%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU736^2 : 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 : n006.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 08:33:11 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 9
% Syntax : Number of formulae : 94 ( 39 unt; 0 typ; 6 def)
% Number of atoms : 738 ( 145 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1068 ( 71 ~; 81 |; 21 &; 727 @)
% ( 6 <=>; 120 =>; 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 : 29 ( 25 usr; 15 con; 0-4 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 153 ( 0 sgn 96 !; 8 ?; 153 :)
% 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,
setminusI: $o ).
thf(func_def_6,type,
contrasubsetT: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,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(f2,axiom,
( contrasubsetT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT) ).
thf(f3,conjecture,
( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,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,[],[f5]) ).
thf(f7,plain,
( contrasubsetT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( contrasubsetT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( subset @ Y0 @ ( setminus @ Y1 @ Y2 ) )
=> ( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setminusI = $true )
=> ( ( contrasubsetT = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f12]) ).
thf(f14,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,[],[f6]) ).
thf(f15,plain,
( contrasubsetT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( subset @ Y0 @ ( setminus @ Y1 @ Y2 ) )
=> ( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
setminusI = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
contrasubsetT = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
( $true
= ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
( $true
= ( in @ sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f26,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,[],[f14,f16]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( subset @ Y0 @ ( setminus @ Y1 @ Y2 ) )
=> ( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f28,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 )
=> ( ( subset @ Y0 @ ( setminus @ Y1 @ Y2 ) )
=> ( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( subset @ X1 @ ( setminus @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ X1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,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 )
=> ( ( subset @ X1 @ ( setminus @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ X1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ Y0 ) )
=> ( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ Y0 ) )
=> ( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,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 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ Y0 ) )
=> ( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ X3 ) )
=> ( ( in @ Y0 @ X3 )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ X3 ) )
=> ( ( in @ Y0 @ X3 )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f36,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 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ X3 ) )
=> ( ( in @ Y0 @ X3 )
=> ~ ( in @ Y0 @ X1 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( subset @ X1 @ ( setminus @ X2 @ X3 ) )
=> ( ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ( subset @ X1 @ ( setminus @ X2 @ X3 ) )
=> ( ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( subset @ X1 @ ( setminus @ X2 @ X3 ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( subset @ X1 @ ( setminus @ X2 @ X3 ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ~ ( in @ X4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( setminus @ X2 @ X3 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f42,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,[],[f26]) ).
thf(f43,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,[],[f42]) ).
thf(f44,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,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,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,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f49,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,[],[f48]) ).
thf(f50,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,[],[f49]) ).
thf(f51,plain,
( ( $true != $true )
| ( $true
= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f23,f50]) ).
thf(f52,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f54,definition,
( spl4_1
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f56,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f58,definition,
( spl4_2
<=> ( $true
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f60,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f61,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f52,f58,f54]) ).
thf(f87,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f41,f20]) ).
thf(f120,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f129,definition,
( spl4_3
<=> ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f131,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f133,definition,
( spl4_4
<=> ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f135,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f137,definition,
( spl4_5
<=> ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f138,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f120,f137,f133,f129]) ).
thf(f141,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f131,f18]) ).
thf(f147,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f148,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f151,plain,
( ( $true = $false )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f135,f19]) ).
thf(f157,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f151]) ).
thf(f158,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f157]) ).
thf(f161,plain,
( ( $true = $false )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f138,f22]) ).
thf(f166,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f168,definition,
( spl4_6
<=> ( $false
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f170,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f172,plain,
( spl4_1
| spl4_6
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f166,f137,f168,f54]) ).
thf(f191,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f170,f60]) ).
thf(f197,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f198,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f197]) ).
thf(f199,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f56,f21]) ).
thf(f205,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f199]) ).
thf(f206,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f205]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f140]) ).
cnf(s5,plain,
~ spl4_3,
inference(sat_conversion,[],[f148]) ).
cnf(s7,plain,
~ spl4_4,
inference(sat_conversion,[],[f158]) ).
cnf(s9,plain,
( spl4_1
| ~ spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f172]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f198]) ).
cnf(s13,plain,
~ spl4_1,
inference(sat_conversion,[],[f206]) ).
cnf(s14,plain,
( ~ spl4_5
| spl4_6 ),
inference(rat,[],[s9,s13]) ).
cnf(s16,plain,
spl4_5,
inference(rat,[],[s3,s7,s5]) ).
cnf(s17,plain,
spl4_6,
inference(rat,[],[s14,s16]) ).
cnf(s18,plain,
~ spl4_2,
inference(rat,[],[s11,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s13]) ).
thf(f207,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU736^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:18:09 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.27 % (789898)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (789909)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3057851600:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (789904)% WARNING: option uhcvi not known.
% 0.18/0.27 % (789909) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-789898-789909"...
% 0.18/0.27 % (789903)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2112539740_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (789904)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3416541526:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (789905)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4290554013:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (789906)dis+10_1_sil=32000:sp=arity:random_seed=2142591990:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (789907)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2950721268:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (789908)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1475797757:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (789904)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (789907)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (789909)...printing done.
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (789904)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (789909)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (789909)------------------------------
% 0.18/0.27 % (789909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (789909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (789909)CaDiCaL version: 2.1.3
% 0.18/0.27 % (789909)Termination reason: Refutation
% 0.18/0.27 % (789909)Time elapsed: 0.008 s
% 0.18/0.27 % (789909)Peak memory usage: 13 MB
% 0.18/0.27 % (789909)Instructions burned: 24 (million)
% 0.18/0.27 % (789898)Success in time 0.042 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------