%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU754^2 : 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 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 170 ( 77 unt; 0 typ; 10 def)
% Number of atoms : 1294 ( 256 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 2005 ( 158 ~; 141 |; 27 &;1373 @)
% ( 10 <=>; 197 =>; 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; 22 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,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
binintersectI: $o ).
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,
binunionTILcontra: $o ).
thf(func_def_10,type,
binunionTIRcontra: $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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
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,
( binunionTILcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(f5,axiom,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(f6,conjecture,
( binintersectI
=> ( setminusI
=> ( setminusER
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a) ).
thf(f7,negated_conjecture,
~ ( binintersectI
=> ( setminusI
=> ( setminusER
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ 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,
( binunionTILcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( binunionTILcontra
= ( !! @ $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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( binunionTIRcontra
= ( !! @ $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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( binintersectI
=> ( setminusI
=> ( setminusER
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( binintersectI = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $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 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( $true
!= ( in @ sK3 @ ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $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,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ 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,
( binunionTILcontra
= ( !! @ $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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( binunionTIRcontra
= ( !! @ $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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
binintersectI = $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,
binunionTILcontra = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
binunionTIRcontra = $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 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
( $true
!= ( in @ sK3 @ ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ 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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ 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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ 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 @ ( binunion @ X1 @ Y1 ) )
=> ~ ( in @ Y2 @ 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 @ ( binunion @ X1 @ Y1 ) )
=> ~ ( in @ Y2 @ 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 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ 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 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ 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 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ X4 @ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ X4 @ 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 @ ( binunion @ X1 @ X3 ) ) ) )
| ( $true
= ( ~ ( in @ X4 @ 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 @ ( binunion @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( in @ X4 @ 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 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X1 @ X3 ) ) )
| ( $false
= ( 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 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
@ 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 @ ( binunion @ X1 @ Y1 ) )
=> ~ ( in @ Y2 @ X1 ) ) ) ) ) ) ) ) ),
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 @ ( binunion @ X1 @ Y1 ) )
=> ~ ( in @ Y2 @ X1 ) ) ) ) ) ) )
@ 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 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) ) ) ),
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 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) ) ) ),
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 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ X1 ) ) ) ) )
@ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ) ),
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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ),
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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ X1 ) ) )
@ 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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ X4 @ X1 ) ) ) ) ),
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 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ X4 @ X1 ) ) ) ),
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 @ ( binunion @ X1 @ X3 ) ) ) )
| ( $true
= ( ~ ( in @ X4 @ X1 ) ) ) ),
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 @ ( binunion @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( in @ X4 @ X1 ) ) ) ),
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 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X1 @ X3 ) ) )
| ( $false
= ( 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 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f91,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( $true = $false )
| ( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f36,f80]) ).
thf(f100,plain,
( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f106,plain,
( ( $true != $true )
| ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f37,f97]) ).
thf(f107,plain,
( ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f109,definition,
( spl4_1
<=> ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f111,plain,
( ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f113,definition,
( spl4_2
<=> ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f115,plain,
( ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f116,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f107,f113,f109]) ).
thf(f120,plain,
( ( $true = $false )
| ( $true
= ( in @ sK3 @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f115,f89]) ).
thf(f123,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f125,definition,
( spl4_3
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f127,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f129,definition,
( spl4_4
<=> ( $true
= ( in @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f131,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f133,plain,
( spl4_3
| spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f123,f113,f129,f125]) ).
thf(f134,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f127,f35]) ).
thf(f138,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f139,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f138]) ).
thf(f179,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK3 @ sK2 ) ) ),
inference(constrained_superposition,[],[f58,f100]) ).
thf(f204,plain,
! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f218,definition,
( spl4_5
<=> ( $false
= ( in @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f220,plain,
( ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f222,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(f223,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f225,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f204,f222,f218]) ).
thf(f226,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_5 ),
inference(constrained_superposition,[],[f220,f131]) ).
thf(f232,plain,
( $false
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f233,plain,
( ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f232]) ).
thf(f240,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f223,f35]) ).
thf(f264,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f280,definition,
( spl4_9
<=> ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f282,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f284,definition,
( spl4_10
<=> ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f286,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f308,plain,
( spl4_9
| spl4_10
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f264,f222,f284,f280]) ).
thf(f317,plain,
( ( $true = $false )
| ~ spl4_9 ),
inference(constrained_superposition,[],[f282,f34]) ).
thf(f323,plain,
( $false
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f324,plain,
~ spl4_9,
inference(avatar_contradiction_clause,[],[f323]) ).
thf(f331,plain,
( ( $true = $false )
| ~ spl4_10 ),
inference(constrained_superposition,[],[f286,f33]) ).
thf(f337,plain,
( $false
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f331]) ).
thf(f338,plain,
~ spl4_10,
inference(avatar_contradiction_clause,[],[f337]) ).
thf(f350,plain,
( ( $true = $false )
| ( $true
= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f111,f89]) ).
thf(f355,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f350]) ).
thf(f357,definition,
( spl4_15
<=> ( $true
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_15])],[avatar_definition]) ).
thf(f359,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f361,plain,
( spl4_3
| spl4_15
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f355,f109,f357,f125]) ).
thf(f391,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f72,f100]) ).
thf(f438,plain,
! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f454,definition,
( spl4_16
<=> ( $false
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
thf(f456,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f454]) ).
thf(f458,plain,
( spl4_16
| spl4_6 ),
inference(avatar_split_clause,[],[f438,f222,f454]) ).
thf(f459,plain,
( ( $true = $false )
| ~ spl4_15
| ~ spl4_16 ),
inference(constrained_superposition,[],[f456,f359]) ).
thf(f465,plain,
( $false
| ~ spl4_15
| ~ spl4_16 ),
inference(trivial_inequality_removal,[],[f459]) ).
thf(f466,plain,
( ~ spl4_15
| ~ spl4_16 ),
inference(avatar_contradiction_clause,[],[f465]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f116]) ).
cnf(s3,plain,
( ~ spl4_2
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
~ spl4_3,
inference(sat_conversion,[],[f139]) ).
cnf(s7,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f225]) ).
cnf(s9,plain,
( ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f233]) ).
cnf(s17,plain,
( ~ spl4_6
| spl4_9
| spl4_10 ),
inference(sat_conversion,[],[f308]) ).
cnf(s20,plain,
~ spl4_9,
inference(sat_conversion,[],[f324]) ).
cnf(s22,plain,
~ spl4_10,
inference(sat_conversion,[],[f338]) ).
cnf(s24,plain,
( ~ spl4_1
| spl4_3
| spl4_15 ),
inference(sat_conversion,[],[f361]) ).
cnf(s26,plain,
( spl4_6
| spl4_16 ),
inference(sat_conversion,[],[f458]) ).
cnf(s28,plain,
( ~ spl4_15
| ~ spl4_16 ),
inference(sat_conversion,[],[f466]) ).
cnf(s29,plain,
~ spl4_6,
inference(rat,[],[s17,s22,s20]) ).
cnf(s30,plain,
spl4_16,
inference(rat,[],[s26,s29]) ).
cnf(s31,plain,
~ spl4_15,
inference(rat,[],[s28,s30]) ).
cnf(s32,plain,
spl4_5,
inference(rat,[],[s7,s29]) ).
cnf(s33,plain,
~ spl4_4,
inference(rat,[],[s9,s32]) ).
cnf(s34,plain,
~ spl4_1,
inference(rat,[],[s24,s31,s5]) ).
cnf(s35,plain,
~ spl4_2,
inference(rat,[],[s3,s33,s5]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s1,s35,s34]) ).
thf(f467,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU754^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:22:18 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.22/0.31 % (2933230)Will run a generic schedule for satisfiability detection.
% 0.22/0.31 % (2933241)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3242269010:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.31 % (2933236)% WARNING: option uhcvi not known.
% 0.22/0.31 % (2933235)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2256267127_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.31 % (2933236)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1399978457:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.31 % (2933236)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.31 % (2933240)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=236195156:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.31 % Exception at run slice level
% 0.22/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.31 % (2933236)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.31 % (2933238)dis+10_1_sil=32000:sp=arity:random_seed=1804697918:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.31 % (2933241) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2933230-2933241"...
% 0.22/0.31 % (2933237)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3730467753:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.31 % (2933239)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3345612338:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.31 % (2933239)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.31 % (2933241)...printing done.
% 0.22/0.31 % (2933241)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (2933241)------------------------------
% 0.22/0.32 % (2933241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (2933241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (2933241)CaDiCaL version: 2.1.3
% 0.22/0.32 % (2933241)Termination reason: Refutation
% 0.22/0.32 % (2933241)Time elapsed: 0.025 s
% 0.22/0.32 % (2933241)Peak memory usage: 12 MB
% 0.22/0.32 % (2933241)Instructions burned: 43 (million)
% 0.22/0.32 % (2933230)Success in time 0.064 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------