
| ( $false
= ( in @ sK3 @ sF5 ) ) )
| ~ spl33_8
| ~ spl33_26 ),
inference(trivial_inequality_removal,[],[f711]) ).
thf(f729,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ X0 @ sF11 ) )
| ( $false
= ( in @ sK3 @ sF5 ) )
| ( $false
= ( in @ X0 @ sF8 ) )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26 ),
inference(forward_demodulation,[],[f712,f267]) ).
thf(f730,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( $true
= ( in @ X0 @ sF11 ) )
| ( $false
= ( in @ X0 @ sF8 ) )
| ( $false
= ( in @ sK3 @ sF5 ) ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26 ),
inference(trivial_inequality_removal,[],[f729]) ).
thf(f731,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sF8 ) )
| ( $true = $false )
| ( $true
= ( in @ X0 @ sF11 ) )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_43 ),
inference(forward_demodulation,[],[f730,f382]) ).
thf(f732,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sF11 ) )
| ( ( in @ X0 @ sK1 )
= $false )
| ( $false
= ( in @ X0 @ sF8 ) ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f731]) ).
thf(f736,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ ( sK29 @ sF11 @ X0 @ X1 ) @ sK1 )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK29 @ sF11 @ X0 @ X1 ) @ sF8 )
= $false )
| ( ( in @ X1 @ ( powerset @ sF11 ) )
= $true )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_37
| ~ spl33_43 ),
inference(constrained_superposition,[],[f354,f732]) ).
thf(f737,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ ( sK29 @ sF11 @ X0 @ X1 ) @ sK1 )
= $false )
| ( ( in @ X1 @ ( powerset @ sF11 ) )
= $true )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK29 @ sF11 @ X0 @ X1 ) @ sF8 )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_37
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f736]) ).
thf(f739,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ ( sK29 @ sF11 @ X0 @ X1 ) @ sF8 )
= $false )
| ( $true
= ( in @ X1 @ sF12 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK29 @ sF11 @ X0 @ X1 ) @ sK1 )
= $false )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_demodulation,[],[f737,f56]) ).
thf(f757,plain,
( ! [X0: $i] :
( ( $true
= ( in @ sF8 @ sF12 ) )
| ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) )
| ( ( in @ ( sK29 @ sF11 @ X0 @ sF8 ) @ sK1 )
= $false )
| ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( $true = $false )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(constrained_superposition,[],[f739,f350]) ).
thf(f761,plain,
( ! [X0: $i] :
( ( ( in @ ( sK29 @ sF11 @ X0 @ sF8 ) @ sK1 )
= $false )
| ( $true = $false )
| ( $true
= ( in @ sF8 @ sF12 ) )
| ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(duplicate_literal_removal,[],[f757]) ).
thf(f762,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) )
| ( ( in @ ( sK29 @ sF11 @ X0 @ sF8 ) @ sK1 )
= $false )
| ( $true
= ( in @ sF8 @ sF12 ) )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false )
| ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) ) )
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f761]) ).
thf(f770,plain,
( ! [X0: $i] :
( ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( ( in @ ( sK29 @ sF11 @ X0 @ sF8 ) @ sK1 )
= $false )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) ) )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_subsumption_resolution,[],[f762,f192]) ).
thf(f776,plain,
( ! [X0: $i] :
( ( ( in @ ( sK29 @ sF11 @ X0 @ sF8 ) @ sK1 )
= $false )
| ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false )
| ( $true
= ( in @ sF8 @ sF12 ) ) )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_demodulation,[],[f770,f56]) ).
thf(f787,plain,
( ! [X0: $i] :
( ( ( in @ ( sK29 @ sF11 @ X0 @ sF8 ) @ sK1 )
= $false )
| ( ( in @ sF11 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ sF8 @ ( powerset @ X0 ) ) ) )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_subsumption_resolution,[],[f776,f192]) ).
thf(f799,plain,
( ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( $false
= ( in @ sF8 @ ( powerset @ sK1 ) ) )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| ( $true = $false )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| ( $false
= ( in @ sF8 @ ( powerset @ sK1 ) ) )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(constrained_superposition,[],[f342,f787]) ).
thf(f803,plain,
( ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( $true = $false )
| ( $false
= ( in @ sF8 @ ( powerset @ sK1 ) ) )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(duplicate_literal_removal,[],[f799]) ).
thf(f804,plain,
( ( $false
= ( in @ sF8 @ ( powerset @ sK1 ) ) )
| ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f803]) ).
thf(f806,plain,
( ( ( in @ sF8 @ sF5 )
= $false )
| ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| spl33_2
| ~ spl33_8
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_demodulation,[],[f804,f42]) ).
thf(f808,plain,
( ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( $true = $false )
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_demodulation,[],[f806,f475]) ).
thf(f809,plain,
( ( $true
= ( in @ sF8 @ ( powerset @ sF11 ) ) )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f808]) ).
thf(f811,plain,
( ( $true
= ( in @ sF8 @ sF12 ) )
| ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_demodulation,[],[f809,f56]) ).
thf(f813,plain,
( ( ( in @ sF11 @ ( powerset @ sK1 ) )
= $false )
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_subsumption_resolution,[],[f811,f192]) ).
thf(f816,plain,
( ( $false
= ( in @ sF11 @ sF5 ) )
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43 ),
inference(forward_demodulation,[],[f813,f42]) ).
thf(f820,plain,
( ( $true = $false )
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43
| ~ spl33_47 ),
inference(forward_demodulation,[],[f816,f462]) ).
thf(f821,plain,
( $false
| spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43
| ~ spl33_47 ),
inference(trivial_inequality_removal,[],[f820]) ).
thf(f822,plain,
( spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43
| ~ spl33_47 ),
inference(avatar_contradiction_clause,[],[f821]) ).
thf(f823,plain,
( ( $true = $false )
| ( ( in @ sF10 @ sF5 )
= $false )
| ( $true
= ( in @ sF11 @ sF5 ) )
| ~ spl33_9
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(forward_demodulation,[],[f545,f516]) ).
thf(f824,plain,
( ( ( in @ sF10 @ sF5 )
= $false )
| ( $true
= ( in @ sF11 @ sF5 ) )
| ~ spl33_9
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f823]) ).
thf(f830,plain,
( ( $true = $false )
| ( $true
= ( in @ sF11 @ sF5 ) )
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(forward_demodulation,[],[f824,f518]) ).
thf(f831,plain,
( ( $true
= ( in @ sF11 @ sF5 ) )
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(trivial_inequality_removal,[],[f830]) ).
thf(f832,plain,
( spl33_47
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43 ),
inference(avatar_split_clause,[],[f831,f380,f336,f265,f225,f218,f460]) ).
thf(f843,plain,
( ( $true = $false )
| ~ spl33_10
| ~ spl33_11 ),
inference(forward_demodulation,[],[f230,f235]) ).
thf(f844,plain,
( $false
| ~ spl33_10
| ~ spl33_11 ),
inference(trivial_inequality_removal,[],[f843]) ).
thf(f845,plain,
( ~ spl33_10
| ~ spl33_11 ),
inference(avatar_contradiction_clause,[],[f844]) ).
cnf(s2,plain,
( spl33_3
| spl33_4 ),
inference(sat_conversion,[],[f203]) ).
cnf(s4,plain,
( spl33_7
| spl33_8 ),
inference(sat_conversion,[],[f221]) ).
cnf(s5,plain,
spl33_6,
inference(sat_conversion,[],[f222]) ).
cnf(s6,plain,
~ spl33_4,
inference(sat_conversion,[],[f223]) ).
cnf(s7,plain,
( spl33_9
| spl33_10 ),
inference(sat_conversion,[],[f231]) ).
cnf(s12,plain,
( spl33_17
| spl33_18 ),
inference(sat_conversion,[],[f268]) ).
cnf(s13,plain,
spl33_15,
inference(sat_conversion,[],[f269]) ).
cnf(s20,plain,
( spl33_26
| spl33_27 ),
inference(sat_conversion,[],[f311]) ).
cnf(s24,plain,
( spl33_32
| spl33_33 ),
inference(sat_conversion,[],[f338]) ).
cnf(s25,plain,
spl33_28,
inference(sat_conversion,[],[f339]) ).
cnf(s26,plain,
( spl33_34
| spl33_35 ),
inference(sat_conversion,[],[f347]) ).
cnf(s27,plain,
( spl33_35
| spl33_36 ),
inference(sat_conversion,[],[f351]) ).
cnf(s28,plain,
( spl33_35
| spl33_37 ),
inference(sat_conversion,[],[f355]) ).
cnf(s33,plain,
( spl33_43
| spl33_44 ),
inference(sat_conversion,[],[f387]) ).
cnf(s35,plain,
spl33_46,
inference(sat_conversion,[],[f397]) ).
cnf(s36,plain,
spl33_11,
inference(sat_conversion,[],[f398]) ).
cnf(s37,plain,
spl33_19,
inference(sat_conversion,[],[f399]) ).
cnf(s38,plain,
spl33_39,
inference(sat_conversion,[],[f400]) ).
cnf(s39,plain,
( ~ spl33_6
| ~ spl33_7 ),
inference(sat_conversion,[],[f403]) ).
cnf(s40,plain,
( ~ spl33_15
| ~ spl33_17 ),
inference(sat_conversion,[],[f407]) ).
cnf(s42,plain,
( ~ spl33_28
| ~ spl33_32 ),
inference(sat_conversion,[],[f426]) ).
cnf(s43,plain,
( ~ spl33_35
| ~ spl33_39 ),
inference(sat_conversion,[],[f433]) ).
cnf(s44,plain,
( ~ spl33_2
| ~ spl33_3 ),
inference(sat_conversion,[],[f438]) ).
cnf(s47,plain,
( ~ spl33_44
| ~ spl33_46 ),
inference(sat_conversion,[],[f450]) ).
cnf(s56,plain,
( ~ spl33_19
| ~ spl33_27 ),
inference(sat_conversion,[],[f630]) ).
cnf(s64,plain,
( spl33_2
| ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_26
| ~ spl33_34
| ~ spl33_36
| ~ spl33_37
| ~ spl33_43
| ~ spl33_47 ),
inference(sat_conversion,[],[f822]) ).
cnf(s66,plain,
( ~ spl33_8
| ~ spl33_9
| ~ spl33_18
| ~ spl33_33
| ~ spl33_43
| spl33_47 ),
inference(sat_conversion,[],[f832]) ).
cnf(s68,plain,
( ~ spl33_10
| ~ spl33_11 ),
inference(sat_conversion,[],[f845]) ).
cnf(s70,plain,
~ spl33_35,
inference(rat,[],[s43,s38]) ).
cnf(s71,plain,
~ spl33_27,
inference(rat,[],[s56,s37]) ).
cnf(s72,plain,
~ spl33_10,
inference(rat,[],[s68,s36]) ).
cnf(s73,plain,
~ spl33_44,
inference(rat,[],[s47,s35]) ).
cnf(s74,plain,
spl33_43,
inference(rat,[],[s33,s73]) ).
cnf(s76,plain,
spl33_37,
inference(rat,[],[s28,s70]) ).
cnf(s77,plain,
spl33_36,
inference(rat,[],[s27,s70]) ).
cnf(s78,plain,
spl33_34,
inference(rat,[],[s26,s70]) ).
cnf(s79,plain,
~ spl33_32,
inference(rat,[],[s42,s25]) ).
cnf(s80,plain,
spl33_33,
inference(rat,[],[s24,s79]) ).
cnf(s81,plain,
spl33_26,
inference(rat,[],[s20,s71]) ).
cnf(s82,plain,
~ spl33_17,
inference(rat,[],[s40,s13]) ).
cnf(s83,plain,
spl33_18,
inference(rat,[],[s12,s82]) ).
cnf(s85,plain,
spl33_9,
inference(rat,[],[s7,s72]) ).
cnf(s87,plain,
~ spl33_7,
inference(rat,[],[s39,s5]) ).
cnf(s88,plain,
spl33_8,
inference(rat,[],[s4,s87]) ).
cnf(s89,plain,
spl33_47,
inference(rat,[],[s66,s85,s74,s80,s83,s88]) ).
cnf(s90,plain,
spl33_2,
inference(rat,[],[s64,s89,s74,s76,s77,s78,s81,s83,s85,s88]) ).
cnf(s91,plain,
~ spl33_3,
inference(rat,[],[s44,s90]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s2,s6,s91]) ).
thf(f850,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU743^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:23:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.32 % (3598273)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (3598278)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1075595116:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (3598284)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (3598284)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.32 % (3598279)lrs+10_16_si=on:nwc=1.5:random_seed=1812660003:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (3598280)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1801056263:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (3598281)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3031176372:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.32 % (3598282)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1265243196:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (3598283)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1545040860:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (3598284)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=354121503:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (3598280)Instruction limit reached!
% 0.20/0.32 % (3598280)------------------------------
% 0.20/0.32 % (3598280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598280)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598280)Termination reason: Instruction limit
% 0.20/0.32 % (3598280)Termination phase: Saturation
% 0.20/0.32 % (3598280)Time elapsed: 0.002 s
% 0.20/0.32 % (3598280)Peak memory usage: 11 MB
% 0.20/0.32 % (3598280)Instructions burned: 3 (million)
% 0.20/0.32 % (3598279)Instruction limit reached!
% 0.20/0.32 % (3598279)------------------------------
% 0.20/0.32 % (3598279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598279)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598279)Termination reason: Instruction limit
% 0.20/0.32 % (3598279)Termination phase: Saturation
% 0.20/0.32 % (3598279)Time elapsed: 0.010 s
% 0.20/0.32 % (3598279)Peak memory usage: 12 MB
% 0.20/0.32 % (3598279)Instructions burned: 20 (million)
% 0.20/0.32 % (3598282)Instruction limit reached!
% 0.20/0.32 % (3598282)------------------------------
% 0.20/0.32 % (3598282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598282)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598282)Termination reason: Instruction limit
% 0.20/0.32 % (3598282)Termination phase: Saturation
% 0.20/0.32 % (3598282)Time elapsed: 0.012 s
% 0.20/0.32 % (3598282)Peak memory usage: 12 MB
% 0.20/0.32 % (3598282)Instructions burned: 24 (million)
% 0.20/0.32 % (3598278)Instruction limit reached!
% 0.20/0.32 % (3598278)------------------------------
% 0.20/0.32 % (3598278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598278)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598278)Termination reason: Instruction limit
% 0.20/0.32 % (3598278)Termination phase: Saturation
% 0.20/0.32 % (3598278)Time elapsed: 0.022 s
% 0.20/0.32 % (3598278)Peak memory usage: 13 MB
% 0.20/0.32 % (3598278)Instructions burned: 88 (million)
% 0.20/0.32 % (3598292)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3778314112:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (3598292)Instruction limit reached!
% 0.20/0.32 % (3598292)------------------------------
% 0.20/0.32 % (3598292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598292)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598292)Termination reason: Instruction limit
% 0.20/0.32 % (3598292)Termination phase: Saturation
% 0.20/0.32 % (3598292)Time elapsed: 0.002 s
% 0.20/0.32 % (3598292)Peak memory usage: 11 MB
% 0.20/0.32 % (3598292)Instructions burned: 4 (million)
% 0.20/0.32 % (3598295)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2972773409:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.32 % (3598294)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (3598293)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4175118654:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.32 % (3598295)Instruction limit reached!
% 0.20/0.32 % (3598295)------------------------------
% 0.20/0.32 % (3598295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598295)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598295)Termination reason: Instruction limit
% 0.20/0.32 % (3598295)Termination phase: Saturation
% 0.20/0.32 % (3598295)Time elapsed: 0.004 s
% 0.20/0.32 % (3598295)Peak memory usage: 12 MB
% 0.20/0.32 % (3598295)Instructions burned: 15 (million)
% 0.20/0.32 % (3598294)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2346761351:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.32 % (3598284) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3598273-3598284"...
% 0.20/0.32 % (3598293)Instruction limit reached!
% 0.20/0.32 % (3598293)------------------------------
% 0.20/0.32 % (3598293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598293)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598293)Termination reason: Instruction limit
% 0.20/0.32 % (3598293)Termination phase: Saturation
% 0.20/0.32 % (3598293)Time elapsed: 0.003 s
% 0.20/0.32 % (3598293)Peak memory usage: 11 MB
% 0.20/0.32 % (3598293)Instructions burned: 6 (million)
% 0.20/0.32 % (3598294)Instruction limit reached!
% 0.20/0.32 % (3598294)------------------------------
% 0.20/0.32 % (3598294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598294)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598294)Termination reason: Instruction limit
% 0.20/0.32 % (3598294)Termination phase: Saturation
% 0.20/0.32 % (3598294)Time elapsed: 0.004 s
% 0.20/0.32 % (3598294)Peak memory usage: 12 MB
% 0.20/0.32 % (3598294)Instructions burned: 8 (million)
% 0.20/0.32 % (3598283)Instruction limit reached!
% 0.20/0.32 % (3598283)------------------------------
% 0.20/0.32 % (3598283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3598283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3598283)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3598283)Termination reason: Instruction limit
% 0.20/0.32 % (3598283)Termination phase: Saturation
% 0.20/0.32 % (3598283)Time elapsed: 0.038 s
% 0.20/0.32 % (3598283)Peak memory usage: 13 MB
% 0.20/0.32 % (3598283)Instructions burned: 75 (million)
% 0.20/0.32 % (3598297)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.32 % (3598297)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (3598300)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3086003124:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.32 % (3598284)...printing done.
% 0.20/0.32 % (3598297)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3255725582:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.32 % (3598284)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.33 % (3598284)------------------------------
% 0.20/0.33 % (3598284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3598284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3598284)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3598284)Termination reason: Refutation
% 0.20/0.33 % (3598284)Time elapsed: 0.040 s
% 0.20/0.33 % (3598284)Peak memory usage: 14 MB
% 0.20/0.33 % (3598284)Instructions burned: 76 (million)
% 0.20/0.33 % (3598273)Success in time 0.077 s
% 0.20/0.33 % Vampire exiting
%------------------------------------------------------------------------------