%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU730^2 : 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 : n018.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 08:33:09 AM UTC 2026
% Result : Theorem 0.19s 0.34s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 4
% Syntax : Number of formulae : 74 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 723 ( 171 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 1324 ( 8 ~; 85 |; 12 &;1041 @)
% ( 0 <=>; 126 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 8 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 184 ( 61 ^; 119 !; 4 ?; 184 :)
% 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,
subset: $i > $i > $o ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
complementT_lem: $o ).
thf(func_def_6,type,
subsetTI: $o ).
thf(func_def_7,type,
doubleComplementE1: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
sK2: $i > $i > $i > $i ).
thf(f1,axiom,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(f2,axiom,
( subsetTI
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(f3,axiom,
( doubleComplementE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(f4,conjecture,
( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(f5,negated_conjecture,
~ ( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( subsetTI
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( subsetTI
= ( !! @ $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 @ Y2 ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( doubleComplementE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( complementT_lem = $true )
=> ( ( subsetTI = $true )
=> ( ( doubleComplementE1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( doubleComplementE1 = $true )
& ( subsetTI = $true )
& ( complementT_lem = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( doubleComplementE1 = $true )
& ( subsetTI = $true )
& ( complementT_lem = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( subset @ ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) @ sK1 ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( doubleComplementE1 = $true )
& ( subsetTI = $true )
& ( complementT_lem = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
thf(f17,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( subsetTI
= ( !! @ $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 @ Y2 ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
complementT_lem = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
subsetTI = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
doubleComplementE1 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
( $true
!= ( subset @ ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f28,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 @ Y2 ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f19,f22]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) )
=> ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) )
=> ( in @ Y1 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( $true
= ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f39,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 @ Y2 ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f40,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 @ Y1 ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,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 @ Y1 ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,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 @ Y0 ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,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 @ Y0 ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,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 @ Y0 ) ) ) )
=> ( subset @ X1 @ Y0 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,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 @ X3 ) ) ) )
=> ( subset @ X1 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,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 @ X3 ) ) ) )
=> ( subset @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f54,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X0 ) ) ),
inference(constrained_superposition,[],[f38,f53]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X3 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f205,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X0 ) )
| ( $true
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X1 ) @ X2 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X0 ) ) ),
inference(constrained_superposition,[],[f51,f89]) ).
thf(f213,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X0 ) )
| ( $true
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X1 ) @ X2 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(duplicate_literal_removal,[],[f205]) ).
thf(f214,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X1 ) @ X2 ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X0 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f319,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(constrained_superposition,[],[f52,f214]) ).
thf(f336,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f319]) ).
thf(f337,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f387,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $false )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f58,f337]) ).
thf(f388,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f387]) ).
thf(f598,plain,
( ( $true != $true )
| ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f24,f388]) ).
thf(f599,plain,
( ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f598]) ).
thf(f602,plain,
( ( $true = $false )
| ( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f599,f23]) ).
thf(f603,plain,
( $false
= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f610,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f58,f603]) ).
thf(f611,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f616,plain,
$true = $false,
inference(constrained_superposition,[],[f23,f611]) ).
thf(f617,plain,
$false,
inference(trivial_inequality_removal,[],[f616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU730^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.16 % Computer : n018.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 14:19:41 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.34 % (146292)Will run a generic schedule for satisfiability detection.
% 0.19/0.34 % (146297)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1536598395_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.34 % Exception at run slice level
% 0.19/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.34 % (146298)% WARNING: option uhcvi not known.
% 0.19/0.34 % (146298)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3170387477:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.34 % (146298)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.34 % (146298)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.34 % (146305)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=485899553:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.34 % Exception at run slice level
% 0.19/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.34 % (146299)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3929079322:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.34 % (146300)dis+10_1_sil=32000:sp=arity:random_seed=314458875:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.34 % (146308)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1621630277:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.34 % (146301)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3331238960:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.34 % (146303)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2358484649:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.34 % (146302)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1456484446:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.34 % (146301)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.34 % (146308)Instruction limit reached!
% 0.19/0.34 % (146308)------------------------------
% 0.19/0.34 % (146308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (146308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (146308)CaDiCaL version: 2.1.3
% 0.19/0.34 % (146308)Termination reason: Instruction limit
% 0.19/0.34 % (146308)Termination phase: Saturation
% 0.19/0.34 % (146308)Time elapsed: 0.035 s
% 0.19/0.34 % (146308)Peak memory usage: 12 MB
% 0.19/0.34 % (146308)Instructions burned: 134 (million)
% 0.19/0.34 % (146298) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-146292-146298"...
% 0.19/0.34 % (146298)...printing done.
% 0.19/0.34 % (146315)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2234730855:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.34 % (146298)Refutation found. Thanks to Tanya!
% 0.19/0.34 % SZS status Theorem for theBenchmark
% 0.19/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.34 % (146298)------------------------------
% 0.19/0.34 % (146298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (146298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (146298)CaDiCaL version: 2.1.3
% 0.19/0.34 % (146298)Termination reason: Refutation
% 0.19/0.34 % (146298)Time elapsed: 0.067 s
% 0.19/0.34 % (146298)Peak memory usage: 12 MB
% 0.19/0.34 % (146298)Instructions burned: 137 (million)
% 0.19/0.34 % (146292)Success in time 0.113 s
% 0.19/0.34 % Vampire exiting
%------------------------------------------------------------------------------