%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU787^2 : 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 : n026.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 08:33:25 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 22 unt; 0 typ; 3 def)
% Number of atoms : 751 ( 152 equ; 0 cnn)
% Maximal formula atoms : 11 ( 11 avg)
% Number of connectives : 1137 ( 24 ~; 115 |; 24 &; 817 @)
% ( 3 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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; 13 con; 0-4 aty)
% ( 41 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 150 ( 0 sgn 92 !; 12 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
breln1: $i > $i > $o ).
thf(func_def_4,type,
breln1unionE: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
sK5: $o ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(f1,axiom,
( breln1unionE
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionE) ).
thf(f2,conjecture,
( breln1unionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ! [X5: $o] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> X5 )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> X5 )
=> X5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionEcases) ).
thf(f3,negated_conjecture,
~ ( breln1unionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ! [X5: $o] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> X5 )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> X5 )
=> X5 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( breln1unionE
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( breln1unionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( binunion @ Y0 @ Y2 ) )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
| ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( breln1unionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ! [X5: $o] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> X5 )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> X5 )
=> X5 ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( breln1unionE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
=> ! [X5: $o] :
( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( $true = X5 ) )
=> ( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( $true = X5 ) )
=> ( $true = X5 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true ) )
& ( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1unionE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true ) )
& ( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1unionE = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ( $true != sK5 )
& ( ( $true = sK5 )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) )
& ( ( $true = sK5 )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK4 @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( breln1 @ sK0 @ sK2 ) )
& ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( breln1unionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f9]) ).
thf(f11,plain,
( breln1unionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( binunion @ Y0 @ Y2 ) )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
| ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
breln1unionE = $true,
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( $true
= ( breln1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
( $true
= ( breln1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f15,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
( $true
= ( in @ sK4 @ sK0 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f17,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
( ( $true = sK5 )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
( ( $true = sK5 )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f20,plain,
$true != sK5,
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( binunion @ Y0 @ Y2 ) )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
| ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f11,f12]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( binunion @ Y0 @ Y2 ) )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
| ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ ( binunion @ X1 @ Y1 ) )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
| ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ ( binunion @ X1 @ Y1 ) )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
| ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ ( binunion @ X1 @ Y0 ) )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
| ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ ( binunion @ X1 @ Y0 ) )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
| ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ ( binunion @ X1 @ Y0 ) )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
| ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
| ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
| ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
| ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X1 )
| ( in @ ( kpair @ X4 @ Y0 ) @ X3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X1 )
| ( in @ ( kpair @ X4 @ Y0 ) @ X3 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X1 )
| ( in @ ( kpair @ X4 @ Y0 ) @ X3 ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
| ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( $true
= ( ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X1 @ X3 ) )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
| ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( $false
= ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X1 @ X3 ) ) )
| ( $true
= ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
| ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( $false
= ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X1 @ X3 ) ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) ) ),
inference(or_proxy_clausification,[],[f38]) ).
thf(f41,definition,
( spl6_1
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f43,plain,
( ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) )
| spl6_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f45,definition,
( spl6_2
<=> ( $true = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f48,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f18,f45,f41]) ).
thf(f50,definition,
( spl6_3
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| spl6_3 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
( ~ spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f19,f45,f50]) ).
thf(f54,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f20,f45]) ).
thf(f85,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X0 @ sK1 ) )
| ( $false
= ( breln1 @ X0 @ sK2 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK4 @ X0 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f17,f39]) ).
thf(f96,plain,
! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK1 ) )
| ( $false
= ( breln1 @ X0 @ sK2 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK4 @ X0 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f111,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK1 ) )
| ( $false
= ( breln1 @ X0 @ sK2 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK4 @ X0 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) )
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f96,f52]) ).
thf(f113,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK2 ) )
| ( $false
= ( in @ sK4 @ X0 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( breln1 @ X0 @ sK1 ) ) )
| spl6_1
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f111,f43]) ).
thf(f124,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl6_1
| spl6_3 ),
inference(constrained_superposition,[],[f16,f113]) ).
thf(f125,plain,
( ( ( breln1 @ sK0 @ sK2 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl6_1
| spl6_3 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f129,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl6_1
| spl6_3 ),
inference(forward_demodulation,[],[f125,f14]) ).
thf(f130,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl6_1
| spl6_3 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f133,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl6_1
| spl6_3 ),
inference(forward_demodulation,[],[f130,f15]) ).
thf(f134,plain,
( ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl6_1
| spl6_3 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f158,plain,
( ( $true = $false )
| spl6_1
| spl6_3 ),
inference(constrained_superposition,[],[f134,f13]) ).
thf(f162,plain,
( $false
| spl6_1
| spl6_3 ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f163,plain,
( spl6_1
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f162]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
~ spl6_2,
inference(sat_conversion,[],[f54]) ).
cnf(s5,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f163]) ).
cnf(s6,plain,
~ spl6_3,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
spl6_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s3,s7]) ).
thf(f165,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU787^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:31:57 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.32 % (678717)Will run a generic schedule for satisfiability detection.
% 0.20/0.32 % (678727)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1428105734:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.32 % (678728)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=496298959:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.32 % (678723)% WARNING: option uhcvi not known.
% 0.20/0.32 % (678726)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4248499383:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.32 % (678724)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=866744212:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.32 % (678726)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.32 % (678727) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-678717-678727"...
% 0.20/0.32 % (678723)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2940118611:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.32 % (678722)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=430648421_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.32 % (678723)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.32 % (678723)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.32 % Exception at run slice level
% 0.20/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.32 % (678727)...printing done.
% 0.20/0.32 % (678726) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-678717-678726"...
% 0.20/0.32 % (678727)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.32 % (678727)------------------------------
% 0.20/0.32 % (678727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (678727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (678727)CaDiCaL version: 2.1.3
% 0.20/0.32 % (678727)Termination reason: Refutation
% 0.20/0.32 % (678727)Time elapsed: 0.023 s
% 0.20/0.32 % (678727)Peak memory usage: 12 MB
% 0.20/0.32 % (678727)Instructions burned: 24 (million)
% 0.20/0.32 % (678717)Success in time 0.07 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------