%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU643^2 : 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 : n001.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 08:30:29 AM UTC 2026
% Result : Theorem 0.37s 0.51s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 35
% Syntax : Number of formulae : 249 ( 80 unt; 0 typ; 28 def)
% Number of atoms : 1989 ( 460 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2736 ( 190 ~; 344 |; 66 &;1884 @)
% ( 21 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 57 usr; 39 con; 0-4 aty)
% ( 75 !!; 38 ??; 0 @@+; 0 @@-)
% Number of variables : 406 ( 0 sgn 166 !; 8 ?; 406 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
setadjoinIL: $o ).
thf(func_def_7,type,
iskpair: $i > $o ).
thf(func_def_8,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
ex1I: $o ).
thf(func_def_11,type,
setukpairinjL1: $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
sF1: $o ).
thf(func_def_26,type,
sF2: $o ).
thf(func_def_27,type,
sF3: $o ).
thf(func_def_30,type,
sF6: $o ).
thf(func_def_31,type,
sF7: $o ).
thf(func_def_40,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
sK16: $i > $o ).
thf(func_def_43,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_44,type,
sK19: $i > $i > ( $i > $o ) > $i ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f4,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(f5,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= ex1I ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(f6,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) )
= setukpairinjL1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(f7,conjecture,
( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(f8,negated_conjecture,
~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X2 ) )
= setukpairinjL1 ),
inference(rectify,[],[f6]) ).
thf(f10,plain,
( setukpairinjL1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f12,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
inference(rectify,[],[f3]) ).
thf(f18,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ( X1 @ X0 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( X1 @ X3 )
=> ( X0 = X3 ) ) )
=> ( ex1 @ X2
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) ) )
= ex1I ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ( ( setadjoinIL = $true )
=> ( ( ex1I = $true )
=> ( ( setukpairinjL1 = $true )
=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) )
& ( setukpairinjL1 = $true )
& ( ex1I = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f24,plain,
( ( setadjoinIL = $true )
& ( ex1I = $true )
& ( setukpairinjL1 = $true )
& ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( setadjoinIL = $true )
& ( ex1I = $true )
& ( setukpairinjL1 = $true )
& ( $true
= ( iskpair @ sK0 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
thf(f26,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
( setukpairinjL1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f28,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f29,plain,
( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f30,plain,
( $true
= ( iskpair @ sK0 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f31,plain,
setukpairinjL1 = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f32,plain,
ex1I = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f33,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f35,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f36,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f39,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f35,f26]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f27,f31]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f33]) ).
thf(f42,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f30,f34]) ).
thf(f43,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ),
inference(definition_unfolding,[],[f29,f26]) ).
thf(f44,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f36,f32,f39]) ).
thf(f45,definition,
( sF1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f46,plain,
$true = sF1,
inference(definition_folding,[],[f40,f45]) ).
thf(f47,definition,
( sF2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f48,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
= sF2 ),
inference(reorient_equations,[],[f47]) ).
thf(f49,plain,
$true = sF2,
inference(definition_folding,[],[f41,f48]) ).
thf(f50,definition,
( sF3
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f51,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ sK0 )
= sF3 ),
inference(reorient_equations,[],[f50]) ).
thf(f52,plain,
$true = sF3,
inference(definition_folding,[],[f42,f51]) ).
thf(f53,definition,
( sF4
= ( setunion @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f54,plain,
( ( setunion @ sK0 )
= sF4 ),
inference(reorient_equations,[],[f53]) ).
thf(f55,definition,
( sF5
= ( dsetconstr @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f56,definition,
( sF6
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f57,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sF5 )
= sF6 ),
inference(reorient_equations,[],[f56]) ).
thf(f58,plain,
$true != sF6,
inference(definition_folding,[],[f43,f57,f55,f54]) ).
thf(f59,definition,
( sF7
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f60,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) )
= sF7 ),
inference(reorient_equations,[],[f59]) ).
thf(f61,plain,
$true = sF7,
inference(definition_folding,[],[f44,f60]) ).
thf(f63,plain,
( ( $false = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f45]) ).
thf(f64,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) ) )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( $false = sF1 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( $false = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) )
@ X3 ) )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $false = sF1 )
| ( $false
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( X1 = X2 )
| ( $false
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f81,plain,
( ( $false = sF2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f48]) ).
thf(f87,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f88,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) )
@ X2 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ sK0 ) )
| ( $false = sF3 ) ),
inference(iff_proxy_clausification,[],[f51]) ).
thf(f101,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y1 @ ( setunion @ sK0 ) ) ) )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f102,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y1 @ ( setunion @ sK0 ) ) ) )
& ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK13 ) )
| ( $false = sF3 ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f103,plain,
( ( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
& ( in @ sK13 @ ( setunion @ sK0 ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
( ( $false = sF3 )
| ( $true
= ( in @ sK13 @ ( setunion @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( ( $false = sF3 )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f103]) ).
thf(f106,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK14 ) )
| ( $false = sF3 ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( ( $false = sF3 )
| ( $true
= ( ( ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ sK14 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ sK14 @ ( setunion @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f109,plain,
( ( $false = sF3 )
| ( $true
= ( ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ sK14 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) ),
inference(and_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( ( $false = sF3 )
| ( sK0
= ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ sK14 @ emptyset ) ) @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[],[f109]) ).
thf(f111,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ( $false = sF7 ) ),
inference(iff_proxy_clausification,[],[f60]) ).
thf(f134,plain,
! [X1: $i] :
( ( $false = sF7 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f111]) ).
thf(f135,plain,
! [X1: $i] :
( ( $false = sF7 )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ X1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ X1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false = sF7 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i > $o,X1: $i] :
( ( $false = sF7 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X2 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X2 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) ) ) ) )
@ X3 ) )
| ( $false = sF7 ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( X3 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) ) ) ) ) )
| ( $false = sF7 ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false = sF7 )
| ( $true
= ( ( X2 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( X3 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) ) ) ) )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( $false = sF7 )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( X3 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) ) ) )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) ) )
| ( $false = sF7 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( X3 = Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( X3 = Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) )
@ ( sK18 @ X1 @ X2 ) )
= $true )
| ( $false = sF7 ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) )
@ ( sK18 @ X1 @ X2 ) )
= $true )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( X3 = Y0 ) ) )
@ ( sK19 @ X3 @ X1 @ X2 ) )
= $false )
| ( $false = sF7 ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) )
=> ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) ) ) )
| ( $true
= ( ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) )
| ( $false = sF7 )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( $false = sF7 )
| ( $true
= ( ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) )
=> ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f151,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) )
| ( $false = sF7 )
| ( $false
= ( X2 @ X3 ) )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) )
=> ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f146]) ).
thf(f152,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false = sF7 )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $false
= ( ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) )
=> ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) ) )
| ( $false
= ( X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f146]) ).
thf(f153,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false = sF7 )
| ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $false
= ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ X3 ) )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( $false = sF7 )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $true
= ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f155,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( sK19 @ X3 @ X1 @ X2 )
!= X3 )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) )
| ( $false = sF7 )
| ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f153]) ).
thf(f156,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( $false
= ( ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) )
=> ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) ) )
| ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( $false = sF7 )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f151]) ).
thf(f157,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( $false
= ( X2 @ X3 ) )
| ( $false
= ( X3
= ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $false = sF7 )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ X1 ) )
| ( $false = sF7 )
| ( $false
= ( X2 @ X3 ) )
| ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( $true
= ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f159,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( ( sK19 @ X3 @ X1 @ X2 )
!= X3 )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false = sF7 )
| ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f157]) ).
thf(f161,plain,
( ( $true = sF6 )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sF5 )
= $false ) ),
inference(iff_proxy_clausification,[],[f57]) ).
thf(f162,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sF5 )
& ( ( setadjoin @ Y0 @ emptyset )
= sF5 ) ) )
= $false )
| ( $true = sF6 ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true = sF6 )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sF5 )
& ( ( setadjoin @ Y0 @ emptyset )
= sF5 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true = sF6 )
| ( $false
= ( ( in @ X1 @ sF5 )
& ( ( setadjoin @ X1 @ emptyset )
= sF5 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( ( setadjoin @ X1 @ emptyset )
= sF5 ) )
| ( $true = sF6 )
| ( ( in @ X1 @ sF5 )
= $false ) ),
inference(and_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( in @ X1 @ sF5 )
= $false )
| ( $true = sF6 )
| ( ( setadjoin @ X1 @ emptyset )
!= sF5 ) ),
inference(equality_proxy_clausification,[],[f165]) ).
thf(f174,definition,
( spl21_1
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
thf(f176,plain,
( ( $false = sF1 )
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f174]) ).
thf(f178,definition,
( spl21_2
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( X1 = X2 )
| ( $false
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
thf(f179,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ( X1 = X2 ) )
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f178]) ).
thf(f180,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f71,f178,f174]) ).
thf(f186,definition,
( spl21_4
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
thf(f188,plain,
( ( $true = sF1 )
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f186]) ).
thf(f196,definition,
( spl21_6
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
thf(f198,plain,
( ( $true = sF2 )
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f205,definition,
( spl21_8
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
thf(f207,plain,
( ( $false = sF2 )
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f209,definition,
( spl21_9
<=> ! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
thf(f210,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) )
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f211,plain,
( spl21_8
| spl21_9 ),
inference(avatar_split_clause,[],[f90,f209,f205]) ).
thf(f212,plain,
spl21_4,
inference(avatar_split_clause,[],[f46,f186]) ).
thf(f213,plain,
spl21_6,
inference(avatar_split_clause,[],[f49,f196]) ).
thf(f218,definition,
( spl21_11
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl21_11])],[avatar_definition]) ).
thf(f220,plain,
( ( $true = sF3 )
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f223,definition,
( spl21_12
<=> ( sK0
= ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ sK14 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
thf(f225,plain,
( ( sK0
= ( setadjoin @ ( setadjoin @ sK13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK13 @ ( setadjoin @ sK14 @ emptyset ) ) @ emptyset ) ) )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f227,definition,
( spl21_13
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition]) ).
thf(f229,plain,
( ( $false = sF3 )
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f230,plain,
( spl21_12
| spl21_13 ),
inference(avatar_split_clause,[],[f110,f227,f223]) ).
thf(f237,definition,
( spl21_15
<=> ( $true
= ( in @ sK13 @ ( setunion @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_15])],[avatar_definition]) ).
thf(f239,plain,
( ( $true
= ( in @ sK13 @ ( setunion @ sK0 ) ) )
| ~ spl21_15 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f240,plain,
( spl21_15
| spl21_13 ),
inference(avatar_split_clause,[],[f104,f227,f237]) ).
thf(f246,definition,
( spl21_17
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition]) ).
thf(f248,plain,
( ( $true = sF7 )
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f264,definition,
( spl21_21
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl21_21])],[avatar_definition]) ).
thf(f266,plain,
( ( $false = sF7 )
| ~ spl21_21 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f276,definition,
( spl21_24
<=> ! [X2: $i > $o,X1: $i,X3: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_24])],[avatar_definition]) ).
thf(f277,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ X3 ) )
| ( $true
= ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ X1 ) ) )
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f278,plain,
( spl21_21
| spl21_24 ),
inference(avatar_split_clause,[],[f154,f276,f264]) ).
thf(f280,definition,
( spl21_25
<=> ! [X2: $i > $o,X1: $i,X3: $i] :
( ( ( sK19 @ X3 @ X1 @ X2 )
!= X3 )
| ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ X3 ) )
| ( $false
= ( in @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_25])],[avatar_definition]) ).
thf(f281,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK18 @ X1 @ X2 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ X3 ) )
| ( ( sK19 @ X3 @ X1 @ X2 )
!= X3 )
| ( $false
= ( in @ X3 @ X1 ) ) )
| ~ spl21_25 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f282,plain,
( spl21_21
| spl21_25 ),
inference(avatar_split_clause,[],[f155,f280,f264]) ).
thf(f284,definition,
( spl21_26
<=> ! [X2: $i > $o,X1: $i,X3: $i] :
( ( $false
= ( in @ X3 @ X1 ) )
| ( $true
= ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( $false
= ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_26])],[avatar_definition]) ).
thf(f285,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( $true
= ( X2 @ ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) ) )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f286,plain,
( spl21_21
| spl21_26 ),
inference(avatar_split_clause,[],[f158,f284,f264]) ).
thf(f288,definition,
( spl21_27
<=> ! [X2: $i > $o,X1: $i,X3: $i] :
( ( $false
= ( X2 @ X3 ) )
| ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( $false
= ( in @ X3 @ X1 ) )
| ( ( sK19 @ X3 @ X1 @ X2 )
!= X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_27])],[avatar_definition]) ).
thf(f289,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( setadjoin @ ( sK18 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X1 @ X2 ) )
| ( ( sK19 @ X3 @ X1 @ X2 )
!= X3 )
| ( $false
= ( in @ X3 @ X1 ) )
| ( $false
= ( X2 @ X3 ) ) )
| ~ spl21_27 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f290,plain,
( spl21_21
| spl21_27 ),
inference(avatar_split_clause,[],[f159,f288,f264]) ).
thf(f292,definition,
( spl21_28
<=> ! [X1: $i] :
( ( ( in @ X1 @ sF5 )
= $false )
| ( ( setadjoin @ X1 @ emptyset )
!= sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_28])],[avatar_definition]) ).
thf(f293,plain,
( ! [X1: $i] :
( ( ( in @ X1 @ sF5 )
= $false )
| ( ( setadjoin @ X1 @ emptyset )
!= sF5 ) )
| ~ spl21_28 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f295,definition,
( spl21_29
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl21_29])],[avatar_definition]) ).
thf(f298,plain,
( spl21_28
| spl21_29 ),
inference(avatar_split_clause,[],[f166,f295,f292]) ).
thf(f313,plain,
~ spl21_29,
inference(avatar_split_clause,[],[f58,f295]) ).
thf(f314,plain,
spl21_11,
inference(avatar_split_clause,[],[f52,f218]) ).
thf(f315,plain,
spl21_17,
inference(avatar_split_clause,[],[f61,f246]) ).
thf(f316,plain,
( ( $true = $false )
| ~ spl21_6
| ~ spl21_8 ),
inference(forward_demodulation,[],[f207,f198]) ).
thf(f317,plain,
( $false
| ~ spl21_6
| ~ spl21_8 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f318,plain,
( ~ spl21_6
| ~ spl21_8 ),
inference(avatar_contradiction_clause,[],[f317]) ).
thf(f332,plain,
( ( $true = $false )
| ~ spl21_11
| ~ spl21_13 ),
inference(forward_demodulation,[],[f229,f220]) ).
thf(f333,plain,
( $false
| ~ spl21_11
| ~ spl21_13 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f334,plain,
( ~ spl21_11
| ~ spl21_13 ),
inference(avatar_contradiction_clause,[],[f333]) ).
thf(f336,plain,
( ( $true = $false )
| ~ spl21_17
| ~ spl21_21 ),
inference(forward_demodulation,[],[f266,f248]) ).
thf(f337,plain,
( $false
| ~ spl21_17
| ~ spl21_21 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f338,plain,
( ~ spl21_17
| ~ spl21_21 ),
inference(avatar_contradiction_clause,[],[f337]) ).
thf(f340,plain,
( ( $true
= ( in @ sK13 @ sF4 ) )
| ~ spl21_15 ),
inference(forward_demodulation,[],[f239,f54]) ).
thf(f344,plain,
( ( $true
= ( in @ ( setadjoin @ sK13 @ emptyset ) @ sK0 ) )
| ~ spl21_9
| ~ spl21_12 ),
inference(constrained_superposition,[],[f210,f225]) ).
thf(f346,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( sK13 = X0 ) )
| ~ spl21_2
| ~ spl21_12 ),
inference(constrained_superposition,[],[f179,f225]) ).
thf(f379,definition,
( spl21_36
<=> ( $true
= ( in
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_36])],[avatar_definition]) ).
thf(f381,plain,
( ( $true
= ( in
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ sF5 ) )
| ~ spl21_36 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f390,plain,
( ! [X0: $i] :
( ( $true
= ( in
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ sF5 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ X0 ) ) )
| ~ spl21_25 ),
inference(constrained_superposition,[],[f281,f55]) ).
thf(f391,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $true
= ( in
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ sF5 ) )
| ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_25 ),
inference(beta-eta_normalization,[],[f390]) ).
thf(f408,plain,
( ! [X0: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ X0 ) )
| ( $true
= ( in
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ sF5 ) )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_24 ),
inference(constrained_superposition,[],[f277,f55]) ).
thf(f409,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $true
= ( in
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ sF5 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $true
= ( in
@ ( setadjoin
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset )
@ sK0 ) ) )
| ~ spl21_24 ),
inference(beta-eta_normalization,[],[f408]) ).
thf(f429,definition,
( spl21_40
<=> ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_40])],[avatar_definition]) ).
thf(f430,plain,
( ! [X0: $i] :
( ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| ~ spl21_40 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f432,plain,
( spl21_36
| spl21_40
| ~ spl21_25 ),
inference(avatar_split_clause,[],[f391,f280,f429,f379]) ).
thf(f434,definition,
( spl21_41
<=> ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $true
= ( in
@ ( setadjoin
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset )
@ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_41])],[avatar_definition]) ).
thf(f435,plain,
( ! [X0: $i] :
( ( $true
= ( in
@ ( setadjoin
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset )
@ sK0 ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f436,plain,
( spl21_41
| spl21_36
| ~ spl21_24 ),
inference(avatar_split_clause,[],[f409,f276,f379,f434]) ).
thf(f449,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $true = $false )
| ( sK13
= ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ~ spl21_2
| ~ spl21_12
| ~ spl21_41 ),
inference(constrained_superposition,[],[f346,f435]) ).
thf(f450,plain,
( ! [X0: $i] :
( ( sK13
= ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_2
| ~ spl21_12
| ~ spl21_41 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f466,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sF4 ) )
| ( sK13 != X0 )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_2
| ~ spl21_12
| ~ spl21_40
| ~ spl21_41 ),
inference(constrained_superposition,[],[f430,f450]) ).
thf(f469,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( sK13 != X0 )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_2
| ~ spl21_12
| ~ spl21_40
| ~ spl21_41 ),
inference(duplicate_literal_removal,[],[f466]) ).
thf(f478,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_2
| ~ spl21_12
| ~ spl21_40
| ~ spl21_41 ),
inference(forward_subsumption_resolution,[],[f469,f346]) ).
thf(f482,plain,
( ( $false
= ( in @ sK13 @ sF4 ) )
| ( $true = $false )
| ~ spl21_2
| ~ spl21_9
| ~ spl21_12
| ~ spl21_40
| ~ spl21_41 ),
inference(constrained_superposition,[],[f478,f344]) ).
thf(f491,plain,
( ( $false
= ( in @ sK13 @ sF4 ) )
| ~ spl21_2
| ~ spl21_9
| ~ spl21_12
| ~ spl21_40
| ~ spl21_41 ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f495,plain,
( ( $true = $false )
| ~ spl21_2
| ~ spl21_9
| ~ spl21_12
| ~ spl21_15
| ~ spl21_40
| ~ spl21_41 ),
inference(forward_demodulation,[],[f491,f340]) ).
thf(f496,plain,
( $false
| ~ spl21_2
| ~ spl21_9
| ~ spl21_12
| ~ spl21_15
| ~ spl21_40
| ~ spl21_41 ),
inference(trivial_inequality_removal,[],[f495]) ).
thf(f497,plain,
( ~ spl21_2
| ~ spl21_9
| ~ spl21_12
| ~ spl21_15
| ~ spl21_40
| ~ spl21_41 ),
inference(avatar_contradiction_clause,[],[f496]) ).
thf(f498,plain,
( ( $true = $false )
| ~ spl21_1
| ~ spl21_4 ),
inference(forward_demodulation,[],[f176,f188]) ).
thf(f499,plain,
( $false
| ~ spl21_1
| ~ spl21_4 ),
inference(trivial_inequality_removal,[],[f498]) ).
thf(f500,plain,
( ~ spl21_1
| ~ spl21_4 ),
inference(avatar_contradiction_clause,[],[f499]) ).
thf(f505,plain,
( ( sF5
!= ( setadjoin
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ( $true = $false )
| ~ spl21_28
| ~ spl21_36 ),
inference(constrained_superposition,[],[f293,f381]) ).
thf(f506,plain,
( ( sF5
!= ( setadjoin
@ ( sK18 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ~ spl21_28
| ~ spl21_36 ),
inference(trivial_inequality_removal,[],[f505]) ).
thf(f508,plain,
( ! [X0: $i] :
( ( sF5
!= ( dsetconstr @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ X0 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ) )
| ~ spl21_26
| ~ spl21_28
| ~ spl21_36 ),
inference(constrained_superposition,[],[f506,f285]) ).
thf(f510,plain,
( ! [X0: $i] :
( ( sF5
!= ( dsetconstr @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ X0 ) )
| ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 )
| ( $false
= ( in @ X0 @ sF4 ) ) )
| ~ spl21_27
| ~ spl21_28
| ~ spl21_36 ),
inference(constrained_superposition,[],[f506,f289]) ).
thf(f511,plain,
( ! [X0: $i] :
( ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( sF5
!= ( dsetconstr @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ~ spl21_27
| ~ spl21_28
| ~ spl21_36 ),
inference(beta-eta_normalization,[],[f510]) ).
thf(f512,plain,
( ! [X0: $i] :
( ( sF5
!= ( dsetconstr @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $true
= ( in
@ ( setadjoin
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset )
@ sK0 ) ) )
| ~ spl21_26
| ~ spl21_28
| ~ spl21_36 ),
inference(beta-eta_normalization,[],[f508]) ).
thf(f514,plain,
( ! [X0: $i] :
( ( ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X0 )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| ~ spl21_27
| ~ spl21_28
| ~ spl21_36 ),
inference(forward_subsumption_resolution,[],[f511,f55]) ).
thf(f515,plain,
( spl21_40
| ~ spl21_27
| ~ spl21_28
| ~ spl21_36 ),
inference(avatar_split_clause,[],[f514,f379,f292,f288,f429]) ).
thf(f516,plain,
( ! [X0: $i] :
( ( $true
= ( in
@ ( setadjoin
@ ( sK19 @ X0 @ sF4
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset )
@ sK0 ) )
| ( $false
= ( in @ X0 @ sF4 ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| ~ spl21_26
| ~ spl21_28
| ~ spl21_36 ),
inference(forward_subsumption_resolution,[],[f512,f55]) ).
thf(f517,plain,
( spl21_41
| ~ spl21_26
| ~ spl21_28
| ~ spl21_36 ),
inference(avatar_split_clause,[],[f516,f379,f292,f284,f434]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f180]) ).
cnf(s5,plain,
( spl21_8
| spl21_9 ),
inference(sat_conversion,[],[f211]) ).
cnf(s6,plain,
spl21_4,
inference(sat_conversion,[],[f212]) ).
cnf(s7,plain,
spl21_6,
inference(sat_conversion,[],[f213]) ).
cnf(s9,plain,
( spl21_12
| spl21_13 ),
inference(sat_conversion,[],[f230]) ).
cnf(s11,plain,
( spl21_13
| spl21_15 ),
inference(sat_conversion,[],[f240]) ).
cnf(s18,plain,
( spl21_21
| spl21_24 ),
inference(sat_conversion,[],[f278]) ).
cnf(s19,plain,
( spl21_21
| spl21_25 ),
inference(sat_conversion,[],[f282]) ).
cnf(s20,plain,
( spl21_21
| spl21_26 ),
inference(sat_conversion,[],[f286]) ).
cnf(s21,plain,
( spl21_21
| spl21_27 ),
inference(sat_conversion,[],[f290]) ).
cnf(s22,plain,
( spl21_28
| spl21_29 ),
inference(sat_conversion,[],[f298]) ).
cnf(s25,plain,
~ spl21_29,
inference(sat_conversion,[],[f313]) ).
cnf(s26,plain,
spl21_11,
inference(sat_conversion,[],[f314]) ).
cnf(s27,plain,
spl21_17,
inference(sat_conversion,[],[f315]) ).
cnf(s28,plain,
( ~ spl21_6
| ~ spl21_8 ),
inference(sat_conversion,[],[f318]) ).
cnf(s29,plain,
( ~ spl21_11
| ~ spl21_13 ),
inference(sat_conversion,[],[f334]) ).
cnf(s30,plain,
( ~ spl21_17
| ~ spl21_21 ),
inference(sat_conversion,[],[f338]) ).
cnf(s36,plain,
( ~ spl21_25
| spl21_36
| spl21_40 ),
inference(sat_conversion,[],[f432]) ).
cnf(s37,plain,
( ~ spl21_24
| spl21_36
| spl21_41 ),
inference(sat_conversion,[],[f436]) ).
cnf(s39,plain,
( ~ spl21_2
| ~ spl21_9
| ~ spl21_12
| ~ spl21_15
| ~ spl21_40
| ~ spl21_41 ),
inference(sat_conversion,[],[f497]) ).
cnf(s40,plain,
( ~ spl21_1
| ~ spl21_4 ),
inference(sat_conversion,[],[f500]) ).
cnf(s41,plain,
( ~ spl21_27
| ~ spl21_28
| ~ spl21_36
| spl21_40 ),
inference(sat_conversion,[],[f515]) ).
cnf(s42,plain,
( ~ spl21_26
| ~ spl21_28
| ~ spl21_36
| spl21_41 ),
inference(sat_conversion,[],[f517]) ).
cnf(s43,plain,
~ spl21_21,
inference(rat,[],[s30,s27]) ).
cnf(s44,plain,
~ spl21_13,
inference(rat,[],[s29,s26]) ).
cnf(s45,plain,
spl21_28,
inference(rat,[],[s22,s25]) ).
cnf(s46,plain,
spl21_27,
inference(rat,[],[s21,s43]) ).
cnf(s47,plain,
spl21_26,
inference(rat,[],[s20,s43]) ).
cnf(s48,plain,
spl21_25,
inference(rat,[],[s19,s43]) ).
cnf(s49,plain,
spl21_24,
inference(rat,[],[s18,s43]) ).
cnf(s52,plain,
spl21_15,
inference(rat,[],[s11,s44]) ).
cnf(s54,plain,
spl21_12,
inference(rat,[],[s9,s44]) ).
cnf(s56,plain,
~ spl21_8,
inference(rat,[],[s28,s7]) ).
cnf(s57,plain,
~ spl21_1,
inference(rat,[],[s40,s6]) ).
cnf(s58,plain,
spl21_9,
inference(rat,[],[s5,s56]) ).
cnf(s59,plain,
spl21_2,
inference(rat,[],[s1,s57]) ).
cnf(s60,plain,
spl21_36,
inference(rat,[],[s39,s36,s37,s54,s52,s58,s59,s48,s49]) ).
cnf(s61,plain,
spl21_41,
inference(rat,[],[s42,s47,s45,s60]) ).
cnf(s62,plain,
spl21_40,
inference(rat,[],[s41,s46,s45,s60]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s39,s59,s58,s52,s54,s61,s62]) ).
thf(f518,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU643^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n001.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 14:08:06 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.31/0.36 Running higher-order theorem proving
% 0.31/0.38 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
% 0.37/0.51 % (1296389)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.37/0.51 % (1296398)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1795788899:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.37/0.51 % (1296400)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.37/0.51 % (1296400)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
% 0.37/0.51 % (1296394)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4233698675:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.37/0.51 % (1296395)lrs+10_16_si=on:nwc=1.5:random_seed=1728896965:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.37/0.51 % (1296396)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3541469272:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.37/0.51 % (1296397)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=2114177496: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)
% 0.37/0.51 % (1296399)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2482892368:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.37/0.51 % (1296398)Instruction limit reached!
% 0.37/0.51 % (1296398)------------------------------
% 0.37/0.51 % (1296398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296398)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296398)Termination reason: Instruction limit
% 0.37/0.51 % (1296398)Termination phase: Saturation
% 0.37/0.51 % (1296398)Time elapsed: 0.014 s
% 0.37/0.51 % (1296398)Peak memory usage: 12 MB
% 0.37/0.51 % (1296398)Instructions burned: 25 (million)
% 0.37/0.51 % (1296400)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=1109721517:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.37/0.51 % (1296396)Instruction limit reached!
% 0.37/0.51 % (1296396)------------------------------
% 0.37/0.51 % (1296396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296396)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296396)Termination reason: Instruction limit
% 0.37/0.51 % (1296396)Termination phase: Saturation
% 0.37/0.51 % (1296396)Time elapsed: 0.003 s
% 0.37/0.51 % (1296396)Peak memory usage: 11 MB
% 0.37/0.51 % (1296396)Instructions burned: 3 (million)
% 0.37/0.51 % (1296395)Instruction limit reached!
% 0.37/0.51 % (1296395)------------------------------
% 0.37/0.51 % (1296395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296395)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296395)Termination reason: Instruction limit
% 0.37/0.51 % (1296395)Termination phase: Saturation
% 0.37/0.51 % (1296395)Time elapsed: 0.017 s
% 0.37/0.51 % (1296395)Peak memory usage: 12 MB
% 0.37/0.51 % (1296395)Instructions burned: 18 (million)
% 0.37/0.51 % (1296408)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4054645775:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.51 % (1296408)Instruction limit reached!
% 0.37/0.51 % (1296408)------------------------------
% 0.37/0.51 % (1296408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296408)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296408)Termination reason: Instruction limit
% 0.37/0.51 % (1296408)Termination phase: Saturation
% 0.37/0.51 % (1296408)Time elapsed: 0.002 s
% 0.37/0.51 % (1296408)Peak memory usage: 11 MB
% 0.37/0.51 % (1296408)Instructions burned: 4 (million)
% 0.37/0.51 % (1296409)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1131085330:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.37/0.51 % (1296412)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3587909233:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.37/0.51 % (1296409)Instruction limit reached!
% 0.37/0.51 % (1296409)------------------------------
% 0.37/0.51 % (1296409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296409)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296409)Termination reason: Instruction limit
% 0.37/0.51 % (1296409)Termination phase: Saturation
% 0.37/0.51 % (1296409)Time elapsed: 0.006 s
% 0.37/0.51 % (1296409)Peak memory usage: 11 MB
% 0.37/0.51 % (1296409)Instructions burned: 6 (million)
% 0.37/0.51 % (1296410)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.51 % (1296412)Instruction limit reached!
% 0.37/0.51 % (1296412)------------------------------
% 0.37/0.51 % (1296412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296412)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296412)Termination reason: Instruction limit
% 0.37/0.51 % (1296412)Termination phase: Saturation
% 0.37/0.51 % (1296412)Time elapsed: 0.006 s
% 0.37/0.51 % (1296412)Peak memory usage: 12 MB
% 0.37/0.51 % (1296412)Instructions burned: 12 (million)
% 0.37/0.51 % (1296400) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1296389-1296400"...
% 0.37/0.51 % (1296410)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=222364661:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.37/0.51 % (1296410)Instruction limit reached!
% 0.37/0.51 % (1296410)------------------------------
% 0.37/0.51 % (1296410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296410)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296410)Termination reason: Instruction limit
% 0.37/0.51 % (1296410)Termination phase: Saturation
% 0.37/0.51 % (1296410)Time elapsed: 0.008 s
% 0.37/0.51 % (1296410)Peak memory usage: 12 MB
% 0.37/0.51 % (1296410)Instructions burned: 7 (million)
% 0.37/0.51 % (1296400)...printing done.
% 0.37/0.51 % (1296416)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=3885531915:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.37/0.51 % (1296400)Refutation found. Thanks to Tanya!
% 0.37/0.51 % SZS status Theorem for theBenchmark
% 0.37/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.51 % (1296400)------------------------------
% 0.37/0.51 % (1296400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.51 % (1296400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.51 % (1296400)CaDiCaL version: 2.1.3
% 0.37/0.51 % (1296400)Termination reason: Refutation
% 0.37/0.51 % (1296400)Time elapsed: 0.061 s
% 0.37/0.51 % (1296400)Peak memory usage: 12 MB
% 0.37/0.51 % (1296400)Instructions burned: 51 (million)
% 0.37/0.51 % (1296389)Success in time 0.12 s
% 0.37/0.51 % Vampire exiting
%------------------------------------------------------------------------------