%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU656^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:32:51 AM UTC 2026
% Result : Theorem 1.08s 0.44s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 10
% Syntax : Number of formulae : 156 ( 91 unt; 0 typ; 0 def)
% Number of atoms : 1818 ( 394 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 4297 ( 18 ~; 92 |; 80 &;3957 @)
% ( 0 <=>; 57 =>; 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 : 37 ( 32 usr; 12 con; 0-4 aty)
% ( 53 !!; 40 ??; 0 @@+; 0 @@-)
% Number of variables : 462 ( 216 ^; 236 !; 10 ?; 462 :)
% 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,
theprop: $o ).
thf(func_def_12,type,
kfst: $i > $i ).
thf(func_def_13,type,
setukpairinjR: $o ).
thf(func_def_14,type,
ksndsingleton: $o ).
thf(func_def_15,type,
ksnd: $i > $i ).
thf(func_def_16,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vNOT: $o > $o ).
thf(func_def_31,type,
sK2: $i > $i ).
thf(func_def_32,type,
sK3: $i > $i > $i ).
thf(func_def_33,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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(f4,axiom,
( kpairp
= ( ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(f5,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f6,axiom,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(f7,axiom,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(f8,axiom,
( ksndsingleton
= ( ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(f9,axiom,
( ksnd
= ( ^ [X0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksnd) ).
thf(f10,conjecture,
( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(f11,negated_conjecture,
~ ( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
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,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f22,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f24,plain,
( ksndsingleton
= ( ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f25,plain,
( ksndsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( ksnd
= ( ^ [X0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( X0
= ( kpair @ ( kfst @ X0 ) @ X1 ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f27,plain,
( ksnd
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
~ ( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f29,plain,
~ ( ( dsetconstrER = $true )
=> ( ( kpairp = $true )
=> ( ( theprop = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( theprop = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f31,plain,
( ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( theprop = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( ( sK1
!= ( ksnd @ ( kpair @ sK0 @ sK1 ) ) )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( theprop = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
thf(f33,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(f34,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(f35,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f36,plain,
( kpairp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( iskpair @ ( kpair @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f37,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f38,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f39,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f40,plain,
( ksndsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f41,plain,
( ksnd
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f42,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f43,plain,
kpairp = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f44,plain,
theprop = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f45,plain,
setukpairinjR = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f46,plain,
ksndsingleton = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f47,plain,
( sK1
!= ( ksnd @ ( kpair @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f50,plain,
( ksnd
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ Y0 )
@ Y1 )
= Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f41,f35]) ).
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,[],[f33,f42]) ).
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,[],[f36,f43,f34,f35]) ).
thf(f53,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,[],[f38,f44,f37]) ).
thf(f54,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y2 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f39,f45,f35,f35]) ).
thf(f55,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] :
( ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ Y0 )
@ Y1 )
= Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f40,f46,f34,f37,f35]) ).
thf(f56,plain,
( sK1
!= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ Y0 )
@ Y1 )
= Y0 ) ) )
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f47,f50,f35]) ).
thf(f57,plain,
( sK1
!= ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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 @ ( 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] :
( ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ Y0 )
@ Y1 )
= Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f59,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f61]) ).
thf(f63,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f65,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) )
& ( ( setadjoin @ ( sK2 @ X1 ) @ emptyset )
= ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f66,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f70,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f71,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f72,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
!= X1 )
| ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X1 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
= ( setadjoin @ ( sK2 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( setunion @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y2 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f76,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X1 ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X1 ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f86,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,[],[f53]) ).
thf(f87,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f89,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,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ X1 )
& ( ( setadjoin @ X2 @ emptyset )
= X1 ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ X2 @ emptyset )
= X1 ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ X2 @ emptyset )
!= X1 )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f91]) ).
thf(f93,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(f94,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,[],[f93]) ).
thf(f95,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,[],[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 ) ) ) )
& ( ?? @ $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,[],[f95]) ).
thf(f97,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,[],[f96]) ).
thf(f98,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,[],[f97]) ).
thf(f99,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,[],[f98]) ).
thf(f100,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,[],[f98]) ).
thf(f101,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,[],[f99]) ).
thf(f102,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,[],[f101]) ).
thf(f103,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,[],[f102]) ).
thf(f104,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,[],[f102]) ).
thf(f105,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,[],[f103]) ).
thf(f106,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(f107,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,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,[],[f107]) ).
thf(f109,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f117,plain,
! [X0: $i] :
( ( $true
= ( in @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) ) )
| ( $false
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(equality_resolution,[],[f92]) ).
thf(f128,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,[],[f70]) ).
thf(f129,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,[],[f74]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( ( sK4 @ X1 @ X0 )
= X3 ) ),
inference(constrained_superposition,[],[f85,f105]) ).
thf(f145,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( sK2 @ ( 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(constrained_superposition,[],[f112,f128]) ).
thf(f146,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( sK2 @ ( 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(trivial_inequality_removal,[],[f145]) ).
thf(f147,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( 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 ) ) @ 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(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( 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 ) ) @ 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_proxy_clausification,[],[f147]) ).
thf(f157,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,[],[f129,f105]) ).
thf(f160,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( 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 ) ) ) ) )
| ( $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,[],[f128,f129]) ).
thf(f161,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( 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(duplicate_literal_removal,[],[f160]) ).
thf(f177,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,f100]) ).
thf(f178,plain,
! [X0: $i,X1: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,[],[f177]) ).
thf(f179,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,[],[f178,f104]) ).
thf(f180,plain,
! [X0: $i,X1: $i] :
( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ 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,[],[f179]) ).
thf(f189,plain,
! [X0: $i,X1: $i] :
( ( sK4 @ X0 @ X1 )
= X0 ),
inference(equality_resolution,[],[f140]) ).
thf(f198,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(constrained_superposition,[],[f104,f189]) ).
thf(f199,plain,
! [X0: $i,X1: $i] :
( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK3 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X0 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ),
inference(constrained_superposition,[],[f105,f189]) ).
thf(f248,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ ( 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 ) ) ) ) ) ),
inference(forward_demodulation,[],[f161,f198]) ).
thf(f249,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( 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 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f251,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( 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 ) ) ) ) ) ),
inference(constrained_superposition,[],[f249,f105]) ).
thf(f252,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ ( 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,[],[f251,f100]) ).
thf(f253,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ ( sK2 @ ( 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,[],[f252]) ).
thf(f376,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] :
( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ X2 ) ) ),
inference(constrained_superposition,[],[f112,f180]) ).
thf(f377,plain,
( sK1
!= ( setunion @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ),
inference(constrained_superposition,[],[f57,f180]) ).
thf(f380,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
= ( ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f376]) ).
thf(f381,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[],[f380]) ).
thf(f405,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( 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 ) ) @ emptyset ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f148,f198]) ).
thf(f406,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( 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 ) ) @ emptyset ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f447,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X3 )
| ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f85,f406]) ).
thf(f851,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
inference(equality_resolution,[],[f447]) ).
thf(f859,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X1 @ X0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
inference(constrained_superposition,[],[f851,f199]) ).
thf(f863,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= X0 ) ),
inference(constrained_superposition,[],[f198,f851]) ).
thf(f864,plain,
! [X0: $i] :
( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= X0 ),
inference(trivial_inequality_removal,[],[f863]) ).
thf(f873,plain,
! [X0: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ),
inference(constrained_superposition,[],[f253,f864]) ).
thf(f1598,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( sK2 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= X0 ) ),
inference(constrained_superposition,[],[f100,f859]) ).
thf(f1599,plain,
! [X0: $i,X1: $i] :
( ( sK2 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= X0 ),
inference(trivial_inequality_removal,[],[f1598]) ).
thf(f1616,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 )
| ( $false
= ( in @ X2 @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f1599,f381]) ).
thf(f1635,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( in @ X2 @ ( setadjoin @ ( sK2 @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ) ),
inference(forward_demodulation,[],[f1616,f1599]) ).
thf(f1645,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(forward_demodulation,[],[f1635,f1599]) ).
thf(f1696,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(constrained_superposition,[],[f117,f1645]) ).
thf(f1697,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f1696]) ).
thf(f1732,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(constrained_superposition,[],[f873,f1697]) ).
thf(f1737,plain,
! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(trivial_inequality_removal,[],[f1732]) ).
thf(f1754,plain,
( sK1
!= ( setunion @ ( setadjoin @ sK1 @ emptyset ) ) ),
inference(forward_demodulation,[],[f377,f1599]) ).
thf(f1755,plain,
$false,
inference(forward_subsumption_resolution,[],[f1754,f1737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU656^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:01:26 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/0.44 % (3417688)Will run a generic schedule for satisfiability detection.
% 1.08/0.44 % (3417695)% WARNING: option uhcvi not known.
% 1.08/0.44 % (3417695)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=707319123:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.08/0.44 % (3417695)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.44 % (3417695)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.08/0.44 % (3417694)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1128728765_2999 on theBenchmark for (2999ds/0Mi)
% 1.08/0.44 % Exception at run slice level
% 1.08/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.44 % (3417698)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=468287931:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.08/0.44 % (3417697)dis+10_1_sil=32000:sp=arity:random_seed=3626358621:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.08/0.44 % (3417699)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3351226331:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.44 % (3417696)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2892943033:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.08/0.44 % (3417698)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.44 % (3417700)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1200663487:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.08/0.44 % (3417703)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3718531263:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.08/0.44 % Exception at run slice level
% 1.08/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.44 % (3417710)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3218331739:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.44 % (3417697)Instruction limit reached!
% 1.08/0.44 % (3417697)------------------------------
% 1.08/0.44 % (3417697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.44 % (3417697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.44 % (3417697)CaDiCaL version: 2.1.3
% 1.08/0.44 % (3417697)Termination reason: Instruction limit
% 1.08/0.44 % (3417697)Termination phase: Saturation
% 1.08/0.44 % (3417697)Time elapsed: 0.084 s
% 1.08/0.44 % (3417697)Peak memory usage: 12 MB
% 1.08/0.44 % (3417697)Instructions burned: 103 (million)
% 1.08/0.44 % (3417698)Instruction limit reached!
% 1.08/0.44 % (3417698)------------------------------
% 1.08/0.44 % (3417698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.44 % (3417698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.44 % (3417698)CaDiCaL version: 2.1.3
% 1.08/0.44 % (3417698)Termination reason: Instruction limit
% 1.08/0.44 % (3417698)Termination phase: Saturation
% 1.08/0.44 % (3417698)Time elapsed: 0.100 s
% 1.08/0.44 % (3417698)Peak memory usage: 12 MB
% 1.08/0.44 % (3417698)Instructions burned: 116 (million)
% 1.08/0.44 % (3417710)Instruction limit reached!
% 1.08/0.44 % (3417710)------------------------------
% 1.08/0.44 % (3417710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.44 % (3417710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.44 % (3417710)CaDiCaL version: 2.1.3
% 1.08/0.44 % (3417710)Termination reason: Instruction limit
% 1.08/0.44 % (3417710)Termination phase: Saturation
% 1.08/0.44 % (3417710)Time elapsed: 0.066 s
% 1.08/0.44 % (3417710)Peak memory usage: 12 MB
% 1.08/0.44 % (3417710)Instructions burned: 132 (million)
% 1.08/0.44 % (3417699)Instruction limit reached!
% 1.08/0.44 % (3417699)------------------------------
% 1.08/0.44 % (3417699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.44 % (3417699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.44 % (3417699)CaDiCaL version: 2.1.3
% 1.08/0.44 % (3417699)Termination reason: Instruction limit
% 1.08/0.44 % (3417699)Termination phase: Saturation
% 1.08/0.44 % (3417699)Time elapsed: 0.114 s
% 1.08/0.44 % (3417699)Peak memory usage: 12 MB
% 1.08/0.44 % (3417699)Instructions burned: 132 (million)
% 1.08/0.44 % (3417712)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=2870776220:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.08/0.44 % (3417713)ott-21_1_sil=16000:fs=off:random_seed=1043163791:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.08/0.44 % (3417712)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.44 % (3417712)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.08/0.44 % (3417714)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1019686027:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.08/0.44 % (3417700)Instruction limit reached!
% 1.08/0.44 % (3417700)------------------------------
% 1.08/0.44 % (3417700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.44 % (3417700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.44 % (3417700)CaDiCaL version: 2.1.3
% 1.08/0.44 % (3417700)Termination reason: Instruction limit
% 1.08/0.44 % (3417700)Termination phase: Saturation
% 1.08/0.44 % (3417700)Time elapsed: 0.139 s
% 1.08/0.44 % (3417700)Peak memory usage: 12 MB
% 1.08/0.44 % (3417700)Instructions burned: 159 (million)
% 1.08/0.44 % (3417715)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1247833880:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.08/0.44 % Exception at run slice level
% 1.08/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.44 % (3417695) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3417688-3417695"...
% 1.08/0.44 % (3417695)...printing done.
% 1.08/0.44 % (3417695)Refutation found. Thanks to Tanya!
% 1.08/0.44 % SZS status Theorem for theBenchmark
% 1.08/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 1.08/0.44 % (3417695)------------------------------
% 1.08/0.44 % (3417695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.44 % (3417695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.44 % (3417695)CaDiCaL version: 2.1.3
% 1.08/0.44 % (3417695)Termination reason: Refutation
% 1.08/0.44 % (3417695)Time elapsed: 0.190 s
% 1.08/0.44 % (3417695)Peak memory usage: 14 MB
% 1.08/0.44 % (3417695)Instructions burned: 813 (million)
% 1.08/0.44 % (3417688)Success in time 0.224 s
% 1.08/0.44 % Vampire exiting
%------------------------------------------------------------------------------