%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU643^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:32:48 AM UTC 2026
% Result : Theorem 19.67s 3.06s
% Output : Refutation 19.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 10
% Syntax : Number of formulae : 132 ( 70 unt; 0 typ; 3 def)
% Number of atoms : 1312 ( 304 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 2122 ( 51 ~; 130 |; 57 &;1706 @)
% ( 3 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 14 con; 0-5 aty)
% ( 50 !!; 27 ??; 0 @@+; 0 @@-)
% Number of variables : 367 ( 9 sgn 140 !; 8 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
setadjoinIL: $o ).
thf(func_def_7,type,
iskpair: $i > $o ).
thf(func_def_8,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
ex1I: $o ).
thf(func_def_11,type,
setukpairinjL1: $o ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_28,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
sK3: $i > $i > ( $i > $o ) > $i ).
thf(func_def_30,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_32,type,
sK6: ( $i > $i ) > $i > $i > ( $i > $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_33,type,
sK7: ( $i > $i ) > ( $i > $i > $o ) > ( $i > $i ) > $i > $i > $i ).
thf(func_def_34,type,
sK8: ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_35,type,
sK9: ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_36,type,
sK10: ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_37,type,
sK11: ( $i > $o ) > ( $i > $i ) > $i ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(f3,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
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
= ( ! [X0: $i,X1: $i > $o,X2: $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,
( setukpairinjL1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(f7,conjecture,
( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(f8,negated_conjecture,
~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ex1I
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X0
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ex1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( setukpairinjL1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( setukpairinjL1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ( ( setadjoinIL = $true )
=> ( ( ex1I = $true )
=> ( ( setukpairinjL1 = $true )
=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ? [X0: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) )
& ( ( iskpair @ X0 )
= $true ) )
& ( setukpairinjL1 = $true )
& ( ex1I = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f24,plain,
( ? [X0: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) )
& ( ( iskpair @ X0 )
= $true ) )
& ( setukpairinjL1 = $true )
& ( ex1I = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
& ( $true
= ( iskpair @ sK0 ) )
& ( setukpairinjL1 = $true )
& ( ex1I = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
thf(f26,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f27,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f28,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ex1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f31,plain,
( setukpairinjL1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f33,plain,
ex1I = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
setukpairinjL1 = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f35,plain,
( $true
= ( iskpair @ sK0 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f36,plain,
( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f39,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f29,f28]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f32]) ).
thf(f41,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f30,f33,f39]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f34]) ).
thf(f43,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ),
inference(definition_unfolding,[],[f36,f28]) ).
thf(f44,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f35,f27]) ).
thf(f45,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( $true
= ( ( in @ sK1 @ ( setunion @ sK0 ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( $true
= ( in @ sK1 @ ( setunion @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f48]) ).
thf(f51,plain,
( $true
= ( ( in @ sK2 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
( $true
= ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) )
= sK0 ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f54,plain,
( sK0
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK0 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f56,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK0 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( $false
= ( ( in @ X1
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
& ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( ( $false
= ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X1 ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
& ( ( setadjoin @ Y6 @ emptyset )
= Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f69,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( X1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( X1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X1 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X2 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X1 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X2 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ X2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ( X2 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ Y0 )
=> ( X1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( X2 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ Y0 )
=> ( X1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ Y0 )
=> ( X1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ Y0 )
=> ( X1 = Y0 ) ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ Y0 )
=> ( X1 = Y0 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ Y0 )
=> ( X1 = Y0 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) )
@ ( sK4 @ X3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 )
=> ( ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) )
=> ( X1
= ( sK3 @ X3 @ X1 @ X2 ) ) ) ) )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X2 ) @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) )
=> ( X1
= ( sK3 @ X3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X2 ) @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f85,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( X1
= ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X2 ) @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f86,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X2 ) @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f87,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f89,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( ( dsetconstr @ X3 @ X2 )
= ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f87]) ).
thf(f90,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( ( sK3 @ X3 @ X1 @ X2 )
!= X1 )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X2 ) @ ( dsetconstr @ X3 @ X2 ) )
& ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f85]) ).
thf(f91,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( X2 @ X1 ) )
| ( ( sK3 @ X3 @ X1 @ X2 )
!= X1 )
| ( $true
= ( ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset )
= ( dsetconstr @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f93,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( sK3 @ X3 @ X1 @ X2 )
!= X1 )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( ( dsetconstr @ X3 @ X2 )
= ( setadjoin @ ( sK4 @ X3 @ X2 ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f91]) ).
thf(f94,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f95,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
( $true
= ( in @ ( setadjoin @ sK1 @ emptyset ) @ sK0 ) ),
inference(constrained_superposition,[],[f97,f54]) ).
thf(f107,plain,
! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( sK1 = X0 ) ),
inference(constrained_superposition,[],[f67,f54]) ).
thf(f138,definition,
( spl5_2
<=> ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f139,plain,
( ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f140,plain,
( ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| spl5_2 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i] :
( ( $true = $false )
| ( sK1 = X0 )
| ( $false
= ( ^ [Y0: $i] :
( in @ ( X1 @ Y0 )
@ ( ^ [Y1: $i] : sK0
@ Y0 ) )
@ X3 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] :
( in @ ( X1 @ Y0 )
@ ( ^ [Y1: $i] : sK0
@ Y0 ) ) )
= ( setadjoin
@ ( sK4 @ X2
@ ^ [Y0: $i] :
( in @ ( X1 @ Y0 )
@ ( ^ [Y1: $i] : sK0
@ Y0 ) ) )
@ emptyset ) )
| ( ( setadjoin @ X0 @ emptyset )
!= ( X1
@ ( sK3 @ X2 @ X3
@ ^ [Y0: $i] : ( in @ ( X1 @ Y0 ) @ sK0 ) ) ) ) ),
inference(constrained_superposition,[],[f107,f89]) ).
thf(f250,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i] :
( ( sK1 = X0 )
| ( $false
= ( ^ [Y0: $i] :
( in @ ( X1 @ Y0 )
@ ( ^ [Y1: $i] : sK0
@ Y0 ) )
@ X3 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] :
( in @ ( X1 @ Y0 )
@ ( ^ [Y1: $i] : sK0
@ Y0 ) ) )
= ( setadjoin
@ ( sK4 @ X2
@ ^ [Y0: $i] :
( in @ ( X1 @ Y0 )
@ ( ^ [Y1: $i] : sK0
@ Y0 ) ) )
@ emptyset ) )
| ( ( setadjoin @ X0 @ emptyset )
!= ( X1
@ ( sK3 @ X2 @ X3
@ ^ [Y0: $i] : ( in @ ( X1 @ Y0 ) @ sK0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( X1
@ ( sK3 @ X2 @ X3
@ ^ [Y0: $i] : ( in @ ( X1 @ Y0 ) @ sK0 ) ) ) )
| ( $false
= ( in @ ( X1 @ X3 ) @ sK0 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( X1 @ Y0 ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ X2
@ ^ [Y0: $i] : ( in @ ( X1 @ Y0 ) @ sK0 ) )
@ emptyset ) )
| ( sK1 = X0 ) ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f789,plain,
( ( $true
= ( in
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f97,f139]) ).
thf(f1140,plain,
! [X2: $i,X3: $i,X0: $i > $i,X1: $i] :
( ( $false
= ( in
@ ( ^ [Y0: $i] :
( setadjoin @ ( X0 @ Y0 )
@ ( ^ [Y1: $i] : emptyset
@ Y0 ) )
@ X1 )
@ sK0 ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] :
( in
@ ( ^ [Y1: $i] :
( setadjoin @ ( X0 @ Y1 )
@ ( ^ [Y2: $i] : emptyset
@ Y1 ) )
@ Y0 )
@ sK0 ) )
= ( setadjoin
@ ( sK4 @ X2
@ ^ [Y0: $i] :
( in
@ ( ^ [Y1: $i] :
( setadjoin @ ( X0 @ Y1 )
@ ( ^ [Y2: $i] : emptyset
@ Y1 ) )
@ Y0 )
@ sK0 ) )
@ emptyset ) )
| ( sK1 = X3 )
| ( ( X0
@ ( sK3 @ X2 @ X1
@ ^ [Y0: $i] : ( in @ ( setadjoin @ ( X0 @ Y0 ) @ emptyset ) @ sK0 ) ) )
!= X3 ) ),
inference(equality_resolution,[],[f251]) ).
thf(f1141,plain,
! [X2: $i,X3: $i,X0: $i > $i,X1: $i] :
( ( $false
= ( in @ ( setadjoin @ ( X0 @ X1 ) @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( setadjoin @ ( X0 @ Y0 ) @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ X2
@ ^ [Y0: $i] : ( in @ ( setadjoin @ ( X0 @ Y0 ) @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ( sK1 = X3 )
| ( ( X0
@ ( sK3 @ X2 @ X1
@ ^ [Y0: $i] : ( in @ ( setadjoin @ ( X0 @ Y0 ) @ emptyset ) @ sK0 ) ) )
!= X3 ) ),
inference(beta-eta_normalization,[],[f1140]) ).
thf(f2807,plain,
( ! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] :
( in
@ ( setadjoin
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ emptyset )
@ sK0 ) ) )
| ( $false
= ( in
@ ( setadjoin
@ ( ^ [Y0: $i] : Y0
@ X0 )
@ emptyset )
@ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( sK1 = X1 )
| ( ( ^ [Y0: $i] : Y0
@ ( sK3 @ ( setunion @ sK0 ) @ X0
@ ^ [Y0: $i] :
( in
@ ( setadjoin
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ emptyset )
@ sK0 ) ) )
!= X1 ) )
| spl5_2 ),
inference(constrained_superposition,[],[f140,f1141]) ).
thf(f2974,plain,
( ! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( sK1 = X1 )
| ( ( sK3 @ ( setunion @ sK0 ) @ X0
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X1 ) )
| spl5_2 ),
inference(beta-eta_normalization,[],[f2807]) ).
thf(f2975,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK3 @ ( setunion @ sK0 ) @ X0
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= X1 )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( sK1 = X1 )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| spl5_2 ),
inference(trivial_inequality_removal,[],[f2974]) ).
thf(f3620,plain,
( ! [X0: $i] :
( ( sK1
= ( sK3 @ ( setunion @ sK0 ) @ X0
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| spl5_2 ),
inference(equality_resolution,[],[f2975]) ).
thf(f3644,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ X0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| spl5_2 ),
inference(constrained_superposition,[],[f93,f3620]) ).
thf(f3661,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( $false
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 )
@ X0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| spl5_2 ),
inference(duplicate_literal_removal,[],[f3644]) ).
thf(f3662,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) ) )
| spl5_2 ),
inference(beta-eta_normalization,[],[f3661]) ).
thf(f3663,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) ) )
| spl5_2 ),
inference(duplicate_literal_removal,[],[f3662]) ).
thf(f3701,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) ) )
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f3663,f107]) ).
thf(f3720,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) ) )
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f3701,f140]) ).
thf(f3722,definition,
( spl5_126
<=> ( $true
= ( in
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_126])],[avatar_definition]) ).
thf(f3724,plain,
( ( $true
= ( in
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) ) ) )
| ~ spl5_126 ),
inference(avatar_component_clause,[],[f3722]) ).
thf(f3726,definition,
( spl5_127
<=> ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_127])],[avatar_definition]) ).
thf(f3727,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setadjoin @ X0 @ emptyset ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) ) )
| ~ spl5_127 ),
inference(avatar_component_clause,[],[f3726]) ).
thf(f3729,plain,
( spl5_127
| spl5_2 ),
inference(avatar_split_clause,[],[f3720,f138,f3726]) ).
thf(f3739,plain,
( ( $true = $false )
| ( $false
= ( in @ sK1 @ ( setunion @ sK0 ) ) )
| ~ spl5_127 ),
inference(constrained_superposition,[],[f98,f3727]) ).
thf(f3756,plain,
( ( $false
= ( in @ sK1 @ ( setunion @ sK0 ) ) )
| ~ spl5_127 ),
inference(trivial_inequality_removal,[],[f3739]) ).
thf(f3776,plain,
( ( $true = $false )
| ~ spl5_127 ),
inference(constrained_superposition,[],[f3756,f49]) ).
thf(f3802,plain,
( $false
| ~ spl5_127 ),
inference(trivial_inequality_removal,[],[f3776]) ).
thf(f3803,plain,
~ spl5_127,
inference(avatar_contradiction_clause,[],[f3802]) ).
thf(f3807,plain,
( spl5_126
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f789,f138,f3722]) ).
thf(f10902,plain,
( ( $true = $false )
| ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ~ spl5_126 ),
inference(constrained_superposition,[],[f3724,f59]) ).
thf(f10929,plain,
( ( ( dsetconstr @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
!= ( setadjoin
@ ( sK4 @ ( setunion @ sK0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK0 ) )
@ emptyset ) )
| ~ spl5_126 ),
inference(trivial_inequality_removal,[],[f10902]) ).
thf(f10933,plain,
( $false
| ~ spl5_2
| ~ spl5_126 ),
inference(forward_subsumption_resolution,[],[f10929,f139]) ).
thf(f10934,plain,
( ~ spl5_2
| ~ spl5_126 ),
inference(avatar_contradiction_clause,[],[f10933]) ).
cnf(s138,plain,
( spl5_2
| spl5_127 ),
inference(sat_conversion,[],[f3729]) ).
cnf(s140,plain,
~ spl5_127,
inference(sat_conversion,[],[f3803]) ).
cnf(s141,plain,
( ~ spl5_2
| spl5_126 ),
inference(sat_conversion,[],[f3807]) ).
cnf(s591,plain,
( ~ spl5_2
| ~ spl5_126 ),
inference(sat_conversion,[],[f10934]) ).
cnf(s595,plain,
spl5_2,
inference(rat,[],[s138,s140]) ).
cnf(s596,plain,
~ spl5_126,
inference(rat,[],[s591,s595]) ).
cnf(s601,plain,
$false,
inference(rat,[],[s141,s596,s595]) ).
thf(f10935,plain,
$false,
inference(avatar_sat_refutation,[],[s601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU643^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:02:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.49/1.07 % (2710262)Will run a generic schedule for satisfiability detection.
% 5.49/1.07 % (2710268)% WARNING: option uhcvi not known.
% 5.49/1.07 % (2710270)dis+10_1_sil=32000:sp=arity:random_seed=275512333:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.49/1.07 % (2710267)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=61502208_2999 on theBenchmark for (2999ds/0Mi)
% 5.49/1.07 % (2710269)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2448052699:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.49/1.07 % (2710268)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=865486231:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.49/1.07 % (2710268)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.49/1.07 % Exception at run slice level
% 5.49/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.49/1.07 % (2710268)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.49/1.07 % (2710273)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2732744122:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.49/1.07 % (2710278)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3895149931:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.49/1.07 % (2710272)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1746262582:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.49/1.07 % Exception at run slice level
% 5.49/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.49/1.07 % (2710271)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3015522041:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.49/1.07 % (2710271)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.49/1.07 % (2710282)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1181515889:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.49/1.07 % (2710270)Instruction limit reached!
% 5.49/1.07 % (2710270)------------------------------
% 5.49/1.07 % (2710270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.49/1.07 % (2710270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.07 % (2710270)CaDiCaL version: 2.1.3
% 5.49/1.07 % (2710270)Termination reason: Instruction limit
% 5.49/1.07 % (2710270)Termination phase: Saturation
% 5.49/1.07 % (2710270)Time elapsed: 0.047 s
% 5.49/1.07 % (2710270)Peak memory usage: 12 MB
% 5.49/1.07 % (2710270)Instructions burned: 103 (million)
% 5.49/1.07 % (2710285)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4089452493:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.49/1.07 % (2710285)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.49/1.07 % (2710285)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.49/1.07 % (2710272)Instruction limit reached!
% 5.49/1.07 % (2710272)------------------------------
% 5.49/1.07 % (2710272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.49/1.07 % (2710272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.07 % (2710272)CaDiCaL version: 2.1.3
% 5.49/1.07 % (2710272)Termination reason: Instruction limit
% 5.49/1.07 % (2710272)Termination phase: Saturation
% 5.49/1.07 % (2710272)Time elapsed: 0.074 s
% 5.49/1.07 % (2710272)Peak memory usage: 12 MB
% 5.49/1.07 % (2710272)Instructions burned: 133 (million)
% 5.49/1.07 % (2710273)Instruction limit reached!
% 5.49/1.07 % (2710273)------------------------------
% 5.49/1.07 % (2710273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.49/1.07 % (2710273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.07 % (2710273)CaDiCaL version: 2.1.3
% 5.49/1.07 % (2710273)Termination reason: Instruction limit
% 5.49/1.07 % (2710273)Termination phase: Saturation
% 5.49/1.07 % (2710273)Time elapsed: 0.078 s
% 5.49/1.07 % (2710273)Peak memory usage: 13 MB
% 5.49/1.07 % (2710273)Instructions burned: 160 (million)
% 5.49/1.07 % (2710282)Instruction limit reached!
% 5.49/1.07 % (2710282)------------------------------
% 5.49/1.07 % (2710282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710282)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710282)Termination reason: Instruction limit
% 19.67/3.06 % (2710282)Termination phase: Saturation
% 19.67/3.06 % (2710282)Time elapsed: 0.066 s
% 19.67/3.06 % (2710282)Peak memory usage: 12 MB
% 19.67/3.06 % (2710282)Instructions burned: 132 (million)
% 19.67/3.06 % (2710287)ott-21_1_sil=16000:fs=off:random_seed=4282281435:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 19.67/3.06 % (2710288)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2160790827:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 19.67/3.06 % (2710289)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2174412433:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710271)Instruction limit reached!
% 19.67/3.06 % (2710271)------------------------------
% 19.67/3.06 % (2710271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710271)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710271)Termination reason: Instruction limit
% 19.67/3.06 % (2710271)Termination phase: Saturation
% 19.67/3.06 % (2710271)Time elapsed: 0.109 s
% 19.67/3.06 % (2710271)Peak memory usage: 12 MB
% 19.67/3.06 % (2710271)Instructions burned: 116 (million)
% 19.67/3.06 % (2710293)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2809245377:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 19.67/3.06 % (2710294)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1777272256:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710297)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2032917002:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 19.67/3.06 % (2710297)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 19.67/3.06 % (2710287)Instruction limit reached!
% 19.67/3.06 % (2710287)------------------------------
% 19.67/3.06 % (2710287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710287)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710287)Termination reason: Instruction limit
% 19.67/3.06 % (2710287)Termination phase: Saturation
% 19.67/3.06 % (2710287)Time elapsed: 0.081 s
% 19.67/3.06 % (2710287)Peak memory usage: 12 MB
% 19.67/3.06 % (2710287)Instructions burned: 180 (million)
% 19.67/3.06 % (2710299)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2374339828:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 19.67/3.06 % (2710299)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 19.67/3.06 % (2710288)Instruction limit reached!
% 19.67/3.06 % (2710288)------------------------------
% 19.67/3.06 % (2710288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710288)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710288)Termination reason: Instruction limit
% 19.67/3.06 % (2710288)Termination phase: Saturation
% 19.67/3.06 % (2710288)Time elapsed: 0.245 s
% 19.67/3.06 % (2710288)Peak memory usage: 13 MB
% 19.67/3.06 % (2710288)Instructions burned: 478 (million)
% 19.67/3.06 % (2710301)fmb+10_1_sil=64000:random_seed=36544515:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 19.67/3.06 % (2710301)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710285)Instruction limit reached!
% 19.67/3.06 % (2710285)------------------------------
% 19.67/3.06 % (2710285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710285)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710285)Termination reason: Instruction limit
% 19.67/3.06 % (2710285)Termination phase: Saturation
% 19.67/3.06 % (2710285)Time elapsed: 0.324 s
% 19.67/3.06 % (2710285)Peak memory usage: 14 MB
% 19.67/3.06 % (2710285)Instructions burned: 686 (million)
% 19.67/3.06 % (2710303)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3988316290:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710304)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2287691363:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710306)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=100565950:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 19.67/3.06 % (2710306)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 19.67/3.06 % (2710308)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2046005136:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 19.67/3.06 % (2710308)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 19.67/3.06 % (2710308)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 19.67/3.06 % (2710299)Instruction limit reached!
% 19.67/3.06 % (2710299)------------------------------
% 19.67/3.06 % (2710299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710299)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710299)Termination reason: Instruction limit
% 19.67/3.06 % (2710299)Termination phase: Saturation
% 19.67/3.06 % (2710299)Time elapsed: 0.428 s
% 19.67/3.06 % (2710299)Peak memory usage: 15 MB
% 19.67/3.06 % (2710299)Instructions burned: 881 (million)
% 19.67/3.06 % (2710311)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1614475467:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710313)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3272128067:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710293)Instruction limit reached!
% 19.67/3.06 % (2710293)------------------------------
% 19.67/3.06 % (2710293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710293)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710293)Termination reason: Instruction limit
% 19.67/3.06 % (2710293)Termination phase: Saturation
% 19.67/3.06 % (2710293)Time elapsed: 0.545 s
% 19.67/3.06 % (2710293)Peak memory usage: 16 MB
% 19.67/3.06 % (2710293)Instructions burned: 1180 (million)
% 19.67/3.06 % (2710315)ott-2_1_sil=16000:newcnf=on:random_seed=2962853487:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 19.67/3.06 % (2710315)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 19.67/3.06 % (2710316)ott+10_1_sil=32000:tgt=ground:random_seed=1726081857:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 19.67/3.06 % (2710297)Instruction limit reached!
% 19.67/3.06 % (2710297)------------------------------
% 19.67/3.06 % (2710297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710297)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710297)Termination reason: Instruction limit
% 19.67/3.06 % (2710297)Termination phase: Saturation
% 19.67/3.06 % (2710297)Time elapsed: 0.570 s
% 19.67/3.06 % (2710297)Peak memory usage: 15 MB
% 19.67/3.06 % (2710297)Instructions burned: 692 (million)
% 19.67/3.06 % (2710319)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1659120548:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710321)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2992930411:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 19.67/3.06 % (2710321)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 19.67/3.06 % (2710315)Instruction limit reached!
% 19.67/3.06 % (2710315)------------------------------
% 19.67/3.06 % (2710315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710315)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710315)Termination reason: Instruction limit
% 19.67/3.06 % (2710315)Termination phase: Saturation
% 19.67/3.06 % (2710315)Time elapsed: 0.399 s
% 19.67/3.06 % (2710315)Peak memory usage: 15 MB
% 19.67/3.06 % (2710315)Instructions burned: 870 (million)
% 19.67/3.06 % (2710323)dis+21_1_sil=32000:sas=cadical:random_seed=2567903576:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 19.67/3.06 % (2710308)Instruction limit reached!
% 19.67/3.06 % (2710308)------------------------------
% 19.67/3.06 % (2710308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710308)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710308)Termination reason: Instruction limit
% 19.67/3.06 % (2710308)Termination phase: Saturation
% 19.67/3.06 % (2710308)Time elapsed: 1.082 s
% 19.67/3.06 % (2710308)Peak memory usage: 19 MB
% 19.67/3.06 % (2710308)Instructions burned: 1472 (million)
% 19.67/3.06 % (2710325)ott+11_1_sil=16000:gs=on:random_seed=2717885835:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2984 on theBenchmark for (2984ds/2251Mi)
% 19.67/3.06 % (2710325)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 19.67/3.06 % (2710321)Instruction limit reached!
% 19.67/3.06 % (2710321)------------------------------
% 19.67/3.06 % (2710321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710321)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710321)Termination reason: Instruction limit
% 19.67/3.06 % (2710321)Termination phase: Saturation
% 19.67/3.06 % (2710321)Time elapsed: 1.714 s
% 19.67/3.06 % (2710321)Peak memory usage: 20 MB
% 19.67/3.06 % (2710321)Instructions burned: 3514 (million)
% 19.67/3.06 % (2710327)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3261995398:fmbsr=1.6:i=67534_2974 on theBenchmark for (2974ds/67534Mi)
% 19.67/3.06 % Exception at run slice level
% 19.67/3.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.67/3.06 % (2710329)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3964586523:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2974 on theBenchmark for (2974ds/4591Mi)
% 19.67/3.06 % (2710325)Instruction limit reached!
% 19.67/3.06 % (2710325)------------------------------
% 19.67/3.06 % (2710325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.06 % (2710325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.06 % (2710325)CaDiCaL version: 2.1.3
% 19.67/3.06 % (2710325)Termination reason: Instruction limit
% 19.67/3.06 % (2710325)Termination phase: Saturation
% 19.67/3.06 % (2710325)Time elapsed: 1.217 s
% 19.67/3.06 % (2710325)Peak memory usage: 17 MB
% 19.67/3.06 % (2710325)Instructions burned: 2252 (million)
% 19.67/3.06 % (2710323) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2710262-2710323"...
% 19.67/3.06 % (2710323)...printing done.
% 19.67/3.06 % (2710323)Refutation found. Thanks to Tanya!
% 19.67/3.06 % SZS status Theorem for theBenchmark
% 19.67/3.06 % SZS output start Proof for theBenchmark
% See solution above
% 19.67/3.07 % (2710323)------------------------------
% 19.67/3.07 % (2710323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.67/3.07 % (2710323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.67/3.07 % (2710323)CaDiCaL version: 2.1.3
% 19.67/3.07 % (2710323)Termination reason: Refutation
% 19.67/3.07 % (2710323)Time elapsed: 1.641 s
% 19.67/3.07 % (2710323)Peak memory usage: 20 MB
% 19.67/3.07 % (2710323)Instructions burned: 3604 (million)
% 19.67/3.07 % (2710262)Success in time 2.822 s
% 19.67/3.07 % Vampire exiting
%------------------------------------------------------------------------------