%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU752^2 : 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 : n010.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 08:33:16 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 167 ( 75 unt; 0 typ; 9 def)
% Number of atoms : 1277 ( 252 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 2004 ( 161 ~; 154 |; 27 &;1369 @)
% ( 9 <=>; 185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 21 con; 0-4 aty)
% ( 99 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 319 ( 0 sgn 195 !; 8 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
binunionE: $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
setminus: $i > $i > $i ).
thf(func_def_7,type,
setminusI: $o ).
thf(func_def_8,type,
setminusER: $o ).
thf(func_def_9,type,
binintersectTELcontra: $o ).
thf(func_def_10,type,
binintersectTERcontra: $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vOR: $o > $o > $o ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f2,axiom,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f3,axiom,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f4,axiom,
( binintersectTELcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(f5,axiom,
( binintersectTERcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(f6,conjecture,
( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1b) ).
thf(f7,negated_conjecture,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( binintersectTELcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( binintersectTELcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( binintersectTERcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( binintersectTERcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( binunionE = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binunionE = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binunionE = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binunionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f21]) ).
thf(f23,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f24,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f26,plain,
( binintersectTELcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( binintersectTERcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
binunionE = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f29,plain,
setminusI = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
setminusER = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
binintersectTELcontra = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
binintersectTERcontra = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
( $true
= ( in @ sK3 @ ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f28]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f24,f29]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f25,f30]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f31]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f32]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X3 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X3 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X3 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( ~ ( in @ X4 @ X3 ) ) )
| ( $true
= ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
= ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f60,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ X1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ X1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X1 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ~ ( in @ X4 @ X1 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( ~ ( in @ X4 @ X1 ) ) )
| ( $true
= ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( in @ X4 @ X1 ) )
| ( $true
= ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f74,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ~ ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ~ ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setminus @ X3 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( ~ ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f82,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( ~ ( in @ X1 @ X2 ) ) )
| ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f91,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binunion @ X3 @ X2 ) )
=> ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f101,plain,
( ( $true != $true )
| ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f37,f89]) ).
thf(f102,plain,
( ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f106,definition,
( spl4_1
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f108,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f110,definition,
( spl4_2
<=> ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f112,plain,
( ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f113,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f102,f110,f106]) ).
thf(f116,plain,
( ( $true = $false )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f36,f97]) ).
thf(f117,plain,
( ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f120,definition,
( spl4_3
<=> ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f122,plain,
( ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f124,definition,
( spl4_4
<=> ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f126,plain,
( ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f127,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f117,f124,f120]) ).
thf(f129,plain,
( ( $true = $false )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f122,f80]) ).
thf(f137,definition,
( spl4_5
<=> ( $true
= ( in @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f139,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f142,plain,
( ( $true = $false )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f80,f126]) ).
thf(f143,plain,
( ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f178,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK3 @ sK2 ) ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f58,f112]) ).
thf(f210,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK3 @ sK2 ) ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f224,definition,
( spl4_6
<=> ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f225,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f227,plain,
( spl4_5
| spl4_6
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f210,f110,f224,f137]) ).
thf(f228,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_5 ),
inference(constrained_superposition,[],[f139,f143]) ).
thf(f232,plain,
( $false
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f233,plain,
( ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f232]) ).
thf(f234,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f108,f35]) ).
thf(f240,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f241,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f240]) ).
thf(f349,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK3 @ sK1 ) ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f72,f112]) ).
thf(f380,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK3 @ sK1 ) ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f349]) ).
thf(f393,definition,
( spl4_7
<=> ( $true
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f395,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f393]) ).
thf(f397,plain,
( spl4_7
| spl4_6
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f380,f110,f224,f393]) ).
thf(f405,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f225,f35]) ).
thf(f427,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f442,definition,
( spl4_10
<=> ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f444,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f442]) ).
thf(f446,definition,
( spl4_11
<=> ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f448,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f446]) ).
thf(f479,plain,
( spl4_10
| spl4_11
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f427,f224,f446,f442]) ).
thf(f517,plain,
( ( $true = $false )
| ~ spl4_10 ),
inference(constrained_superposition,[],[f444,f34]) ).
thf(f523,plain,
( $false
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f517]) ).
thf(f524,plain,
~ spl4_10,
inference(avatar_contradiction_clause,[],[f523]) ).
thf(f539,plain,
( ( $true = $false )
| ~ spl4_11 ),
inference(constrained_superposition,[],[f448,f33]) ).
thf(f545,plain,
( $false
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f539]) ).
thf(f546,plain,
~ spl4_11,
inference(avatar_contradiction_clause,[],[f545]) ).
thf(f547,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f550,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_7 ),
inference(constrained_superposition,[],[f547,f395]) ).
thf(f556,plain,
( $false
| ~ spl4_3
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f550]) ).
thf(f557,plain,
( ~ spl4_3
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f556]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f113]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
( ~ spl4_2
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f227]) ).
cnf(s8,plain,
( ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f233]) ).
cnf(s10,plain,
~ spl4_1,
inference(sat_conversion,[],[f241]) ).
cnf(s12,plain,
( ~ spl4_2
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f397]) ).
cnf(s20,plain,
( ~ spl4_6
| spl4_10
| spl4_11 ),
inference(sat_conversion,[],[f479]) ).
cnf(s25,plain,
~ spl4_10,
inference(sat_conversion,[],[f524]) ).
cnf(s27,plain,
~ spl4_11,
inference(sat_conversion,[],[f546]) ).
cnf(s29,plain,
( ~ spl4_3
| ~ spl4_7 ),
inference(sat_conversion,[],[f557]) ).
cnf(s30,plain,
~ spl4_6,
inference(rat,[],[s20,s27,s25]) ).
cnf(s31,plain,
( ~ spl4_2
| spl4_7 ),
inference(rat,[],[s12,s30]) ).
cnf(s33,plain,
( ~ spl4_2
| spl4_5 ),
inference(rat,[],[s6,s30]) ).
cnf(s36,plain,
spl4_2,
inference(rat,[],[s1,s10]) ).
cnf(s37,plain,
spl4_7,
inference(rat,[],[s31,s36]) ).
cnf(s38,plain,
spl4_5,
inference(rat,[],[s33,s36]) ).
cnf(s39,plain,
~ spl4_3,
inference(rat,[],[s29,s37]) ).
cnf(s40,plain,
~ spl4_4,
inference(rat,[],[s8,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s2,s40,s39]) ).
thf(f558,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU752^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 % Computer : n010.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 14:22:03 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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 % (2932797)Will run a generic schedule for satisfiability detection.
% 0.22/0.32 % (2932806)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3239171057:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.32 % (2932806)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (2932808)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3553012674:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.32 % (2932803)% WARNING: option uhcvi not known.
% 0.22/0.32 % (2932803)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=412958731:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.32 % (2932802)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=24172380_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.32 % (2932803)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (2932807)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1733357378:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (2932804)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3504325432:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.32 % (2932803)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 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 % (2932805)dis+10_1_sil=32000:sp=arity:random_seed=3263117870:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.32 % (2932808) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2932797-2932808"...
% 0.22/0.32 % (2932806) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2932797-2932806"...
% 0.22/0.32 % (2932806)...printing done.
% 0.22/0.32 % (2932808)...printing done.
% 0.22/0.32 % (2932816)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1108055760:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.32 % (2932808)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 % (2932808)------------------------------
% 0.22/0.32 % (2932808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (2932808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (2932808)CaDiCaL version: 2.1.3
% 0.22/0.32 % (2932808)Termination reason: Refutation
% 0.22/0.32 % (2932808)Time elapsed: 0.031 s
% 0.22/0.32 % (2932808)Peak memory usage: 13 MB
% 0.22/0.32 % (2932808)Instructions burned: 57 (million)
% 0.22/0.32 % (2932797)Success in time 0.068 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------