%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU813^2 : 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 : n012.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 08:33:31 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 96 ( 65 unt; 0 typ; 2 def)
% Number of atoms : 603 ( 121 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 742 ( 23 ~; 26 |; 18 &; 535 @)
% ( 2 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 26 ( 22 usr; 12 con; 0-4 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 158 ( 0 sgn 82 !; 4 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
binintersect: $i > $i > $i ).
thf(func_def_3,type,
binintersectSubset5: $o ).
thf(func_def_5,type,
binintersectEL: $o ).
thf(func_def_6,type,
binintersectER: $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
transitivesetOp1: $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_21,type,
sK3: $i > $i ).
thf(f1,axiom,
( binintersectSubset5
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(f2,axiom,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f3,axiom,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(f4,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(f6,conjecture,
( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
thf(f7,negated_conjecture,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( binintersectSubset5
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( binintersectSubset5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ( ( transitivesetOp1 = $true )
=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
= ( transitiveset @ sK1 ) )
& ( $true
= ( transitiveset @ sK0 ) )
& ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
thf(f23,plain,
( binintersectSubset5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f24,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f26,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f28,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f29,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( $true
= ( transitiveset @ sK0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( $true
= ( transitiveset @ sK1 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f28]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f24,f29]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f25,f30]) ).
thf(f41,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ ( binintersect @ sK0 @ sK1 ) ) ),
inference(definition_unfolding,[],[f34,f26]) ).
thf(f42,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(definition_unfolding,[],[f33,f26]) ).
thf(f43,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f32,f26]) ).
thf(f44,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK1 )
=> ( subset @ X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ Y0 @ ( binintersect @ sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f53,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ Y0 @ ( binintersect @ sK0 @ sK1 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( $false
= ( ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( $false
= ( subset @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $true
= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f67,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f75,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f82,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( subset @ X1 @ Y0 )
=> ( subset @ X1 @ ( binintersect @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( subset @ X1 @ Y0 )
=> ( subset @ X1 @ ( binintersect @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X3 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ X3 ) )
| ( $true
= ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( $false
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f90,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f56,f73]) ).
thf(f91,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f94,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f56,f80]) ).
thf(f95,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f120,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ sK1 ) )
| ( $false
= ( subset @ sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f88,f55]) ).
thf(f127,plain,
( ( $false
= ( subset @ sK2 @ sK1 ) )
| ( $false
= ( subset @ sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f129,definition,
( spl4_1
<=> ( $false
= ( subset @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f131,plain,
( ( $false
= ( subset @ sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f133,definition,
( spl4_2
<=> ( $false
= ( subset @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f135,plain,
( ( $false
= ( subset @ sK2 @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f137,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f127,f133,f129]) ).
thf(f140,plain,
( ( $true = $false )
| ( $false
= ( in @ sK2 @ sK1 ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f51,f135]) ).
thf(f141,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f143,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f141,f91]) ).
thf(f147,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f148,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f150,plain,
( ( $true = $false )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f47,f131]) ).
thf(f151,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f154,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f151,f95]) ).
thf(f158,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f159,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f158]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f137]) ).
cnf(s4,plain,
~ spl4_2,
inference(sat_conversion,[],[f148]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f159]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s6]) ).
thf(f160,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU813^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:33:18 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 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
% 0.08/0.16 % (187246)Will run a generic schedule for satisfiability detection.
% 0.08/0.16 % (187256)% WARNING: option uhcvi not known.
% 0.08/0.16 % (187258)dis+10_1_sil=32000:sp=arity:random_seed=1873389941:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.16 % (187259)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2601545027:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.16 % (187255)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=524920840_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.16 % (187256)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3233161730:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.16 % (187257)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=682395959:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.16 % (187260)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1709122400:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.16 % (187261)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=967348493:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.16 % (187259)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.16 % (187256)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.16 % Exception at run slice level% (187256)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.16
% 0.08/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.16 % (187261) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187246-187261"...
% 0.08/0.16 % (187259) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187246-187259"...
% 0.08/0.16 % (187260) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187246-187260"...
% 0.08/0.16 % (187258) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187246-187258"...
% 0.08/0.16 % (187256) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187246-187256"...
% 0.08/0.16 % (187257) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187246-187257"...
% 0.08/0.16 % (187261)...printing done.
% 0.08/0.16 % (187259)...printing done.
% 0.08/0.16 % (187260)...printing done.
% 0.08/0.16 % (187261)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.16 % (187261)------------------------------
% 0.08/0.16 % (187261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (187261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (187261)CaDiCaL version: 2.1.3
% 0.08/0.16 % (187261)Termination reason: Refutation
% 0.08/0.16 % (187261)Time elapsed: 0.004 s
% 0.08/0.16 % (187261)Peak memory usage: 13 MB
% 0.08/0.16 % (187261)Instructions burned: 14 (million)
% 0.08/0.16 % (187246)Success in time 0.034 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------