%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU764^2 : 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 : n009.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 08:33:19 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 6
% Syntax : Number of formulae : 92 ( 43 unt; 0 typ; 2 def)
% Number of atoms : 805 ( 178 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 1530 ( 36 ~; 58 |; 21 &;1274 @)
% ( 2 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 28 ( 24 usr; 13 con; 0-4 aty)
% ( 48 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 0 sgn 95 !; 10 ?; 162 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_5,type,
binunionT_lem: $o ).
thf(func_def_7,type,
demorgan1: $o ).
thf(func_def_8,type,
demorgan2: $o ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vIMP: $o > $o > $o ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(f1,axiom,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(f2,axiom,
( demorgan1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).
thf(f3,axiom,
( demorgan2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2) ).
thf(f4,conjecture,
( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_2) ).
thf(f5,negated_conjecture,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( binunionT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( demorgan1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( demorgan1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
= ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( demorgan2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( demorgan2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) )
= ( binintersect @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( binunionT_lem = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan2 = $true )
& ( demorgan1 = $true )
& ( binunionT_lem = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan2 = $true )
& ( demorgan1 = $true )
& ( binunionT_lem = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( demorgan2 = $true )
& ( demorgan1 = $true )
& ( binunionT_lem = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f15]) ).
thf(f17,plain,
( binunionT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( demorgan1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
= ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( demorgan2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) )
= ( binintersect @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
binunionT_lem = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
demorgan1 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
demorgan2 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( $true
= ( in @ sK3 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( $true
= ( in @ sK4 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
= ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) )
= ( binintersect @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f19,f22]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) )
= ( binintersect @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( binunion @ X1 @ Y1 ) )
= ( binintersect @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( binunion @ X1 @ Y1 ) )
= ( binintersect @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binunion @ X1 @ X3 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( setminus @ X2 @ ( binunion @ X1 @ X3 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( setminus @ X2 @ ( binunion @ X1 @ X3 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
= ( binunion @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) )
= ( binunion @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) )
= ( binunion @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ Y1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ Y0 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( in @ ( binunion @ Y0 @ Y2 ) @ ( powerset @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f52,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ X1 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ X1 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ Y0 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ Y0 ) @ ( powerset @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X1 @ X3 ) @ ( powerset @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( binunion @ X1 @ X3 ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f68,plain,
( ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f27,f41]) ).
thf(f69,plain,
( ( $true = $false )
| ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f68,f24]) ).
thf(f70,plain,
( ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f73,plain,
( ( $true = $false )
| ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) ) ),
inference(forward_demodulation,[],[f70,f23]) ).
thf(f74,plain,
( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( binintersect @ ( setminus @ sK0 @ sK3 ) @ ( setminus @ sK0 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f77,plain,
( ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( setminus @ sK0 @ ( binunion @ sK3 @ sK4 ) ) ) )
| ( ( in @ sK4 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f74,f41]) ).
thf(f78,plain,
( ( $true = $false )
| ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( setminus @ sK0 @ ( binunion @ sK3 @ sK4 ) ) ) )
| ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f77,f26]) ).
thf(f79,plain,
( ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( setminus @ sK0 @ ( binunion @ sK3 @ sK4 ) ) ) )
| ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ( $true = $false )
| ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( setminus @ sK0 @ ( binunion @ sK3 @ sK4 ) ) ) ) ),
inference(forward_demodulation,[],[f79,f25]) ).
thf(f81,plain,
( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( binunion @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) @ ( setminus @ sK0 @ ( binunion @ sK3 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f88,plain,
( ( ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) )
!= ( setminus @ sK0 @ ( binintersect @ ( binunion @ sK1 @ sK2 ) @ ( binunion @ sK3 @ sK4 ) ) ) )
| ( $false
= ( in @ ( binunion @ sK3 @ sK4 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binunion @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f81,f50]) ).
thf(f89,plain,
( ( $false
= ( in @ ( binunion @ sK3 @ sK4 ) @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( binunion @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f91,definition,
( spl5_1
<=> ( $false
= ( in @ ( binunion @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f93,plain,
( ( $false
= ( in @ ( binunion @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f95,definition,
( spl5_2
<=> ( $false
= ( in @ ( binunion @ sK3 @ sK4 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f97,plain,
( ( $false
= ( in @ ( binunion @ sK3 @ sK4 ) @ ( powerset @ sK0 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f98,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f89,f95,f91]) ).
thf(f101,plain,
( ( $true = $false )
| ( ( in @ sK4 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f58,f97]) ).
thf(f102,plain,
( ( ( in @ sK4 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f105,plain,
( ( $true = $false )
| ( ( in @ sK4 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f102,f25]) ).
thf(f106,plain,
( ( ( in @ sK4 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f110,plain,
( ( $true = $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f106,f26]) ).
thf(f116,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f117,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f116]) ).
thf(f120,plain,
( ( $true = $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f58,f93]) ).
thf(f121,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f124,plain,
( ( $true = $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f121,f23]) ).
thf(f125,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f128,plain,
( ( $true = $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f125,f24]) ).
thf(f134,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f135,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f134]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f98]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f117]) ).
cnf(s5,plain,
~ spl5_1,
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f136,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU764^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:23:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (4072840)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (4072846)% WARNING: option uhcvi not known.
% 0.09/0.25 % (4072846)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1675429334:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (4072846)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (4072846)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.25 % (4072846) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4072840-4072846"...
% 0.09/0.25 % (4072846)...printing done.
% 0.09/0.25 % (4072846)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (4072846)------------------------------
% 0.09/0.25 % (4072846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (4072846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (4072846)CaDiCaL version: 2.1.3
% 0.09/0.25 % (4072846)Termination reason: Refutation
% 0.09/0.25 % (4072846)Time elapsed: 0.006 s
% 0.09/0.25 % (4072846)Peak memory usage: 13 MB
% 0.09/0.25 % (4072846)Instructions burned: 21 (million)
% 0.09/0.25 % (4072840)Success in time 0.031 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------