%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU645^2 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:49 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 10
% Syntax : Number of formulae : 150 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 1545 ( 322 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 3311 ( 14 ~; 89 |; 80 &;2988 @)
% ( 0 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 31 usr; 12 con; 0-4 aty)
% ( 44 !!; 40 ??; 0 @@+; 0 @@-)
% Number of variables : 426 ( 194 ^; 222 !; 10 ?; 426 :)
% 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,
dsetconstrER: $o ).
thf(func_def_7,type,
iskpair: $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
kpairp: $o ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_11,type,
setukpairinjL1: $o ).
thf(func_def_12,type,
kfstsingleton: $o ).
thf(func_def_13,type,
theprop: $o ).
thf(func_def_14,type,
kfst: $i > $i ).
thf(func_def_15,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vIMP: $o > $o > $o ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
sK2: $i > $i ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
sK3: $i > $i > $i ).
thf(func_def_32,type,
sK4: $i > $i > $i ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
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,
( 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(f4,axiom,
( kpairp
= ( ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(f5,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
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,axiom,
( kfstsingleton
= ( ! [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,axiom,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(f9,axiom,
( kfst
= ( ^ [X0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfst) ).
thf(f10,conjecture,
( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f11,negated_conjecture,
~ ( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f12,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f13,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,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(f15,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,[],[f14]) ).
thf(f16,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f17,plain,
( kpairp
= ( ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f18,plain,
( kpairp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( iskpair @ ( kpair @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,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(f22,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,[],[f21]) ).
thf(f23,plain,
( kfstsingleton
= ( ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f24,plain,
( kfstsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f26,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( kfst
= ( ^ [X0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f28,plain,
( kfst
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
~ ( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f30,plain,
~ ( ( dsetconstrER = $true )
=> ( ( kpairp = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f30]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(flattening,[],[f31]) ).
thf(f33,plain,
( ( sK0
!= ( kfst @ ( kpair @ sK0 @ sK1 ) ) )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
thf(f34,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f35,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,[],[f15]) ).
thf(f36,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f37,plain,
( kpairp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( iskpair @ ( kpair @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f38,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f39,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,[],[f22]) ).
thf(f40,plain,
( kfstsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f41,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f42,plain,
( kfst
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f43,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f44,plain,
kpairp = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f45,plain,
setukpairinjL1 = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f46,plain,
kfstsingleton = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f47,plain,
theprop = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f48,plain,
( sK0
!= ( kfst @ ( kpair @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f51,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f34,f43]) ).
thf(f52,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y2 ) )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ ( setunion @ Y2 ) )
& ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y4 @ emptyset ) ) @ emptyset ) )
= Y2 ) ) ) ) )
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f37,f44,f35,f36]) ).
thf(f53,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,[],[f39,f45]) ).
thf(f54,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y1 ) )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y1 ) )
& ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= Y1 ) ) ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( setadjoin @ Y2 @ emptyset )
= Y1 ) ) )
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f40,f46,f35,f38]) ).
thf(f55,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( setadjoin @ Y2 @ emptyset )
= Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f41,f47,f38]) ).
thf(f56,plain,
( sK0
!= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) )
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f48,f42,f36]) ).
thf(f57,plain,
( sK0
!= ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( setadjoin @ Y2 @ emptyset )
= Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f59,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) )
@ X2 ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ X1 )
& ( ( setadjoin @ X2 @ emptyset )
= X1 ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ X2 @ emptyset )
= X1 ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ X2 @ emptyset )
!= X1 )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y1 ) )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y1 ) )
& ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= Y1 ) ) ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( setadjoin @ Y2 @ emptyset )
= Y1 ) ) )
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f66,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
@ X2 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ X1 ) ) ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ ( setunion @ X1 ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) )
| ( $true
= ( ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
| ( $true
= ( ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
@ X3 ) )
| ( $true
= ( ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
& ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
@ X3 ) )
| ( $true
= ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
@ X3 ) )
| ( $true
= ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( in @ X3 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
| ( $true
= ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= X1 ) )
| ( $true
= ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
!= X1 )
| ( $true
= ( in @ ( sK2 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
@ X3 ) )
| ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f73]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( in @ X3 @ ( setunion @ X1 ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
| ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= X1 ) )
| ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
!= X1 )
| ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f82,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,[],[f53]) ).
thf(f83,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,[],[f82]) ).
thf(f84,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,[],[f83]) ).
thf(f85,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,[],[f84]) ).
thf(f86,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,[],[f85]) ).
thf(f87,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,[],[f86]) ).
thf(f88,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,[],[f87]) ).
thf(f89,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,[],[f88]) ).
thf(f90,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y2 ) )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ ( setunion @ Y2 ) )
& ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y4 @ emptyset ) ) @ emptyset ) )
= Y2 ) ) ) ) )
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f91,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
@ ( sK3 @ X1 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ ( sK3 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ ( sK4 @ X1 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f96]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ ( sK4 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ ( setadjoin @ ( sK4 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ ( setadjoin @ ( sK4 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X1 @ X2 ) @ ( setadjoin @ ( sK4 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f100]) ).
thf(f103,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f104,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f114,plain,
! [X0: $i] :
( ( $true
= ( in @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(equality_resolution,[],[f64]) ).
thf(f126,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(equality_resolution,[],[f77]) ).
thf(f137,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(equality_resolution,[],[f81]) ).
thf(f143,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
| ( $false
= ( in @ ( sK3 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f126,f102]) ).
thf(f150,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f143,f97]) ).
thf(f151,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f152,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f151,f101]) ).
thf(f153,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f157,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
| ( $false
= ( in @ ( sK3 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f137,f102]) ).
thf(f158,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ X2 ) )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f109,f137]) ).
thf(f162,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) )
| ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f176,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f157,f97]) ).
thf(f177,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ),
inference(forward_demodulation,[],[f177,f101]) ).
thf(f179,plain,
! [X0: $i,X1: $i] :
( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f246,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f109,f153]) ).
thf(f247,plain,
! [X0: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f248,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f260,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X0 ) ),
inference(constrained_superposition,[],[f89,f248]) ).
thf(f261,plain,
! [X0: $i,X1: $i] :
( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X0 ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f272,plain,
( sK0
!= ( setunion @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ),
inference(constrained_superposition,[],[f57,f179]) ).
thf(f277,plain,
! [X0: $i,X1: $i] :
( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= ( sK3 @ X1 @ X0 ) ),
inference(constrained_superposition,[],[f261,f102]) ).
thf(f279,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X0
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f153,f261]) ).
thf(f283,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ),
inference(forward_demodulation,[],[f279,f179]) ).
thf(f284,plain,
! [X0: $i,X1: $i] :
( ( sK3 @ X1 @ X0 )
= X0 ),
inference(forward_demodulation,[],[f277,f261]) ).
thf(f286,plain,
! [X0: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ),
inference(forward_demodulation,[],[f283,f261]) ).
thf(f293,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(constrained_superposition,[],[f97,f284]) ).
thf(f333,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f162,f261]) ).
thf(f337,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f333,f293]) ).
thf(f338,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f352,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( X0 = X1 )
| ( $false
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f89,f338]) ).
thf(f355,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f406,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X2 @ ( setadjoin @ ( sK3 @ X1 @ X0 ) @ emptyset ) ) )
| ( ( sK3 @ X1 @ X0 )
= X2 ) ),
inference(constrained_superposition,[],[f355,f102]) ).
thf(f415,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X2 @ ( setadjoin @ ( sK3 @ X1 @ X0 ) @ emptyset ) ) )
| ( ( sK3 @ X1 @ X0 )
= X2 ) ),
inference(forward_demodulation,[],[f406,f101]) ).
thf(f416,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ ( sK3 @ X1 @ X0 ) @ emptyset ) ) )
| ( ( sK3 @ X1 @ X0 )
= X2 ) ),
inference(trivial_inequality_removal,[],[f415]) ).
thf(f418,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( sK3 @ X1 @ X0 )
= X2 ) ),
inference(forward_demodulation,[],[f416,f284]) ).
thf(f420,plain,
! [X2: $i,X0: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X2 ) ),
inference(forward_demodulation,[],[f418,f284]) ).
thf(f424,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(constrained_superposition,[],[f114,f420]) ).
thf(f425,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f428,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(forward_demodulation,[],[f425,f286]) ).
thf(f429,plain,
! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f443,plain,
( sK0
!= ( sK2 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(forward_demodulation,[],[f272,f429]) ).
thf(f444,plain,
$false,
inference(forward_subsumption_resolution,[],[f443,f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU645^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:07:36 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.22/0.32 % (1294813)Will run a generic schedule for satisfiability detection.
% 0.22/0.32 % (1294818)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3343304029_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.32 % Exception at run slice level
% 0.22/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.32 % (1294819)% WARNING: option uhcvi not known.
% 0.22/0.32 % (1294819)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4134018686:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.32 % (1294820)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=781833951:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.32 % (1294821)dis+10_1_sil=32000:sp=arity:random_seed=3055911646:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.32 % (1294824)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=408590077:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.32 % (1294822)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2175158591:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.32 % (1294819)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (1294823)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1850770427:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (1294822)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (1294819)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.32 % (1294831)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=796780533:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.32 % Exception at run slice level
% 0.22/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.32 % (1294841)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1856337608:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (1294841)Instruction limit reached!
% 0.22/0.32 % (1294841)------------------------------
% 0.22/0.32 % (1294841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1294841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1294841)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1294841)Termination reason: Instruction limit
% 0.22/0.32 % (1294841)Termination phase: Saturation
% 0.22/0.32 % (1294841)Time elapsed: 0.036 s
% 0.22/0.32 % (1294841)Peak memory usage: 13 MB
% 0.22/0.32 % (1294841)Instructions burned: 133 (million)
% 0.22/0.32 % (1294821) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1294813-1294821"...
% 0.22/0.32 % (1294822)Instruction limit reached!
% 0.22/0.32 % (1294822)------------------------------
% 0.22/0.32 % (1294822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1294822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1294822)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1294822)Termination reason: Instruction limit
% 0.22/0.32 % (1294822)Termination phase: Saturation
% 0.22/0.32 % (1294822)Time elapsed: 0.057 s
% 0.22/0.32 % (1294822)Peak memory usage: 12 MB
% 0.22/0.32 % (1294822)Instructions burned: 116 (million)
% 0.22/0.32 % (1294821)...printing done.
% 0.22/0.32 % (1294821)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (1294821)------------------------------
% 0.22/0.32 % (1294821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1294821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1294821)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1294821)Termination reason: Refutation
% 0.22/0.32 % (1294821)Time elapsed: 0.060 s
% 0.22/0.32 % (1294821)Peak memory usage: 12 MB
% 0.22/0.32 % (1294821)Instructions burned: 120 (million)
% 0.22/0.32 % (1294813)Success in time 0.085 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------