%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL716^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:14:33 AM UTC 2026
% Result : Theorem 0.68s 0.46s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of formulae : 94 ( 51 unt; 0 typ; 1 def)
% Number of atoms : 649 ( 172 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 965 ( 97 ~; 135 |; 15 &; 642 @)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 131 ( 131 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 51 usr; 7 con; 0-4 aty)
% ( 52 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 273 ( 1 sgn 102 !; 3 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_49,type,
sK2: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f25,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( X0 @ X1 @ X2 )
=> ? [X3: $i] :
( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) ) ) )
= mweakly_dense ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mweakly_dense) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) )
=> ( mweakly_dense @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) )
=> ( mweakly_dense @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f35,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) )
=> ( mweakly_dense @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f36,plain,
~ ! [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) )
=> ( ( mweakly_dense @ X0 )
= $true ) ),
inference(fool_elimination,[],[f35]) ).
thf(f46,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f47,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f55,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f56,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f61,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f62,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f72,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f73,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ? [X4: $i] :
( ( X0 @ X4 @ X2 )
& ( X0 @ X1 @ X4 ) ) ) )
= mweakly_dense ),
inference(rectify,[],[f25]) ).
thf(f75,plain,
( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f85,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f86,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( mweakly_dense @ X0 )
!= $true )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
thf(f88,plain,
( ( $true
!= ( mweakly_dense @ sK0 ) )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f90,plain,
( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f94,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f96,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f97,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f99,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f100,plain,
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f101,plain,
( $true
!= ( mweakly_dense @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f104,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f105,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f109,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f94,f97,f104]) ).
thf(f115,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f101,f90]) ).
thf(f116,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f100,f105,f99,f109,f96,f96,f96]) ).
thf(f117,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ ( sK1 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X3 )
| ( X2 @ X3 ) ) )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK1 @ X1 @ X2 ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK1 @ X1 @ X2 ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( ~ ( sK0 @ X1 @ ( sK1 @ X1 @ X2 ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) ) ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $true
= ( X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK1 @ X1 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f131,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) )
@ ( sK2 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f129]) ).
thf(f133,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) )
| ( X2 @ ( sK2 @ X1 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $true
= ( X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( sK0 @ ( sK1 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $true
= ( X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f133]) ).
thf(f136,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X1 @ X2 ) @ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ sK3 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ sK3 ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( $false
= ( ( sK0 @ sK4 @ sK3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( $true
= ( sK0 @ sK4 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f144,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X1: $i] :
( $false
= ( ( sK0 @ sK4 @ X1 )
& ( sK0 @ X1 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( ( sK0 @ X1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f152,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( sK0 @ ( sK1 @ sK4 @ X0 ) @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true = $false ) ),
inference(superposition,[],[f146,f131]) ).
thf(f156,plain,
! [X0: $i > $o,X1: $i] :
( ( ( sK0 @ ( sK1 @ sK4 @ X0 ) @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f166,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ X0
@ ^ [Y0: $i] : ( Y0 != X1 ) )
= X1 )
| ( ( sK0 @ X0 @ X1 )
= $false ) ),
inference(leibniz_equality_elimination,[],[f134]) ).
thf(f184,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 )
= $true )
| ( $true
= ( sK0
@ ( sK1 @ X1
@ ^ [Y0: $i] : ( Y0 != X0 ) )
@ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(superposition,[],[f136,f166]) ).
thf(f185,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ X0 )
= $false )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( X2 != X0 )
= $true )
| ( $true
= ( sK0
@ ( sK1 @ X1
@ ^ [Y0: $i] : ( Y0 != X0 ) )
@ X0 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( X2 = X0 )
= $false )
| ( $true
= ( sK0
@ ( sK1 @ X1
@ ^ [Y0: $i] : ( Y0 != X0 ) )
@ X0 ) )
| ( ( sK0 @ X1 @ X0 )
= $false ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0
@ ( sK1 @ X1
@ ^ [Y0: $i] : ( Y0 != X0 ) )
@ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f186]) ).
thf(f241,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK4 @ X0 ) )
| ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != sK3 )
@ X1 ) )
| ( $true = $false ) ),
inference(superposition,[],[f187,f156]) ).
thf(f247,plain,
! [X0: $i,X1: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != sK3 )
@ X1 ) )
| ( $false
= ( sK0 @ sK4 @ X0 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f248,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( X1 != sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X0 ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ( ( X1 = sK3 )
= $false )
| ( $false
= ( sK0 @ sK4 @ X0 ) )
| ( sK3 != X0 ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X0: $i,X1: $i] :
( ( sK3 != X1 )
| ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK4 @ X0 ) )
| ( $false
= ( sK0 @ sK4 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f249]) ).
thf(f253,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true = $false )
| ( $false
= ( sK0 @ sK4 @ X0 ) )
| ( sK3 != X1 )
| ( sK3 != X0 ) ),
inference(forward_demodulation,[],[f250,f143]) ).
thf(f254,plain,
! [X0: $i,X1: $i] :
( ( sK3 != X1 )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f256,definition,
( spl5_3
<=> ! [X0: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f257,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK0 @ sK4 @ X0 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f259,plain,
( spl5_3
| spl5_3 ),
inference(avatar_split_clause,[],[f254,f256,f256]) ).
thf(f261,plain,
( ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ~ spl5_3 ),
inference(equality_resolution,[],[f257]) ).
thf(f275,plain,
( ( $true = $false )
| ~ spl5_3 ),
inference(superposition,[],[f143,f261]) ).
thf(f279,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f275]) ).
thf(f280,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f279]) ).
cnf(s4,plain,
( spl5_3
| spl5_3 ),
inference(sat_conversion,[],[f259]) ).
cnf(s5,plain,
spl5_3,
inference(rat,[],[s4]) ).
cnf(s7,plain,
~ spl5_3,
inference(sat_conversion,[],[f280]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s5,s7]) ).
thf(f281,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL716^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n013.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 09:52:02 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.22/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.40 % (1884402)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.40 % (1884409)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=599701246:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.40 % (1884407)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1600870430:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.40 % (1884408)lrs+10_16_si=on:nwc=1.5:random_seed=3661604621:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.40 % (1884410)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3549396626:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.68/0.40 % (1884411)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3084351440:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.40 % (1884409)Instruction limit reached!
% 0.68/0.40 % (1884409)------------------------------
% 0.68/0.40 % (1884409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (1884409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (1884409)CaDiCaL version: 2.1.3
% 0.68/0.40 % (1884409)Termination reason: Instruction limit
% 0.68/0.40 % (1884409)Termination phase: Function definition elimination
% 0.68/0.40 % (1884409)Time elapsed: 0.003 s
% 0.68/0.40 % (1884409)Peak memory usage: 10 MB
% 0.68/0.40 % (1884409)Instructions burned: 6 (million)
% 0.68/0.40 % (1884408)Instruction limit reached!
% 0.68/0.40 % (1884408)------------------------------
% 0.68/0.40 % (1884408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (1884408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (1884408)CaDiCaL version: 2.1.3
% 0.68/0.40 % (1884408)Termination reason: Instruction limit
% 0.68/0.40 % (1884408)Termination phase: Saturation
% 0.68/0.40 % (1884408)Time elapsed: 0.009 s
% 0.68/0.40 % (1884408)Peak memory usage: 12 MB
% 0.68/0.40 % (1884408)Instructions burned: 18 (million)
% 0.68/0.40 % (1884413)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.40 % (1884413)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.40 % (1884412)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3732209407:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.40 % (1884411)Instruction limit reached!
% 0.68/0.40 % (1884411)------------------------------
% 0.68/0.40 % (1884411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (1884411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (1884411)CaDiCaL version: 2.1.3
% 0.68/0.40 % (1884411)Termination reason: Instruction limit
% 0.68/0.40 % (1884411)Termination phase: Saturation
% 0.68/0.40 % (1884411)Time elapsed: 0.013 s
% 0.68/0.40 % (1884411)Peak memory usage: 12 MB
% 0.68/0.40 % (1884411)Instructions burned: 24 (million)
% 0.68/0.40 % (1884413)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3540970383:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.40 % (1884419)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2284414525:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.40 % (1884419)Instruction limit reached!
% 0.68/0.40 % (1884419)------------------------------
% 0.68/0.40 % (1884419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.40 % (1884419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.40 % (1884419)CaDiCaL version: 2.1.3
% 0.68/0.40 % (1884419)Termination reason: Instruction limit
% 0.68/0.40 % (1884419)Termination phase: Saturation
% 0.68/0.40 % (1884419)Time elapsed: 0.003 s
% 0.68/0.40 % (1884419)Peak memory usage: 11 MB
% 0.68/0.40 % (1884419)Instructions burned: 7 (million)
% 0.68/0.40 % (1884422)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.44 % (1884413)Refutation not found, incomplete strategy
% 0.68/0.44 % (1884413)------------------------------
% 0.68/0.44 % (1884413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.44 % (1884413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.44 % (1884413)CaDiCaL version: 2.1.3
% 0.68/0.44 % (1884413)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.44 % (1884413)Time elapsed: 0.015 s
% 0.68/0.44 % (1884413)Peak memory usage: 12 MB
% 0.68/0.44 % (1884413)Instructions burned: 15 (million)
% 0.68/0.44 % (1884413)------------------------------
% 0.68/0.44 % (1884413)------------------------------
% 0.68/0.44 % (1884422)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=697863243:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.44 % (1884420)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=286080347:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.44 % (1884422)Instruction limit reached!
% 0.68/0.44 % (1884422)------------------------------
% 0.68/0.44 % (1884422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.44 % (1884422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.44 % (1884422)CaDiCaL version: 2.1.3
% 0.68/0.44 % (1884422)Termination reason: Instruction limit
% 0.68/0.44 % (1884422)Termination phase: Saturation
% 0.68/0.44 % (1884422)Time elapsed: 0.004 s
% 0.68/0.44 % (1884422)Peak memory usage: 11 MB
% 0.68/0.44 % (1884422)Instructions burned: 8 (million)
% 0.68/0.44 % (1884420)Instruction limit reached!
% 0.68/0.44 % (1884420)------------------------------
% 0.68/0.44 % (1884420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.44 % (1884420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.44 % (1884420)CaDiCaL version: 2.1.3
% 0.68/0.44 % (1884420)Termination reason: Instruction limit
% 0.68/0.44 % (1884420)Termination phase: Function definition elimination
% 0.68/0.44 % (1884420)Time elapsed: 0.006 s
% 0.68/0.44 % (1884420)Peak memory usage: 10 MB
% 0.68/0.44 % (1884420)Instructions burned: 6 (million)
% 0.68/0.44 % (1884407)Instruction limit reached!
% 0.68/0.44 % (1884407)------------------------------
% 0.68/0.44 % (1884407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.44 % (1884407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.44 % (1884407)CaDiCaL version: 2.1.3
% 0.68/0.44 % (1884407)Termination reason: Instruction limit
% 0.68/0.44 % (1884407)Termination phase: Saturation
% 0.68/0.44 % (1884407)Time elapsed: 0.044 s
% 0.68/0.44 % (1884407)Peak memory usage: 12 MB
% 0.68/0.44 % (1884407)Instructions burned: 88 (million)
% 0.68/0.44 % (1884425)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1266084556:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.44 % (1884425)Instruction limit reached!
% 0.68/0.44 % (1884425)------------------------------
% 0.68/0.44 % (1884425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.44 % (1884425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.44 % (1884425)CaDiCaL version: 2.1.3
% 0.68/0.44 % (1884425)Termination reason: Instruction limit
% 0.68/0.44 % (1884425)Termination phase: Saturation
% 0.68/0.44 % (1884425)Time elapsed: 0.006 s
% 0.68/0.44 % (1884425)Peak memory usage: 12 MB
% 0.68/0.44 % (1884425)Instructions burned: 12 (million)
% 0.68/0.44 % (1884427)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.44 % (1884427)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.44 % (1884427)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=275234430:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.44 % (1884432)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.44 % (1884429)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2436960640:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.46 % (1884432)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=233161400:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.46 % (1884432)Instruction limit reached!
% 0.68/0.46 % (1884432)------------------------------
% 0.68/0.46 % (1884432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884432)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884432)Termination reason: Instruction limit
% 0.68/0.46 % (1884432)Termination phase: Function definition elimination
% 0.68/0.46 % (1884432)Time elapsed: 0.003 s
% 0.68/0.46 % (1884432)Peak memory usage: 10 MB
% 0.68/0.46 % (1884432)Instructions burned: 6 (million)
% 0.68/0.46 % (1884427)Instruction limit reached!
% 0.68/0.46 % (1884427)------------------------------
% 0.68/0.46 % (1884427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884427)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884427)Termination reason: Instruction limit
% 0.68/0.46 % (1884427)Termination phase: Saturation
% 0.68/0.46 % (1884427)Time elapsed: 0.014 s
% 0.68/0.46 % (1884427)Peak memory usage: 12 MB
% 0.68/0.46 % (1884427)Instructions burned: 30 (million)
% 0.68/0.46 % (1884433)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=600723905:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.68/0.46 % (1884430)lrs+10_1_si=on:cs=on:random_seed=155027246:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.46 % (1884433)Refutation not found, incomplete strategy
% 0.68/0.46 % (1884433)------------------------------
% 0.68/0.46 % (1884433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884433)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884433)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.46 % (1884433)Time elapsed: 0.006 s
% 0.68/0.46 % (1884433)Peak memory usage: 12 MB
% 0.68/0.46 % (1884433)Instructions burned: 10 (million)
% 0.68/0.46 % (1884433)------------------------------
% 0.68/0.46 % (1884433)------------------------------
% 0.68/0.46 % (1884412)Instruction limit reached!
% 0.68/0.46 % (1884412)------------------------------
% 0.68/0.46 % (1884412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884412)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884412)Termination reason: Instruction limit
% 0.68/0.46 % (1884412)Termination phase: Saturation
% 0.68/0.46 % (1884412)Time elapsed: 0.067 s
% 0.68/0.46 % (1884412)Peak memory usage: 13 MB
% 0.68/0.46 % (1884412)Instructions burned: 75 (million)
% 0.68/0.46 % (1884430)Instruction limit reached!
% 0.68/0.46 % (1884430)------------------------------
% 0.68/0.46 % (1884430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884430)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884430)Termination reason: Instruction limit
% 0.68/0.46 % (1884430)Termination phase: Saturation
% 0.68/0.46 % (1884430)Time elapsed: 0.007 s
% 0.68/0.46 % (1884430)Peak memory usage: 12 MB
% 0.68/0.46 % (1884430)Instructions burned: 8 (million)
% 0.68/0.46 % (1884437)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2412816320:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.68/0.46 % (1884437)Refutation not found, incomplete strategy
% 0.68/0.46 % (1884437)------------------------------
% 0.68/0.46 % (1884437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884437)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884437)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.46 % (1884437)Time elapsed: 0.005 s
% 0.68/0.46 % (1884437)Peak memory usage: 12 MB
% 0.68/0.46 % (1884437)Instructions burned: 8 (million)
% 0.68/0.46 % (1884437)------------------------------
% 0.68/0.46 % (1884437)------------------------------
% 0.68/0.46 % (1884429)Instruction limit reached!
% 0.68/0.46 % (1884429)------------------------------
% 0.68/0.46 % (1884429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884429)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884429)Termination reason: Instruction limit
% 0.68/0.46 % (1884429)Termination phase: Saturation
% 0.68/0.46 % (1884429)Time elapsed: 0.036 s
% 0.68/0.46 % (1884429)Peak memory usage: 12 MB
% 0.68/0.46 % (1884429)Instructions burned: 87 (million)
% 0.68/0.46 % (1884441)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2126197784:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.68/0.46 % (1884439)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=726029740:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.68/0.46 % (1884441)Instruction limit reached!
% 0.68/0.46 % (1884441)------------------------------
% 0.68/0.46 % (1884441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884441)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884441)Termination reason: Instruction limit
% 0.68/0.46 % (1884441)Termination phase: Saturation
% 0.68/0.46 % (1884441)Time elapsed: 0.008 s
% 0.68/0.46 % (1884441)Peak memory usage: 12 MB
% 0.68/0.46 % (1884441)Instructions burned: 16 (million)
% 0.68/0.46 % (1884445)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3794765420:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.68/0.46 % (1884445)Instruction limit reached!
% 0.68/0.46 % (1884445)------------------------------
% 0.68/0.46 % (1884445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884445)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884445)Termination reason: Instruction limit
% 0.68/0.46 % (1884445)Termination phase: Property scanning
% 0.68/0.46 % (1884445)Time elapsed: 0.001 s
% 0.68/0.46 % (1884445)Peak memory usage: 10 MB
% 0.68/0.46 % (1884445)Instructions burned: 3 (million)
% 0.68/0.46 % (1884446)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1864150403:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.68/0.46 % (1884442)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1876159592:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.68/0.46 % (1884443)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3380968198:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.68/0.46 % (1884449)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2171360577:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.68/0.46 % (1884446)Instruction limit reached!
% 0.68/0.46 % (1884446)------------------------------
% 0.68/0.46 % (1884446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884446)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884446)Termination reason: Instruction limit
% 0.68/0.46 % (1884446)Termination phase: Saturation
% 0.68/0.46 % (1884446)Time elapsed: 0.014 s
% 0.68/0.46 % (1884446)Peak memory usage: 12 MB
% 0.68/0.46 % (1884446)Instructions burned: 26 (million)
% 0.68/0.46 % (1884443)Instruction limit reached!
% 0.68/0.46 % (1884443)------------------------------
% 0.68/0.46 % (1884443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884443)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884443)Termination reason: Instruction limit
% 0.68/0.46 % (1884443)Termination phase: Saturation
% 0.68/0.46 % (1884443)Time elapsed: 0.014 s
% 0.68/0.46 % (1884443)Peak memory usage: 12 MB
% 0.68/0.46 % (1884443)Instructions burned: 15 (million)
% 0.68/0.46 % (1884451)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=916279949:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.68/0.46 % (1884439)Instruction limit reached!
% 0.68/0.46 % (1884439)------------------------------
% 0.68/0.46 % (1884439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884439)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884439)Termination reason: Instruction limit
% 0.68/0.46 % (1884439)Termination phase: Saturation
% 0.68/0.46 % (1884439)Time elapsed: 0.031 s
% 0.68/0.46 % (1884439)Peak memory usage: 12 MB
% 0.68/0.46 % (1884439)Instructions burned: 26 (million)
% 0.68/0.46 % (1884449)Instruction limit reached!
% 0.68/0.46 % (1884449)------------------------------
% 0.68/0.46 % (1884449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884449)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884449)Termination reason: Instruction limit
% 0.68/0.46 % (1884449)Termination phase: Saturation
% 0.68/0.46 % (1884449)Time elapsed: 0.013 s
% 0.68/0.46 % (1884449)Peak memory usage: 12 MB
% 0.68/0.46 % (1884449)Instructions burned: 24 (million)
% 0.68/0.46 % (1884442) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1884402-1884442"...
% 0.68/0.46 % (1884456)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.46 % (1884456)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.68/0.46 % (1884442)...printing done.
% 0.68/0.46 % (1884456)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3746204816:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.68/0.46 % (1884442)Refutation found. Thanks to Tanya!
% 0.68/0.46 % SZS status Theorem for theBenchmark
% 0.68/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.68/0.46 % (1884442)------------------------------
% 0.68/0.46 % (1884442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (1884442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (1884442)CaDiCaL version: 2.1.3
% 0.68/0.46 % (1884442)Termination reason: Refutation
% 0.68/0.46 % (1884442)Time elapsed: 0.028 s
% 0.68/0.46 % (1884442)Peak memory usage: 13 MB
% 0.68/0.46 % (1884442)Instructions burned: 24 (million)
% 0.68/0.46 % (1884402)Success in time 0.187 s
% 0.68/0.46 % Vampire exiting
%------------------------------------------------------------------------------