%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU655^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:30:32 AM UTC 2026
% Result : Theorem 5.27s 1.15s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 37
% Syntax : Number of formulae : 275 ( 85 unt; 0 typ; 29 def)
% Number of atoms : 2836 ( 626 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 4115 ( 295 ~; 465 |; 68 &;3030 @)
% ( 21 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 64 ( 59 usr; 40 con; 0-4 aty)
% ( 85 !!; 38 ??; 0 @@+; 0 @@-)
% Number of variables : 506 ( 0 sgn 182 !; 8 ?; 506 :)
% 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,
iskpair: $i > $o ).
thf(func_def_7,type,
kpair: $i > $i > $i ).
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,
kfst: $i > $i ).
thf(func_def_12,type,
kfstpairEq: $o ).
thf(func_def_13,type,
setukpairinjR: $o ).
thf(func_def_14,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
sF1: $o ).
thf(func_def_28,type,
sF2: $o ).
thf(func_def_29,type,
sF3: $o ).
thf(func_def_30,type,
sF4: $o ).
thf(func_def_34,type,
sF8: $o ).
thf(func_def_35,type,
sK9: ( $i > $o ) > $i > $i > $i ).
thf(func_def_36,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_39,type,
sK13: $i > $o ).
thf(f1,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(f2,axiom,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f4,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f5,axiom,
( ex1I
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(f6,axiom,
( kfstpairEq
= ( ! [X1: $i,X0: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f7,axiom,
( setukpairinjR
= ( ! [X1: $i,X0: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(f8,conjecture,
( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
thf(f9,negated_conjecture,
~ ( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( kfstpairEq
= ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f11,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f13,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
~ ( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f17,plain,
~ ( ( ex1I = $true )
=> ( ( kfstpairEq = $true )
=> ( ( setukpairinjR = $true )
=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X1 @ X0 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y1 @ Y0 )
= ( kpair @ Y2 @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ex1I
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( X0 @ X3 )
=> ( X1 = X3 ) ) )
=> ( ex1 @ X2
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f21,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f23,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
inference(rectify,[],[f3]) ).
thf(f24,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) ) ) )
& ( setukpairinjR = $true )
& ( kfstpairEq = $true )
& ( ex1I = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f26,plain,
( ( setukpairinjR = $true )
& ( ex1I = $true )
& ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) ) ) )
& ( kfstpairEq = $true ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( setukpairinjR = $true )
& ( ex1I = $true )
& ( ( iskpair @ sK0 )
= $true )
& ( ( singleton
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ sK0 ) @ Y0 )
= sK0 ) ) )
!= $true )
& ( kfstpairEq = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f26]) ).
thf(f28,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y1 @ Y0 )
= ( kpair @ Y2 @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f30,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f31,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f32,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f33,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
kfstpairEq = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f35,plain,
( ( singleton
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ sK0 ) @ Y0 )
= sK0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f36,plain,
( ( iskpair @ sK0 )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f37,plain,
ex1I = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f38,plain,
setukpairinjR = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f39,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f42,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,[],[f30,f39]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f38,f33,f33]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = 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] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f37,f42]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
= Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f32,f34,f33]) ).
thf(f46,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f36,f29]) ).
thf(f47,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] :
( ( ^ [Y1: $i,Y2: $i] : ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ sK0 )
@ Y0 )
= sK0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f35,f39,f33]) ).
thf(f48,definition,
( sF1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f49,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f48]) ).
thf(f50,plain,
$true = sF1,
inference(definition_folding,[],[f43,f49]) ).
thf(f51,definition,
( sF2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = 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] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f52,plain,
sF2 = $true,
inference(definition_folding,[],[f44,f51]) ).
thf(f53,definition,
( sF3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
= Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f54,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
= Y0 ) ) )
= sF3 ),
inference(reorient_equations,[],[f53]) ).
thf(f55,plain,
sF3 = $true,
inference(definition_folding,[],[f45,f54]) ).
thf(f56,definition,
( sF4
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f57,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ sK0 )
= sF4 ),
inference(reorient_equations,[],[f56]) ).
thf(f58,plain,
sF4 = $true,
inference(definition_folding,[],[f46,f57]) ).
thf(f59,definition,
( sF5
= ( setunion @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f60,definition,
( sF6
= ( kfst @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f61,definition,
( sF7
= ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( ^ [Y1: $i,Y2: $i] : ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
@ sF6
@ Y0 )
= sK0 ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f62,plain,
( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( ^ [Y1: $i,Y2: $i] : ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
@ sF6
@ Y0 )
= sK0 ) )
= sF7 ),
inference(reorient_equations,[],[f61]) ).
thf(f63,definition,
( sF8
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sF7 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f64,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sF7 )
= sF8 ),
inference(reorient_equations,[],[f63]) ).
thf(f65,plain,
sF8 != $true,
inference(definition_folding,[],[f47,f64,f62,f60,f59]) ).
thf(f67,plain,
( ( sF2 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = 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] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f51]) ).
thf(f68,plain,
! [X1: $i] :
( ( sF2 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = 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] : ( Y2 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y1 @ Y2 )
=> ( Y0 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ X1 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ) ) )
= $true )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y1 @ Y2 )
=> ( Y0 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ X1 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ( sF2 = $false ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( X2 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) ) )
= $true )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( sF2 = $false )
| ( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( X2 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( sF2 = $false )
| ( ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ( X3 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) ) ) ) )
= $true )
| ( sF2 = $false ) ),
inference(imp_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) ) ) ) )
| ( $false
= ( X3 @ X2 ) )
| ( sF2 = $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( sF2 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) ) )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) )
@ ( sK9 @ X3 @ X1 @ X2 ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) ) ) )
| ( sF2 = $false ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( sF2 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) )
@ ( sK10 @ X3 @ X1 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) )
@ ( sK9 @ X3 @ X1 @ X2 ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( ( in @ ( sK9 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
=> ( X2
= ( sK9 @ X3 @ X1 @ X2 ) ) ) )
= $false )
| ( $false
= ( X3 @ X2 ) )
| ( ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
=> ( X2
= ( sK9 @ X3 @ X1 @ X2 ) ) ) )
| ( $false
= ( X3 @ X2 ) )
| ( ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) )
= $true )
| ( sF2 = $false ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f85,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X2
= ( sK9 @ X3 @ X1 @ X2 ) ) )
| ( sF2 = $false )
| ( ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) )
= $true )
| ( $false
= ( X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f86,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( sF2 = $false )
| ( ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) )
= $true )
| ( $false
= ( X3 @ X2 ) )
| ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f87,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( sF2 = $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) )
| ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( sF2 = $false ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f89,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( $false
= ( X3 @ X2 ) )
| ( sF2 = $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( dsetconstr @ X1 @ X3 )
= ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f87]) ).
thf(f90,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( X3 @ X2 ) )
| ( ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
& ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) ) )
= $true )
| ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( ( in @ X2 @ X1 )
= $false )
| ( sF2 = $false ) ),
inference(equality_proxy_clausification,[],[f85]) ).
thf(f91,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset )
= ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( $false
= ( X3 @ X2 ) )
| ( sF2 = $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( sF2 = $false )
| ( $false
= ( X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f93,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( dsetconstr @ X1 @ X3 )
= ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset ) )
| ( sF2 = $false )
| ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f91]) ).
thf(f116,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sF7 )
= $false )
| ( sF8 = $true ) ),
inference(iff_proxy_clausification,[],[f64]) ).
thf(f117,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sF7 )
& ( ( setadjoin @ Y0 @ emptyset )
= sF7 ) ) )
= $false )
| ( sF8 = $true ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sF7 )
& ( ( setadjoin @ Y0 @ emptyset )
= sF7 ) )
@ X1 )
= $false )
| ( sF8 = $true ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X1: $i] :
( ( $false
= ( ( in @ X1 @ sF7 )
& ( ( setadjoin @ X1 @ emptyset )
= sF7 ) ) )
| ( sF8 = $true ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X1: $i] :
( ( ( ( setadjoin @ X1 @ emptyset )
= sF7 )
= $false )
| ( ( in @ X1 @ sF7 )
= $false )
| ( sF8 = $true ) ),
inference(and_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= sF7 )
| ( sF8 = $true )
| ( ( in @ X1 @ sF7 )
= $false ) ),
inference(equality_proxy_clausification,[],[f120]) ).
thf(f128,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ sK0 )
= $true )
| ( sF4 = $false ) ),
inference(iff_proxy_clausification,[],[f57]) ).
thf(f138,plain,
( ( sF4 = $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y1 @ ( setunion @ sK0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f139,plain,
( ( sF4 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y1 @ ( setunion @ sK0 ) ) ) ) )
@ sK15 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( $true
= ( ( in @ sK15 @ ( setunion @ sK0 ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) ) ) )
| ( sF4 = $false ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
= $true )
| ( sF4 = $false ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( ( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK16 )
= $true )
| ( sF4 = $false ) ),
inference(sigma_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( ( sF4 = $false )
| ( ( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ sK16 @ ( setunion @ sK0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
( ( sF4 = $false )
| ( ( in @ sK16 @ ( setunion @ sK0 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 )
= $true )
| ( sF4 = $false ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f147,plain,
( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 )
| ( sF4 = $false ) ),
inference(equality_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= sF7 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f149,plain,
( ( $false = sF3 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
= Y0 ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f54]) ).
thf(f156,plain,
! [X1: $i] :
( ( $false = sF3 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
= Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f157,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= X1 ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= X1 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( $false = sF3 )
| ( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
inference(equality_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f49]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) )
@ X1 )
= $true )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = X1 ) ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = X1 ) ) ) )
@ X2 )
= $true )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) ) ) )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) )
@ X4 )
= $true )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF1 )
| ( ( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( X4 = X1 )
= $true )
| ( $false = sF1 )
| ( $false
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( X1 = X4 )
| ( $false = sF1 )
| ( $false
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(equality_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( X1 = X4 )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( $false = sF1 ) ),
inference(equality_proxy_clausification,[],[f184]) ).
thf(f187,definition,
( spl23_1
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
thf(f189,plain,
( ( sF2 = $false )
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f199,definition,
( spl23_4
<=> ! [X2: $i,X1: $i,X3: $i > $o] :
( ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl23_4])],[avatar_definition]) ).
thf(f200,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true ) )
| ~ spl23_4 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f201,plain,
( spl23_1
| spl23_4 ),
inference(avatar_split_clause,[],[f88,f199,f187]) ).
thf(f203,definition,
( spl23_5
<=> ! [X2: $i,X1: $i,X3: $i > $o] :
( ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( dsetconstr @ X1 @ X3 )
= ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
thf(f204,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( dsetconstr @ X1 @ X3 )
= ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset ) )
| ( ( X3 @ ( sK9 @ X3 @ X1 @ X2 ) )
= $true )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false ) )
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f205,plain,
( spl23_5
| spl23_1 ),
inference(avatar_split_clause,[],[f89,f187,f203]) ).
thf(f207,definition,
( spl23_6
<=> ! [X2: $i,X1: $i,X3: $i > $o] :
( ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition]) ).
thf(f208,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ ( sK10 @ X3 @ X1 ) @ ( dsetconstr @ X1 @ X3 ) )
= $true ) )
| ~ spl23_6 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f209,plain,
( spl23_1
| spl23_6 ),
inference(avatar_split_clause,[],[f92,f207,f187]) ).
thf(f211,definition,
( spl23_7
<=> ! [X2: $i,X1: $i,X3: $i > $o] :
( ( ( dsetconstr @ X1 @ X3 )
= ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset ) )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_7])],[avatar_definition]) ).
thf(f212,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( sK9 @ X3 @ X1 @ X2 )
!= X2 )
| ( ( dsetconstr @ X1 @ X3 )
= ( setadjoin @ ( sK10 @ X3 @ X1 ) @ emptyset ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( X3 @ X2 ) ) )
| ~ spl23_7 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f213,plain,
( spl23_7
| spl23_1 ),
inference(avatar_split_clause,[],[f93,f187,f211]) ).
thf(f215,definition,
( spl23_8
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition]) ).
thf(f217,plain,
( ( sF2 = $true )
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f237,definition,
( spl23_13
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_13])],[avatar_definition]) ).
thf(f241,definition,
( spl23_14
<=> ! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= sF7 )
| ( ( in @ X1 @ sF7 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl23_14])],[avatar_definition]) ).
thf(f242,plain,
( ! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= sF7 )
| ( ( in @ X1 @ sF7 )
= $false ) )
| ~ spl23_14 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl23_13
| spl23_14 ),
inference(avatar_split_clause,[],[f121,f241,f237]) ).
thf(f262,definition,
( spl23_19
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_19])],[avatar_definition]) ).
thf(f264,plain,
( ( sF4 = $true )
| ~ spl23_19 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f271,definition,
( spl23_21
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl23_21])],[avatar_definition]) ).
thf(f273,plain,
( ( sF4 = $false )
| ~ spl23_21 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f276,definition,
( spl23_22
<=> ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl23_22])],[avatar_definition]) ).
thf(f278,plain,
( ( ( setadjoin @ ( setadjoin @ sK15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK15 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 )
| ~ spl23_22 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f279,plain,
( spl23_21
| spl23_22 ),
inference(avatar_split_clause,[],[f147,f276,f271]) ).
thf(f281,definition,
( spl23_23
<=> ( ( in @ sK16 @ ( setunion @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl23_23])],[avatar_definition]) ).
thf(f283,plain,
( ( ( in @ sK16 @ ( setunion @ sK0 ) )
= $true )
| ~ spl23_23 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f284,plain,
( spl23_21
| spl23_23 ),
inference(avatar_split_clause,[],[f145,f281,f271]) ).
thf(f285,plain,
spl23_19,
inference(avatar_split_clause,[],[f58,f262]) ).
thf(f287,definition,
( spl23_24
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_24])],[avatar_definition]) ).
thf(f289,plain,
( ( sF3 = $true )
| ~ spl23_24 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f296,definition,
( spl23_26
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl23_26])],[avatar_definition]) ).
thf(f298,plain,
( ( $false = sF3 )
| ~ spl23_26 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f300,definition,
( spl23_27
<=> ! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl23_27])],[avatar_definition]) ).
thf(f301,plain,
( ! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 )
| ~ spl23_27 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f302,plain,
( spl23_26
| spl23_27 ),
inference(avatar_split_clause,[],[f160,f300,f296]) ).
thf(f304,definition,
( spl23_28
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl23_28])],[avatar_definition]) ).
thf(f306,plain,
( ( $true = sF1 )
| ~ spl23_28 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f318,definition,
( spl23_31
<=> ! [X2: $i,X4: $i,X3: $i,X1: $i] :
( ( X1 = X4 )
| ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_31])],[avatar_definition]) ).
thf(f319,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( X1 = X4 ) )
| ~ spl23_31 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f321,definition,
( spl23_32
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl23_32])],[avatar_definition]) ).
thf(f323,plain,
( ( $false = sF1 )
| ~ spl23_32 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f324,plain,
( spl23_31
| spl23_32 ),
inference(avatar_split_clause,[],[f185,f321,f318]) ).
thf(f325,plain,
~ spl23_13,
inference(avatar_split_clause,[],[f65,f237]) ).
thf(f326,plain,
spl23_8,
inference(avatar_split_clause,[],[f52,f215]) ).
thf(f327,plain,
spl23_28,
inference(avatar_split_clause,[],[f50,f304]) ).
thf(f328,plain,
spl23_24,
inference(avatar_split_clause,[],[f55,f287]) ).
thf(f330,plain,
( ( $false = $true )
| ~ spl23_24
| ~ spl23_26 ),
inference(superposition,[],[f289,f298]) ).
thf(f333,plain,
( $false
| ~ spl23_24
| ~ spl23_26 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f334,plain,
( ~ spl23_24
| ~ spl23_26 ),
inference(avatar_contradiction_clause,[],[f333]) ).
thf(f337,plain,
( ( $false = $true )
| ~ spl23_19
| ~ spl23_21 ),
inference(superposition,[],[f273,f264]) ).
thf(f341,plain,
( $false
| ~ spl23_19
| ~ spl23_21 ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f342,plain,
( ~ spl23_19
| ~ spl23_21 ),
inference(avatar_contradiction_clause,[],[f341]) ).
thf(f345,plain,
( ( $true
= ( in @ sK16 @ sF5 ) )
| ~ spl23_23 ),
inference(forward_demodulation,[],[f283,f59]) ).
thf(f347,plain,
( ( ( kfst @ sK0 )
= sK15 )
| ~ spl23_22
| ~ spl23_27 ),
inference(superposition,[],[f301,f278]) ).
thf(f351,plain,
( ( sF6 = sK15 )
| ~ spl23_22
| ~ spl23_27 ),
inference(forward_demodulation,[],[f347,f60]) ).
thf(f352,plain,
( ( sK0
= ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) ) )
| ~ spl23_22
| ~ spl23_27 ),
inference(superposition,[],[f278,f351]) ).
thf(f360,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= sK0 )
| ( sK16 = X1 ) )
| ~ spl23_22
| ~ spl23_31 ),
inference(superposition,[],[f319,f278]) ).
thf(f391,definition,
( spl23_35
<=> ! [X0: $i] :
( ( ( in @ X0 @ sF5 )
= $false )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
!= sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_35])],[avatar_definition]) ).
thf(f392,plain,
( ! [X0: $i] :
( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
!= sK0 )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ( ( in @ X0 @ sF5 )
= $false ) )
| ~ spl23_35 ),
inference(avatar_component_clause,[],[f391]) ).
thf(f394,definition,
( spl23_36
<=> ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl23_36])],[avatar_definition]) ).
thf(f396,plain,
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ~ spl23_36 ),
inference(avatar_component_clause,[],[f394]) ).
thf(f398,plain,
( ( $false = $true )
| ~ spl23_1
| ~ spl23_8 ),
inference(superposition,[],[f189,f217]) ).
thf(f402,plain,
( $false
| ~ spl23_1
| ~ spl23_8 ),
inference(trivial_inequality_removal,[],[f398]) ).
thf(f403,plain,
( ~ spl23_1
| ~ spl23_8 ),
inference(avatar_contradiction_clause,[],[f402]) ).
thf(f412,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 ) )
= $true )
| ( ( in @ X0 @ sF5 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ X0 ) )
| ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true ) )
| ~ spl23_4 ),
inference(superposition,[],[f200,f148]) ).
thf(f413,plain,
( ! [X0: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
| ( ( in @ X0 @ sF5 )
= $false )
| ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ( $true
= ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 ) ) )
| ~ spl23_4 ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f414,plain,
( ! [X0: $i] :
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
!= sK0 )
| ( $true
= ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 ) )
| ( ( in @ X0 @ sF5 )
= $false ) )
| ~ spl23_4 ),
inference(equality_proxy_clausification,[],[f413]) ).
thf(f415,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF5 )
= $false )
| ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
!= sK0 ) )
| ~ spl23_4 ),
inference(equality_proxy_clausification,[],[f414]) ).
thf(f416,plain,
( spl23_36
| spl23_35
| ~ spl23_4 ),
inference(avatar_split_clause,[],[f415,f199,f391,f394]) ).
thf(f419,plain,
( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( dsetconstr @ X0 @ X1 )
!= sF7 )
| ( ( in @ ( sK10 @ X1 @ X0 ) @ sF7 )
= $false )
| ( ( X1 @ X2 )
= $false )
| ( ( X1 @ ( sK9 @ X1 @ X0 @ X2 ) )
= $true )
| ( ( in @ X2 @ X0 )
= $false ) )
| ~ spl23_5
| ~ spl23_14 ),
inference(superposition,[],[f242,f204]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 ) )
= $true )
| ( sF7 != sF7 )
| ( ( in @ X0 @ sF5 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ X0 ) ) )
| ~ spl23_5
| ~ spl23_14 ),
inference(superposition,[],[f419,f148]) ).
thf(f430,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ X0 ) )
| ( ( in @ X0 @ sF5 )
= $false )
| ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) ) )
| ~ spl23_5
| ~ spl23_14 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f431,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF5 )
= $false )
| ( $true
= ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 ) )
| ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ( $false
= ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
| ~ spl23_5
| ~ spl23_14 ),
inference(beta-eta_normalization,[],[f430]) ).
thf(f432,plain,
( ! [X0: $i] :
( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ( $false
= ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
| ( ( in @ X0 @ sF5 )
= $false ) )
| ~ spl23_5
| ~ spl23_14 ),
inference(equality_proxy_clausification,[],[f431]) ).
thf(f433,plain,
( ! [X0: $i] :
( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
!= sK0 )
| ( ( in @ X0 @ sF5 )
= $false )
| ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ X0 )
@ emptyset ) )
@ emptyset ) )
= sK0 ) )
| ~ spl23_5
| ~ spl23_14 ),
inference(equality_proxy_clausification,[],[f432]) ).
thf(f435,definition,
( spl23_38
<=> ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_38])],[avatar_definition]) ).
thf(f437,plain,
( ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ~ spl23_38 ),
inference(avatar_component_clause,[],[f435]) ).
thf(f438,plain,
( spl23_38
| spl23_35
| ~ spl23_5
| ~ spl23_14 ),
inference(avatar_split_clause,[],[f433,f241,f203,f391,f435]) ).
thf(f806,plain,
( ( sK0 != sK0 )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ sK16 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_22
| ~ spl23_27
| ~ spl23_35 ),
inference(superposition,[],[f392,f352]) ).
thf(f807,plain,
( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ sK16 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_22
| ~ spl23_27
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f806]) ).
thf(f808,plain,
( ( $false = $true )
| ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ sK16 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_35 ),
inference(forward_demodulation,[],[f807,f345]) ).
thf(f809,plain,
( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset )
@ ( setadjoin
@ ( setadjoin @ sF6
@ ( setadjoin
@ ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ sK16 )
@ emptyset ) )
@ emptyset ) )
= sK0 )
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f808]) ).
thf(f815,plain,
( ( ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ sK16 )
= sK16 )
| ( sK0 != sK0 )
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(superposition,[],[f360,f809]) ).
thf(f832,plain,
( ( ( sK9
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5
@ sK16 )
= sK16 )
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f815]) ).
thf(f863,plain,
( ( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ( sK16 != sK16 )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sK16 )
= $false )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(superposition,[],[f212,f832]) ).
thf(f864,plain,
( ( $false
= ( in @ sK16 @ sF5 ) )
| ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sK16 )
= $false )
| ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
= $true )
| ( sK16 != sK16 )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(superposition,[],[f208,f832]) ).
thf(f865,plain,
( ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sK16 )
= $false )
| ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
= $true )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f864]) ).
thf(f866,plain,
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 )
= $false )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(beta-eta_normalization,[],[f865]) ).
thf(f867,plain,
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
= $true )
| ( sK0
!= ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(equality_proxy_clausification,[],[f866]) ).
thf(f868,plain,
( ( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sK16 )
= $false )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f863]) ).
thf(f869,plain,
( ( ( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) )
= sK0 )
= $false )
| ( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(beta-eta_normalization,[],[f868]) ).
thf(f870,plain,
( ( sK0
!= ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ sK16 @ emptyset ) ) @ emptyset ) ) )
| ( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(equality_proxy_clausification,[],[f869]) ).
thf(f871,plain,
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
= $true )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(forward_subsumption_resolution,[],[f867,f352]) ).
thf(f872,plain,
( ( ( dsetconstr @ sF5
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(forward_subsumption_resolution,[],[f870,f352]) ).
thf(f873,plain,
( ( $false
= ( in @ sK16 @ sF5 ) )
| ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(forward_demodulation,[],[f871,f148]) ).
thf(f874,plain,
( ( sF7
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ( $false
= ( in @ sK16 @ sF5 ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(forward_demodulation,[],[f872,f148]) ).
thf(f875,plain,
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ( $false = $true )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(forward_demodulation,[],[f873,f345]) ).
thf(f876,plain,
( ( ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 )
= $true )
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f875]) ).
thf(f877,plain,
( ( $false = $true )
| ( sF7
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(forward_demodulation,[],[f874,f345]) ).
thf(f878,plain,
( ( sF7
= ( setadjoin
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ emptyset ) )
| ~ spl23_7
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f877]) ).
thf(f879,plain,
( spl23_36
| ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(avatar_split_clause,[],[f876,f391,f318,f300,f281,f276,f207,f394]) ).
thf(f880,plain,
( ( $false = $true )
| ~ spl23_28
| ~ spl23_32 ),
inference(superposition,[],[f323,f306]) ).
thf(f884,plain,
( $false
| ~ spl23_28
| ~ spl23_32 ),
inference(trivial_inequality_removal,[],[f880]) ).
thf(f885,plain,
( ~ spl23_28
| ~ spl23_32 ),
inference(avatar_contradiction_clause,[],[f884]) ).
thf(f927,plain,
( ( sF7 != sF7 )
| ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ~ spl23_7
| ~ spl23_14
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(superposition,[],[f242,f878]) ).
thf(f955,plain,
( ( $false
= ( in
@ ( sK10
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ sF6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sF6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
@ sF5 )
@ sF7 ) )
| ~ spl23_7
| ~ spl23_14
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(trivial_inequality_removal,[],[f927]) ).
thf(f976,plain,
( spl23_38
| ~ spl23_7
| ~ spl23_14
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35 ),
inference(avatar_split_clause,[],[f955,f391,f318,f300,f281,f276,f241,f211,f435]) ).
thf(f1064,plain,
( ( $false = $true )
| ~ spl23_36
| ~ spl23_38 ),
inference(superposition,[],[f396,f437]) ).
thf(f1065,plain,
( $false
| ~ spl23_36
| ~ spl23_38 ),
inference(trivial_inequality_removal,[],[f1064]) ).
thf(f1066,plain,
( ~ spl23_36
| ~ spl23_38 ),
inference(avatar_contradiction_clause,[],[f1065]) ).
cnf(s3,plain,
( spl23_1
| spl23_4 ),
inference(sat_conversion,[],[f201]) ).
cnf(s4,plain,
( spl23_1
| spl23_5 ),
inference(sat_conversion,[],[f205]) ).
cnf(s5,plain,
( spl23_1
| spl23_6 ),
inference(sat_conversion,[],[f209]) ).
cnf(s6,plain,
( spl23_1
| spl23_7 ),
inference(sat_conversion,[],[f213]) ).
cnf(s11,plain,
( spl23_13
| spl23_14 ),
inference(sat_conversion,[],[f243]) ).
cnf(s16,plain,
( spl23_21
| spl23_22 ),
inference(sat_conversion,[],[f279]) ).
cnf(s17,plain,
( spl23_21
| spl23_23 ),
inference(sat_conversion,[],[f284]) ).
cnf(s18,plain,
spl23_19,
inference(sat_conversion,[],[f285]) ).
cnf(s20,plain,
( spl23_26
| spl23_27 ),
inference(sat_conversion,[],[f302]) ).
cnf(s23,plain,
( spl23_31
| spl23_32 ),
inference(sat_conversion,[],[f324]) ).
cnf(s24,plain,
~ spl23_13,
inference(sat_conversion,[],[f325]) ).
cnf(s25,plain,
spl23_8,
inference(sat_conversion,[],[f326]) ).
cnf(s26,plain,
spl23_28,
inference(sat_conversion,[],[f327]) ).
cnf(s27,plain,
spl23_24,
inference(sat_conversion,[],[f328]) ).
cnf(s29,plain,
( ~ spl23_24
| ~ spl23_26 ),
inference(sat_conversion,[],[f334]) ).
cnf(s31,plain,
( ~ spl23_19
| ~ spl23_21 ),
inference(sat_conversion,[],[f342]) ).
cnf(s37,plain,
( ~ spl23_1
| ~ spl23_8 ),
inference(sat_conversion,[],[f403]) ).
cnf(s39,plain,
( ~ spl23_4
| spl23_35
| spl23_36 ),
inference(sat_conversion,[],[f416]) ).
cnf(s40,plain,
( ~ spl23_5
| ~ spl23_14
| spl23_35
| spl23_38 ),
inference(sat_conversion,[],[f438]) ).
cnf(s63,plain,
( ~ spl23_6
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35
| spl23_36 ),
inference(sat_conversion,[],[f879]) ).
cnf(s65,plain,
( ~ spl23_28
| ~ spl23_32 ),
inference(sat_conversion,[],[f885]) ).
cnf(s72,plain,
( ~ spl23_7
| ~ spl23_14
| ~ spl23_22
| ~ spl23_23
| ~ spl23_27
| ~ spl23_31
| ~ spl23_35
| spl23_38 ),
inference(sat_conversion,[],[f976]) ).
cnf(s96,plain,
( ~ spl23_36
| ~ spl23_38 ),
inference(sat_conversion,[],[f1066]) ).
cnf(s98,plain,
~ spl23_26,
inference(rat,[],[s29,s27]) ).
cnf(s99,plain,
~ spl23_32,
inference(rat,[],[s65,s26]) ).
cnf(s100,plain,
~ spl23_1,
inference(rat,[],[s37,s25]) ).
cnf(s101,plain,
spl23_31,
inference(rat,[],[s23,s99]) ).
cnf(s102,plain,
spl23_27,
inference(rat,[],[s20,s98]) ).
cnf(s104,plain,
~ spl23_21,
inference(rat,[],[s31,s18]) ).
cnf(s105,plain,
spl23_23,
inference(rat,[],[s17,s104]) ).
cnf(s106,plain,
spl23_22,
inference(rat,[],[s16,s104]) ).
cnf(s108,plain,
spl23_14,
inference(rat,[],[s11,s24]) ).
cnf(s109,plain,
spl23_7,
inference(rat,[],[s6,s100]) ).
cnf(s110,plain,
spl23_6,
inference(rat,[],[s5,s100]) ).
cnf(s111,plain,
spl23_5,
inference(rat,[],[s4,s100]) ).
cnf(s112,plain,
spl23_4,
inference(rat,[],[s3,s100]) ).
cnf(s115,plain,
spl23_35,
inference(rat,[],[s96,s40,s39,s108,s111,s112]) ).
cnf(s121,plain,
spl23_36,
inference(rat,[],[s63,s110,s106,s101,s102,s105,s115]) ).
cnf(s122,plain,
spl23_38,
inference(rat,[],[s72,s109,s108,s101,s102,s105,s106,s115]) ).
cnf(s127,plain,
$false,
inference(rat,[],[s96,s122,s121]) ).
thf(f1069,plain,
$false,
inference(avatar_sat_refutation,[],[s127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU655^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.20 % Computer : n020.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 14:04:05 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 Running higher-order theorem proving
% 0.12/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.41 % (1105508)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.41 % (1105519)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.41 % (1105519)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
% 0.68/0.41 % (1105519)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=1440386099:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.41 % (1105513)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1867986176:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.41 % (1105517)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3389198279:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.41 % (1105518)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=306971435:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.41 % (1105516)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=922621123: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)
% 0.68/0.41 % (1105515)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3248331261:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.41 % (1105514)lrs+10_16_si=on:nwc=1.5:random_seed=3052403195:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.41 % (1105515)Instruction limit reached!
% 0.68/0.41 % (1105515)------------------------------
% 0.68/0.41 % (1105515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.41 % (1105515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.41 % (1105515)CaDiCaL version: 2.1.3
% 0.68/0.41 % (1105515)Termination reason: Instruction limit
% 0.68/0.41 % (1105515)Termination phase: Saturation
% 0.68/0.41 % (1105515)Time elapsed: 0.003 s
% 0.68/0.41 % (1105515)Peak memory usage: 11 MB
% 0.68/0.41 % (1105515)Instructions burned: 5 (million)
% 0.68/0.41 % (1105517)Instruction limit reached!
% 0.68/0.41 % (1105517)------------------------------
% 0.68/0.41 % (1105517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.41 % (1105517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.41 % (1105517)CaDiCaL version: 2.1.3
% 0.68/0.41 % (1105517)Termination reason: Instruction limit
% 0.68/0.41 % (1105517)Termination phase: Saturation
% 0.68/0.41 % (1105517)Time elapsed: 0.015 s
% 0.68/0.41 % (1105517)Peak memory usage: 12 MB
% 0.68/0.41 % (1105517)Instructions burned: 24 (million)
% 0.68/0.41 % (1105514)Instruction limit reached!
% 0.68/0.41 % (1105514)------------------------------
% 0.68/0.41 % (1105514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.41 % (1105514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.41 % (1105514)CaDiCaL version: 2.1.3
% 0.68/0.41 % (1105514)Termination reason: Instruction limit
% 0.68/0.41 % (1105514)Termination phase: Saturation
% 0.68/0.41 % (1105514)Time elapsed: 0.013 s
% 0.68/0.41 % (1105514)Peak memory usage: 12 MB
% 0.68/0.41 % (1105514)Instructions burned: 18 (million)
% 0.68/0.41 % (1105527)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2557340604:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.41 % (1105527)Instruction limit reached!
% 0.68/0.41 % (1105527)------------------------------
% 0.68/0.41 % (1105527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.41 % (1105527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.41 % (1105527)CaDiCaL version: 2.1.3
% 0.68/0.41 % (1105527)Termination reason: Instruction limit
% 0.68/0.41 % (1105527)Termination phase: Property scanning
% 0.68/0.41 % (1105527)Time elapsed: 0.002 s
% 0.68/0.41 % (1105527)Peak memory usage: 10 MB
% 0.68/0.41 % (1105527)Instructions burned: 3 (million)
% 0.68/0.41 % (1105529)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.45 % (1105518)Instruction limit reached!
% 0.68/0.45 % (1105518)------------------------------
% 0.68/0.45 % (1105518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1105518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1105518)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1105518)Termination reason: Instruction limit
% 0.68/0.45 % (1105518)Termination phase: Saturation
% 0.68/0.45 % (1105518)Time elapsed: 0.041 s
% 0.68/0.45 % (1105518)Peak memory usage: 13 MB
% 0.68/0.45 % (1105518)Instructions burned: 76 (million)
% 0.68/0.45 % (1105528)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1781338107:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.45 % (1105529)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1020775363:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.45 % (1105513)Instruction limit reached!
% 0.68/0.45 % (1105513)------------------------------
% 0.68/0.45 % (1105513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1105513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1105513)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1105513)Termination reason: Instruction limit
% 0.68/0.45 % (1105513)Termination phase: Saturation
% 0.68/0.45 % (1105513)Time elapsed: 0.044 s
% 0.68/0.45 % (1105513)Peak memory usage: 13 MB
% 0.68/0.45 % (1105513)Instructions burned: 87 (million)
% 0.68/0.45 % (1105528)Instruction limit reached!
% 0.68/0.45 % (1105528)------------------------------
% 0.68/0.45 % (1105528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1105528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1105528)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1105528)Termination reason: Instruction limit
% 0.68/0.45 % (1105528)Termination phase: Saturation
% 0.68/0.45 % (1105528)Time elapsed: 0.007 s
% 0.68/0.45 % (1105528)Peak memory usage: 11 MB
% 0.68/0.45 % (1105528)Instructions burned: 6 (million)
% 0.68/0.45 % (1105529)Instruction limit reached!
% 0.68/0.45 % (1105529)------------------------------
% 0.68/0.45 % (1105529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1105529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1105529)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1105529)Termination reason: Instruction limit
% 0.68/0.45 % (1105529)Termination phase: Saturation
% 0.68/0.45 % (1105529)Time elapsed: 0.005 s
% 0.68/0.45 % (1105529)Peak memory usage: 12 MB
% 0.68/0.45 % (1105529)Instructions burned: 10 (million)
% 0.68/0.45 % (1105531)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=941322359:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.45 % (1105519)Instruction limit reached!
% 0.68/0.45 % (1105519)------------------------------
% 0.68/0.45 % (1105519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1105519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1105519)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1105519)Termination reason: Instruction limit
% 0.68/0.45 % (1105519)Termination phase: Saturation
% 0.68/0.45 % (1105519)Time elapsed: 0.061 s
% 0.68/0.45 % (1105519)Peak memory usage: 12 MB
% 0.68/0.45 % (1105519)Instructions burned: 158 (million)
% 0.68/0.45 % (1105534)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
% 0.68/0.45 % (1105534)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.45 % (1105531)Instruction limit reached!
% 0.68/0.45 % (1105531)------------------------------
% 0.68/0.45 % (1105531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1105531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1105531)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1105531)Termination reason: Instruction limit
% 0.68/0.45 % (1105531)Termination phase: Saturation
% 0.68/0.45 % (1105531)Time elapsed: 0.007 s
% 0.68/0.45 % (1105531)Peak memory usage: 12 MB
% 0.68/0.45 % (1105531)Instructions burned: 12 (million)
% 0.68/0.45 % (1105534)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=260692486:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.39/0.50 % (1105535)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=588162552:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.39/0.50 % (1105536)lrs+10_1_si=on:cs=on:random_seed=98231591:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.39/0.50 % (1105539)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1411009731:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.39/0.50 % (1105536)Instruction limit reached!
% 1.39/0.50 % (1105536)------------------------------
% 1.39/0.50 % (1105536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.50 % (1105536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.50 % (1105536)CaDiCaL version: 2.1.3
% 1.39/0.50 % (1105536)Termination reason: Instruction limit
% 1.39/0.50 % (1105536)Termination phase: Saturation
% 1.39/0.50 % (1105536)Time elapsed: 0.005 s
% 1.39/0.50 % (1105536)Peak memory usage: 11 MB
% 1.39/0.50 % (1105536)Instructions burned: 10 (million)
% 1.39/0.50 % (1105539)Refutation not found, incomplete strategy
% 1.39/0.50 % (1105539)------------------------------
% 1.39/0.50 % (1105539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.50 % (1105539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.50 % (1105539)CaDiCaL version: 2.1.3
% 1.39/0.50 % (1105539)Termination reason: Refutation not found, incomplete strategy
% 1.39/0.50 % (1105539)Time elapsed: 0.004 s
% 1.39/0.50 % (1105539)Peak memory usage: 12 MB
% 1.39/0.50 % (1105539)Instructions burned: 8 (million)
% 1.39/0.50 % (1105537)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.39/0.50 % (1105539)------------------------------
% 1.39/0.50 % (1105539)------------------------------
% 1.39/0.50 % (1105534)Instruction limit reached!
% 1.39/0.50 % (1105534)------------------------------
% 1.39/0.50 % (1105534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.50 % (1105534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.50 % (1105534)CaDiCaL version: 2.1.3
% 1.39/0.50 % (1105534)Termination reason: Instruction limit
% 1.39/0.50 % (1105534)Termination phase: Saturation
% 1.39/0.50 % (1105534)Time elapsed: 0.015 s
% 1.39/0.50 % (1105534)Peak memory usage: 12 MB
% 1.39/0.50 % (1105534)Instructions burned: 30 (million)
% 1.39/0.50 % (1105540)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1504293316:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.39/0.50 % (1105537)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2604024382:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.39/0.50 % (1105537)Instruction limit reached!
% 1.39/0.50 % (1105537)------------------------------
% 1.39/0.50 % (1105537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.50 % (1105537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.50 % (1105537)CaDiCaL version: 2.1.3
% 1.39/0.50 % (1105537)Termination reason: Instruction limit
% 1.39/0.50 % (1105537)Termination phase: Property scanning
% 1.39/0.50 % (1105537)Time elapsed: 0.003 s
% 1.39/0.50 % (1105537)Peak memory usage: 10 MB
% 1.39/0.50 % (1105537)Instructions burned: 3 (million)
% 1.39/0.50 % (1105545)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2704360881:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.39/0.50 % (1105546)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2776907830:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.39/0.50 % (1105547)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1008300172:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.39/0.50 % (1105546)Instruction limit reached!
% 1.39/0.50 % (1105546)------------------------------
% 1.39/0.50 % (1105546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105546)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105546)Termination reason: Instruction limit
% 1.39/0.57 % (1105546)Termination phase: Saturation
% 1.39/0.57 % (1105546)Time elapsed: 0.008 s
% 1.39/0.57 % (1105546)Peak memory usage: 12 MB
% 1.39/0.57 % (1105546)Instructions burned: 14 (million)
% 1.39/0.57 % (1105545)Instruction limit reached!
% 1.39/0.57 % (1105545)------------------------------
% 1.39/0.57 % (1105545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105545)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105545)Termination reason: Instruction limit
% 1.39/0.57 % (1105545)Termination phase: Saturation
% 1.39/0.57 % (1105545)Time elapsed: 0.016 s
% 1.39/0.57 % (1105545)Peak memory usage: 12 MB
% 1.39/0.57 % (1105545)Instructions burned: 26 (million)
% 1.39/0.57 % (1105535)Instruction limit reached!
% 1.39/0.57 % (1105535)------------------------------
% 1.39/0.57 % (1105535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105535)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105535)Termination reason: Instruction limit
% 1.39/0.57 % (1105535)Termination phase: Saturation
% 1.39/0.57 % (1105535)Time elapsed: 0.051 s
% 1.39/0.57 % (1105535)Peak memory usage: 12 MB
% 1.39/0.57 % (1105535)Instructions burned: 89 (million)
% 1.39/0.57 % (1105550)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1300834988:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.39/0.57 % (1105554)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3765512832:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.39/0.57 % (1105554)Instruction limit reached!
% 1.39/0.57 % (1105554)------------------------------
% 1.39/0.57 % (1105554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105554)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105554)Termination reason: Instruction limit
% 1.39/0.57 % (1105554)Termination phase: Twee Goal Transformation
% 1.39/0.57 % (1105554)Time elapsed: 0.002 s
% 1.39/0.57 % (1105554)Peak memory usage: 10 MB
% 1.39/0.57 % (1105554)Instructions burned: 3 (million)
% 1.39/0.57 % (1105556)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1964293030:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.39/0.57 % (1105555)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1531054753:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.39/0.57 % (1105550)Instruction limit reached!
% 1.39/0.57 % (1105550)------------------------------
% 1.39/0.57 % (1105550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105550)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105550)Termination reason: Instruction limit
% 1.39/0.57 % (1105550)Termination phase: Saturation
% 1.39/0.57 % (1105550)Time elapsed: 0.015 s
% 1.39/0.57 % (1105550)Peak memory usage: 12 MB
% 1.39/0.57 % (1105550)Instructions burned: 16 (million)
% 1.39/0.57 % (1105556)Instruction limit reached!
% 1.39/0.57 % (1105556)------------------------------
% 1.39/0.57 % (1105556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105556)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105556)Termination reason: Instruction limit
% 1.39/0.57 % (1105556)Termination phase: Saturation
% 1.39/0.57 % (1105556)Time elapsed: 0.011 s
% 1.39/0.57 % (1105556)Peak memory usage: 12 MB
% 1.39/0.57 % (1105556)Instructions burned: 25 (million)
% 1.39/0.57 % (1105555)Instruction limit reached!
% 1.39/0.57 % (1105555)------------------------------
% 1.39/0.57 % (1105555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.57 % (1105555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.57 % (1105555)CaDiCaL version: 2.1.3
% 1.39/0.57 % (1105555)Termination reason: Instruction limit
% 1.39/0.57 % (1105555)Termination phase: Saturation
% 2.54/0.66 % (1105555)Time elapsed: 0.015 s
% 2.54/0.66 % (1105555)Peak memory usage: 12 MB
% 2.54/0.66 % (1105555)Instructions burned: 28 (million)
% 2.54/0.66 % (1105560)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1074344550:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.54/0.66 % (1105562)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 2.54/0.66 % (1105562)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.54/0.66 % (1105564)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2343128491:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.54/0.66 % (1105563)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.54/0.66 % (1105562)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=971935918:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.54/0.66 % (1105563)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1055147962:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.54/0.66 % (1105564)Instruction limit reached!
% 2.54/0.66 % (1105564)------------------------------
% 2.54/0.66 % (1105564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.66 % (1105564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.66 % (1105564)CaDiCaL version: 2.1.3
% 2.54/0.66 % (1105564)Termination reason: Instruction limit
% 2.54/0.66 % (1105564)Termination phase: Saturation
% 2.54/0.66 % (1105564)Time elapsed: 0.016 s
% 2.54/0.66 % (1105564)Peak memory usage: 12 MB
% 2.54/0.66 % (1105564)Instructions burned: 31 (million)
% 2.54/0.66 % (1105560)Instruction limit reached!
% 2.54/0.66 % (1105560)------------------------------
% 2.54/0.66 % (1105560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.66 % (1105560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.66 % (1105560)CaDiCaL version: 2.1.3
% 2.54/0.66 % (1105560)Termination reason: Instruction limit
% 2.54/0.66 % (1105560)Termination phase: Saturation
% 2.54/0.66 % (1105560)Time elapsed: 0.033 s
% 2.54/0.66 % (1105560)Peak memory usage: 12 MB
% 2.54/0.66 % (1105560)Instructions burned: 61 (million)
% 2.54/0.66 % (1105563)Instruction limit reached!
% 2.54/0.66 % (1105563)------------------------------
% 2.54/0.66 % (1105563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.66 % (1105563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.66 % (1105563)CaDiCaL version: 2.1.3
% 2.54/0.66 % (1105563)Termination reason: Instruction limit
% 2.54/0.66 % (1105563)Termination phase: Saturation
% 2.54/0.66 % (1105563)Time elapsed: 0.004 s
% 2.54/0.66 % (1105563)Peak memory usage: 11 MB
% 2.54/0.66 % (1105563)Instructions burned: 8 (million)
% 2.54/0.66 % (1105562)Instruction limit reached!
% 2.54/0.66 % (1105562)------------------------------
% 2.54/0.66 % (1105562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.66 % (1105562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.66 % (1105562)CaDiCaL version: 2.1.3
% 2.54/0.66 % (1105562)Termination reason: Instruction limit
% 2.54/0.66 % (1105562)Termination phase: Saturation
% 2.54/0.66 % (1105562)Time elapsed: 0.013 s
% 2.54/0.66 % (1105562)Peak memory usage: 12 MB
% 2.54/0.66 % (1105562)Instructions burned: 14 (million)
% 2.54/0.66 % (1105570)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3364740037:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.54/0.66 % (1105569)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1474016837:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.54/0.66 % (1105570)Instruction limit reached!
% 2.54/0.66 % (1105570)------------------------------
% 2.54/0.66 % (1105570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.66 % (1105571)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3682228987:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.90/0.71 % (1105570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.71 % (1105570)CaDiCaL version: 2.1.3
% 2.90/0.71 % (1105570)Termination reason: Instruction limit
% 2.90/0.71 % (1105570)Termination phase: Saturation
% 2.90/0.71 % (1105570)Time elapsed: 0.006 s
% 2.90/0.71 % (1105570)Peak memory usage: 12 MB
% 2.90/0.71 % (1105570)Instructions burned: 26 (million)
% 2.90/0.71 % (1105572)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=864117662:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.90/0.71 % (1105569)Instruction limit reached!
% 2.90/0.71 % (1105569)------------------------------
% 2.90/0.71 % (1105569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.71 % (1105569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.71 % (1105569)CaDiCaL version: 2.1.3
% 2.90/0.71 % (1105569)Termination reason: Instruction limit
% 2.90/0.71 % (1105569)Termination phase: Saturation
% 2.90/0.71 % (1105569)Time elapsed: 0.005 s
% 2.90/0.71 % (1105569)Peak memory usage: 12 MB
% 2.90/0.71 % (1105569)Instructions burned: 9 (million)
% 2.90/0.71 % (1105571)Instruction limit reached!
% 2.90/0.71 % (1105571)------------------------------
% 2.90/0.71 % (1105571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.71 % (1105571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.71 % (1105571)CaDiCaL version: 2.1.3
% 2.90/0.71 % (1105571)Termination reason: Instruction limit
% 2.90/0.71 % (1105571)Termination phase: Saturation
% 2.90/0.71 % (1105571)Time elapsed: 0.012 s
% 2.90/0.71 % (1105571)Peak memory usage: 12 MB
% 2.90/0.71 % (1105571)Instructions burned: 20 (million)
% 2.90/0.71 % (1105577)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=496866069:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.90/0.71 % (1105578)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2935594475:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.90/0.71 % (1105540)Instruction limit reached!
% 2.90/0.71 % (1105540)------------------------------
% 2.90/0.71 % (1105540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.71 % (1105540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.71 % (1105540)CaDiCaL version: 2.1.3
% 2.90/0.71 % (1105540)Termination reason: Instruction limit
% 2.90/0.71 % (1105540)Termination phase: Saturation
% 2.90/0.71 % (1105540)Time elapsed: 0.147 s
% 2.90/0.71 % (1105540)Peak memory usage: 13 MB
% 2.90/0.71 % (1105540)Instructions burned: 250 (million)
% 2.90/0.71 % (1105579)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1130837599:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.90/0.71 % (1105582)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.90/0.71 % (1105582)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3907765429:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.90/0.71 % (1105577)Instruction limit reached!
% 2.90/0.71 % (1105577)------------------------------
% 2.90/0.71 % (1105577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.71 % (1105577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.71 % (1105577)CaDiCaL version: 2.1.3
% 2.90/0.71 % (1105577)Termination reason: Instruction limit
% 2.90/0.71 % (1105577)Termination phase: Saturation
% 2.90/0.71 % (1105577)Time elapsed: 0.042 s
% 2.90/0.71 % (1105577)Peak memory usage: 13 MB
% 2.90/0.71 % (1105577)Instructions burned: 145 (million)
% 2.90/0.71 % (1105579)Instruction limit reached!
% 2.90/0.71 % (1105579)------------------------------
% 2.90/0.71 % (1105579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.71 % (1105579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.71 % (1105579)CaDiCaL version: 2.1.3
% 2.90/0.71 % (1105579)Termination reason: Instruction limit
% 2.90/0.71 % (1105579)Termination phase: Saturation
% 2.90/0.71 % (1105579)Time elapsed: 0.037 s
% 2.90/0.71 % (1105579)Peak memory usage: 12 MB
% 2.90/0.71 % (1105579)Instructions burned: 42 (million)
% 3.24/0.83 % (1105582)Instruction limit reached!
% 3.24/0.83 % (1105582)------------------------------
% 3.24/0.83 % (1105582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (1105582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (1105582)CaDiCaL version: 2.1.3
% 3.24/0.83 % (1105582)Termination reason: Instruction limit
% 3.24/0.83 % (1105582)Termination phase: Saturation
% 3.24/0.83 % (1105582)Time elapsed: 0.007 s
% 3.24/0.83 % (1105582)Peak memory usage: 12 MB
% 3.24/0.83 % (1105582)Instructions burned: 8 (million)
% 3.24/0.83 % (1105585)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1414042793:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 3.24/0.83 % (1105586)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3401393092:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.24/0.83 % (1105587)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.24/0.83 % (1105587)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1067164815:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.24/0.83 % (1105587)Instruction limit reached!
% 3.24/0.83 % (1105587)------------------------------
% 3.24/0.83 % (1105587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (1105587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (1105587)CaDiCaL version: 2.1.3
% 3.24/0.83 % (1105587)Termination reason: Instruction limit
% 3.24/0.83 % (1105587)Termination phase: Saturation
% 3.24/0.83 % (1105587)Time elapsed: 0.006 s
% 3.24/0.83 % (1105587)Peak memory usage: 11 MB
% 3.24/0.83 % (1105587)Instructions burned: 7 (million)
% 3.24/0.83 % (1105547)Instruction limit reached!
% 3.24/0.83 % (1105547)------------------------------
% 3.24/0.83 % (1105547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (1105547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (1105547)CaDiCaL version: 2.1.3
% 3.24/0.83 % (1105547)Termination reason: Instruction limit
% 3.24/0.83 % (1105547)Termination phase: Saturation
% 3.24/0.83 % (1105547)Time elapsed: 0.223 s
% 3.24/0.83 % (1105547)Peak memory usage: 13 MB
% 3.24/0.83 % (1105547)Instructions burned: 327 (million)
% 3.24/0.83 % (1105585)Instruction limit reached!
% 3.24/0.83 % (1105585)------------------------------
% 3.24/0.83 % (1105585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (1105585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (1105585)CaDiCaL version: 2.1.3
% 3.24/0.83 % (1105585)Termination reason: Instruction limit
% 3.24/0.83 % (1105585)Termination phase: Saturation
% 3.24/0.83 % (1105585)Time elapsed: 0.050 s
% 3.24/0.83 % (1105585)Peak memory usage: 13 MB
% 3.24/0.83 % (1105585)Instructions burned: 182 (million)
% 3.24/0.83 % (1105593)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1431609576:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.24/0.83 % (1105591)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2048968344:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.24/0.83 % (1105593)Refutation not found, incomplete strategy
% 3.24/0.83 % (1105593)------------------------------
% 3.24/0.83 % (1105593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (1105593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (1105593)CaDiCaL version: 2.1.3
% 3.24/0.83 % (1105593)Termination reason: Refutation not found, incomplete strategy
% 3.24/0.83 % (1105593)Time elapsed: 0.006 s
% 3.24/0.83 % (1105593)Peak memory usage: 12 MB
% 3.24/0.83 % (1105593)Instructions burned: 23 (million)
% 3.24/0.83 % (1105593)------------------------------
% 3.24/0.83 % (1105593)------------------------------
% 3.24/0.83 % (1105596)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3274918538:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.72/0.91 % (1105591)Instruction limit reached!
% 3.72/0.91 % (1105591)------------------------------
% 3.72/0.91 % (1105591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.72/0.91 % (1105591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/0.91 % (1105591)CaDiCaL version: 2.1.3
% 3.72/0.91 % (1105591)Termination reason: Instruction limit
% 3.72/0.91 % (1105591)Termination phase: Saturation
% 3.72/0.91 % (1105591)Time elapsed: 0.021 s
% 3.72/0.91 % (1105591)Peak memory usage: 12 MB
% 3.72/0.91 % (1105591)Instructions burned: 23 (million)
% 3.72/0.91 % (1105578)Instruction limit reached!
% 3.72/0.91 % (1105578)------------------------------
% 3.72/0.91 % (1105578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.72/0.91 % (1105578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/0.91 % (1105578)CaDiCaL version: 2.1.3
% 3.72/0.91 % (1105578)Termination reason: Instruction limit
% 3.72/0.91 % (1105578)Termination phase: Saturation
% 3.72/0.91 % (1105578)Time elapsed: 0.137 s
% 3.72/0.91 % (1105578)Peak memory usage: 13 MB
% 3.72/0.91 % (1105578)Instructions burned: 193 (million)
% 3.72/0.91 % (1105592)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2435297326:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.72/0.91 % (1105592)Refutation not found, incomplete strategy
% 3.72/0.91 % (1105592)------------------------------
% 3.72/0.91 % (1105592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.72/0.91 % (1105592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/0.91 % (1105592)CaDiCaL version: 2.1.3
% 3.72/0.91 % (1105592)Termination reason: Refutation not found, incomplete strategy
% 3.72/0.91 % (1105592)Time elapsed: 0.009 s
% 3.72/0.91 % (1105592)Peak memory usage: 12 MB
% 3.72/0.91 % (1105592)Instructions burned: 16 (million)
% 3.72/0.91 % (1105592)------------------------------
% 3.72/0.91 % (1105592)------------------------------
% 3.72/0.91 % (1105586)Instruction limit reached!
% 3.72/0.91 % (1105586)------------------------------
% 3.72/0.91 % (1105586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.72/0.91 % (1105586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/0.91 % (1105586)CaDiCaL version: 2.1.3
% 3.72/0.91 % (1105586)Termination reason: Instruction limit
% 3.72/0.91 % (1105586)Termination phase: Saturation
% 3.72/0.91 % (1105586)Time elapsed: 0.087 s
% 3.72/0.91 % (1105586)Peak memory usage: 12 MB
% 3.72/0.91 % (1105586)Instructions burned: 169 (million)
% 3.72/0.91 % (1105601)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3923144279:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 3.72/0.91 % (1105598)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3733479571:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.72/0.91 % (1105602)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.72/0.91 % (1105600)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1969965670:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.72/0.91 % (1105602)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3728590174:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 3.72/0.91 % (1105600)Refutation not found, incomplete strategy
% 3.72/0.91 % (1105600)------------------------------
% 3.72/0.91 % (1105600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.72/0.91 % (1105600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/0.91 % (1105600)CaDiCaL version: 2.1.3
% 3.72/0.91 % (1105600)Termination reason: Refutation not found, incomplete strategy
% 3.72/0.91 % (1105600)Time elapsed: 0.005 s
% 3.72/0.91 % (1105600)Peak memory usage: 12 MB
% 3.72/0.91 % (1105600)Instructions burned: 4 (million)
% 3.72/0.91 % (1105600)------------------------------
% 3.72/0.91 % (1105600)------------------------------
% 3.72/0.91 % (1105601)Instruction limit reached!
% 3.72/0.91 % (1105601)------------------------------
% 5.27/1.07 % (1105601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (1105601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (1105601)CaDiCaL version: 2.1.3
% 5.27/1.07 % (1105601)Termination reason: Instruction limit
% 5.27/1.07 % (1105601)Termination phase: Saturation
% 5.27/1.07 % (1105601)Time elapsed: 0.013 s
% 5.27/1.07 % (1105601)Peak memory usage: 12 MB
% 5.27/1.07 % (1105601)Instructions burned: 22 (million)
% 5.27/1.07 % (1105608)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3267150572:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.27/1.07 % (1105516)Instruction limit reached!
% 5.27/1.07 % (1105516)------------------------------
% 5.27/1.07 % (1105516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (1105516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (1105516)CaDiCaL version: 2.1.3
% 5.27/1.07 % (1105516)Termination reason: Instruction limit
% 5.27/1.07 % (1105516)Termination phase: Saturation
% 5.27/1.07 % (1105516)Time elapsed: 0.436 s
% 5.27/1.07 % (1105516)Peak memory usage: 14 MB
% 5.27/1.07 % (1105516)Instructions burned: 635 (million)
% 5.27/1.07 % (1105598)Instruction limit reached!
% 5.27/1.07 % (1105598)------------------------------
% 5.27/1.07 % (1105598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (1105598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (1105598)CaDiCaL version: 2.1.3
% 5.27/1.07 % (1105598)Termination reason: Instruction limit
% 5.27/1.07 % (1105598)Termination phase: Saturation
% 5.27/1.07 % (1105598)Time elapsed: 0.044 s
% 5.27/1.07 % (1105598)Peak memory usage: 12 MB
% 5.27/1.07 % (1105598)Instructions burned: 46 (million)
% 5.27/1.07 % (1105607)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3220089267:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 5.27/1.07 % (1105607)Instruction limit reached!
% 5.27/1.07 % (1105607)------------------------------
% 5.27/1.07 % (1105607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (1105607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (1105607)CaDiCaL version: 2.1.3
% 5.27/1.07 % (1105607)Termination reason: Instruction limit
% 5.27/1.07 % (1105607)Termination phase: Saturation
% 5.27/1.07 % (1105607)Time elapsed: 0.009 s
% 5.27/1.07 % (1105607)Peak memory usage: 12 MB
% 5.27/1.07 % (1105607)Instructions burned: 13 (million)
% 5.27/1.07 % (1105613)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4134685509:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 5.27/1.07 % (1105612)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3399088061:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.27/1.07 % (1105610)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=322189160:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.27/1.07 % (1105608)Instruction limit reached!
% 5.27/1.07 % (1105608)------------------------------
% 5.27/1.07 % (1105608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (1105608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (1105608)CaDiCaL version: 2.1.3
% 5.27/1.07 % (1105608)Termination reason: Instruction limit
% 5.27/1.07 % (1105608)Termination phase: Saturation
% 5.27/1.07 % (1105608)Time elapsed: 0.081 s
% 5.27/1.07 % (1105608)Peak memory usage: 13 MB
% 5.27/1.07 % (1105608)Instructions burned: 67 (million)
% 5.27/1.07 % (1105602)Instruction limit reached!
% 5.27/1.07 % (1105602)------------------------------
% 5.27/1.07 % (1105602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.07 % (1105602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.07 % (1105602)CaDiCaL version: 2.1.3
% 5.27/1.07 % (1105602)Termination reason: Instruction limit
% 5.27/1.07 % (1105602)Termination phase: Saturation
% 5.27/1.07 % (1105602)Time elapsed: 0.108 s
% 5.27/1.07 % (1105602)Peak memory usage: 12 MB
% 5.27/1.07 % (1105602)Instructions burned: 201 (million)
% 5.27/1.07 % (1105618)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=153254667:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 5.27/1.15 % (1105612)Instruction limit reached!
% 5.27/1.15 % (1105612)------------------------------
% 5.27/1.15 % (1105612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105612)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105612)Termination reason: Instruction limit
% 5.27/1.15 % (1105612)Termination phase: Saturation
% 5.27/1.15 % (1105612)Time elapsed: 0.036 s
% 5.27/1.15 % (1105612)Peak memory usage: 12 MB
% 5.27/1.15 % (1105612)Instructions burned: 31 (million)
% 5.27/1.15 % (1105610)Instruction limit reached!
% 5.27/1.15 % (1105610)------------------------------
% 5.27/1.15 % (1105610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105610)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105610)Termination reason: Instruction limit
% 5.27/1.15 % (1105610)Termination phase: Saturation
% 5.27/1.15 % (1105610)Time elapsed: 0.039 s
% 5.27/1.15 % (1105610)Peak memory usage: 12 MB
% 5.27/1.15 % (1105610)Instructions burned: 51 (million)
% 5.27/1.15 % (1105617)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2983267159:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 5.27/1.15 % (1105627)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.27/1.15 % (1105627)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=350804338:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 5.27/1.15 % (1105618)Instruction limit reached!
% 5.27/1.15 % (1105618)------------------------------
% 5.27/1.15 % (1105618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105618)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105618)Termination reason: Instruction limit
% 5.27/1.15 % (1105618)Termination phase: Saturation
% 5.27/1.15 % (1105618)Time elapsed: 0.037 s
% 5.27/1.15 % (1105618)Peak memory usage: 12 MB
% 5.27/1.15 % (1105618)Instructions burned: 67 (million)
% 5.27/1.15 % (1105628)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1705922641:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.27/1.15 % (1105617)Instruction limit reached!
% 5.27/1.15 % (1105617)------------------------------
% 5.27/1.15 % (1105617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105617)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105617)Termination reason: Instruction limit
% 5.27/1.15 % (1105617)Termination phase: Saturation
% 5.27/1.15 % (1105617)Time elapsed: 0.031 s
% 5.27/1.15 % (1105617)Peak memory usage: 12 MB
% 5.27/1.15 % (1105617)Instructions burned: 34 (million)
% 5.27/1.15 % (1105631)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2601220023:cond=on:i=96:bd=all:rtra=on_2993 on theBenchmark for (2993ds/96Mi)
% 5.27/1.15 % (1105596)Instruction limit reached!
% 5.27/1.15 % (1105596)------------------------------
% 5.27/1.15 % (1105596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105596)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105596)Termination reason: Instruction limit
% 5.27/1.15 % (1105596)Termination phase: Saturation
% 5.27/1.15 % (1105596)Time elapsed: 0.247 s
% 5.27/1.15 % (1105596)Peak memory usage: 14 MB
% 5.27/1.15 % (1105596)Instructions burned: 858 (million)
% 5.27/1.15 % (1105613)Instruction limit reached!
% 5.27/1.15 % (1105613)------------------------------
% 5.27/1.15 % (1105613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105613)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105613)Termination reason: Instruction limit
% 5.27/1.15 % (1105613)Termination phase: Saturation
% 5.27/1.15 % (1105613)Time elapsed: 0.121 s
% 5.27/1.15 % (1105613)Peak memory usage: 13 MB
% 5.27/1.15 % (1105613)Instructions burned: 138 (million)
% 5.27/1.15 % (1105633)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1327300372:i=427:sd=1:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/427Mi)
% 5.27/1.15 % (1105635)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1932854004:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/874Mi)
% 5.27/1.15 % (1105636)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=442042036:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/515Mi)
% 5.27/1.15 % (1105631)Instruction limit reached!
% 5.27/1.15 % (1105631)------------------------------
% 5.27/1.15 % (1105631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105631)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105631)Termination reason: Instruction limit
% 5.27/1.15 % (1105631)Termination phase: Saturation
% 5.27/1.15 % (1105631)Time elapsed: 0.052 s
% 5.27/1.15 % (1105631)Peak memory usage: 12 MB
% 5.27/1.15 % (1105631)Instructions burned: 98 (million)
% 5.27/1.15 % (1105640)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2025897389:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 5.27/1.15 % (1105627)Instruction limit reached!
% 5.27/1.15 % (1105627)------------------------------
% 5.27/1.15 % (1105627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105627)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105627)Termination reason: Instruction limit
% 5.27/1.15 % (1105627)Termination phase: Saturation
% 5.27/1.15 % (1105627)Time elapsed: 0.108 s
% 5.27/1.15 % (1105627)Peak memory usage: 13 MB
% 5.27/1.15 % (1105627)Instructions burned: 180 (million)
% 5.27/1.15 % (1105642)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=978889316:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 5.27/1.15 % (1105642)Instruction limit reached!
% 5.27/1.15 % (1105642)------------------------------
% 5.27/1.15 % (1105642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105642)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105642)Termination reason: Instruction limit
% 5.27/1.15 % (1105642)Termination phase: Saturation
% 5.27/1.15 % (1105642)Time elapsed: 0.029 s
% 5.27/1.15 % (1105642)Peak memory usage: 12 MB
% 5.27/1.15 % (1105642)Instructions burned: 45 (million)
% 5.27/1.15 % (1105640)Instruction limit reached!
% 5.27/1.15 % (1105640)------------------------------
% 5.27/1.15 % (1105640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105640)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105640)Termination reason: Instruction limit
% 5.27/1.15 % (1105640)Termination phase: Saturation
% 5.27/1.15 % (1105640)Time elapsed: 0.068 s
% 5.27/1.15 % (1105640)Peak memory usage: 12 MB
% 5.27/1.15 % (1105640)Instructions burned: 131 (million)
% 5.27/1.15 % (1105644)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3647489702:s2a=on:i=571:nm=16:rtra=on_2992 on theBenchmark for (2992ds/571Mi)
% 5.27/1.15 % (1105645)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=321970050:i=450:rtra=on:ixr=off:ntd=on_2992 on theBenchmark for (2992ds/450Mi)
% 5.27/1.15 % (1105644)Refutation not found, incomplete strategy
% 5.27/1.15 % (1105644)------------------------------
% 5.27/1.15 % (1105644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105644)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105644)Termination reason: Refutation not found, incomplete strategy
% 5.27/1.15 % (1105644)Time elapsed: 0.004 s
% 5.27/1.15 % (1105644)Peak memory usage: 12 MB
% 5.27/1.15 % (1105644)Instructions burned: 5 (million)
% 5.27/1.15 % (1105644)------------------------------
% 5.27/1.15 % (1105644)------------------------------
% 5.27/1.15 % (1105648)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3753030713:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 5.27/1.15 % (1105628)Instruction limit reached!
% 5.27/1.15 % (1105628)------------------------------
% 5.27/1.15 % (1105628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105628)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105628)Termination reason: Instruction limit
% 5.27/1.15 % (1105628)Termination phase: Saturation
% 5.27/1.15 % (1105628)Time elapsed: 0.201 s
% 5.27/1.15 % (1105628)Peak memory usage: 13 MB
% 5.27/1.15 % (1105628)Instructions burned: 246 (million)
% 5.27/1.15 % (1105650)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=4040496131:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2991 on theBenchmark for (2991ds/65Mi)
% 5.27/1.15 % (1105572)Instruction limit reached!
% 5.27/1.15 % (1105572)------------------------------
% 5.27/1.15 % (1105572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105572)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105572)Termination reason: Instruction limit
% 5.27/1.15 % (1105572)Termination phase: Saturation
% 5.27/1.15 % (1105572)Time elapsed: 0.611 s
% 5.27/1.15 % (1105572)Peak memory usage: 15 MB
% 5.27/1.15 % (1105572)Instructions burned: 1242 (million)
% 5.27/1.15 % (1105648)Instruction limit reached!
% 5.27/1.15 % (1105648)------------------------------
% 5.27/1.15 % (1105648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105648)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105648)Termination reason: Instruction limit
% 5.27/1.15 % (1105648)Termination phase: Saturation
% 5.27/1.15 % (1105648)Time elapsed: 0.050 s
% 5.27/1.15 % (1105648)Peak memory usage: 12 MB
% 5.27/1.15 % (1105648)Instructions burned: 96 (million)
% 5.27/1.15 % (1105645) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1105508-1105645"...
% 5.27/1.15 % (1105653)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=1269194326:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 5.27/1.15 % (1105635)Instruction limit reached!
% 5.27/1.15 % (1105635)------------------------------
% 5.27/1.15 % (1105635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.27/1.15 % (1105635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.15 % (1105635)CaDiCaL version: 2.1.3
% 5.27/1.15 % (1105635)Termination reason: Instruction limit
% 5.27/1.15 % (1105635)Termination phase: Saturation
% 5.27/1.15 % (1105635)Time elapsed: 0.224 s
% 5.27/1.15 % (1105635)Peak memory usage: 13 MB
% 5.27/1.15 % (1105635)Instructions burned: 877 (million)
% 5.27/1.15 % (1105645)...printing done.
% 5.27/1.15 % (1105652)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=681009893:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2991 on theBenchmark for (2991ds/105Mi)
% 5.27/1.15 % (1105645)Refutation found. Thanks to Tanya!
% 5.27/1.15 % SZS status Theorem for theBenchmark
% 5.27/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.15 % (1105645)------------------------------
% 0.20/1.15 % (1105645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/1.15 % (1105645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.15 % (1105645)CaDiCaL version: 2.1.3
% 0.20/1.15 % (1105645)Termination reason: Refutation
% 0.20/1.15 % (1105645)Time elapsed: 0.092 s
% 0.20/1.15 % (1105645)Peak memory usage: 13 MB
% 0.20/1.15 % (1105645)Instructions burned: 182 (million)
% 0.20/1.15 % (1105508)Success in time 0.877 s
% 0.20/1.15 % Vampire exiting
%------------------------------------------------------------------------------