TSTP Solution File: SEU189+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:39:10 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 100 ( 38 unt; 0 def)
% Number of atoms : 197 ( 113 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 181 ( 84 ~; 68 |; 20 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc5_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_rng(A)) ) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(t65_relat_1,conjecture,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ) ).
fof(t60_relat_1,axiom,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& relation_dom(A) = empty_set )
=> relation_rng(A) = empty_set ),
inference(strip,[],[t65_relat_1]) ).
fof(subgoal_1,plain,
! [A] :
( ( relation(A)
& relation_rng(A) = empty_set )
=> relation_dom(A) = empty_set ),
inference(strip,[],[t65_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& relation_dom(A) = empty_set )
=> relation_rng(A) = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( relation_rng(A) != empty_set
& relation_dom(A) = empty_set
& relation(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( relation_rng(skolemFOFtoCNF_A_4) != empty_set
& relation_dom(skolemFOFtoCNF_A_4) = empty_set
& relation(skolemFOFtoCNF_A_4) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
relation_rng(skolemFOFtoCNF_A_4) != empty_set,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(canonicalize,[],[t60_relat_1]) ).
fof(normalize_0_4,plain,
relation_rng(empty_set) = empty_set,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[fc5_relat_1]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
relation_dom(skolemFOFtoCNF_A_4) = empty_set,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(canonicalize,[],[fc4_relat_1]) ).
fof(normalize_0_11,plain,
empty(empty_set),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
relation(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
relation_rng(skolemFOFtoCNF_A_4) != empty_set,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
relation_rng(empty_set) = empty_set,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ empty(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_A_4 = empty_set ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_4,plain,
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ empty(relation_dom(skolemFOFtoCNF_A_4))
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_6,plain,
relation_dom(skolemFOFtoCNF_A_4) = empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( relation_dom(skolemFOFtoCNF_A_4) != empty_set
| ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_A_4)) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_dom(skolemFOFtoCNF_A_4)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_8,plain,
( ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ empty(empty_set)
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(relation_dom(skolemFOFtoCNF_A_4)) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
relation(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
empty(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_A_4 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_4) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
relation_rng(skolemFOFtoCNF_A_4) = relation_rng(skolemFOFtoCNF_A_4),
introduced(tautology,[refl,[$fot(relation_rng(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_16,plain,
( relation_rng(skolemFOFtoCNF_A_4) != relation_rng(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_A_4 != empty_set
| relation_rng(skolemFOFtoCNF_A_4) = relation_rng(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_A_4 != empty_set
| relation_rng(skolemFOFtoCNF_A_4) = relation_rng(empty_set) ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
relation_rng(skolemFOFtoCNF_A_4) = relation_rng(empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_4,empty_set) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( relation_rng(empty_set) != empty_set
| relation_rng(skolemFOFtoCNF_A_4) != relation_rng(empty_set)
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
inference(subst,[],[refute_0_23:[bind(X,$fot(relation_rng(skolemFOFtoCNF_A_4))),bind(Y,$fot(relation_rng(empty_set))),bind(Z,$fot(empty_set))]]) ).
cnf(refute_0_25,plain,
( relation_rng(empty_set) != empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),relation_rng(empty_set)) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
relation_rng(skolemFOFtoCNF_A_4) = empty_set,
inference(resolve,[$cnf( $equal(relation_rng(empty_set),empty_set) )],[refute_0_1,refute_0_25]) ).
cnf(refute_0_27,plain,
( empty_set != empty_set
| relation_rng(skolemFOFtoCNF_A_4) != empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_28,plain,
( empty_set != empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_28,refute_0_0]) ).
cnf(refute_0_30,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_30,refute_0_29]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( relation(A)
& relation_rng(A) = empty_set )
=> relation_dom(A) = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( relation_dom(A) != empty_set
& relation_rng(A) = empty_set
& relation(A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( relation_dom(skolemFOFtoCNF_A_5) != empty_set
& relation_rng(skolemFOFtoCNF_A_5) = empty_set
& relation(skolemFOFtoCNF_A_5) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
relation_dom(skolemFOFtoCNF_A_5) != empty_set,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(canonicalize,[],[t60_relat_1]) ).
fof(normalize_1_4,plain,
relation_dom(empty_set) = empty_set,
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_1_6,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[fc6_relat_1]) ).
fof(normalize_1_8,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
relation_rng(skolemFOFtoCNF_A_5) = empty_set,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_10,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(canonicalize,[],[fc4_relat_1]) ).
fof(normalize_1_11,plain,
empty(empty_set),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
relation(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
relation_dom(skolemFOFtoCNF_A_5) != empty_set,
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
relation_dom(empty_set) = empty_set,
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( ~ empty(skolemFOFtoCNF_A_5)
| skolemFOFtoCNF_A_5 = empty_set ),
inference(subst,[],[refute_1_2:[bind(A,$fot(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_1_4,plain,
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( ~ empty(relation_rng(skolemFOFtoCNF_A_5))
| ~ relation(skolemFOFtoCNF_A_5)
| empty(skolemFOFtoCNF_A_5) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_1_6,plain,
relation_rng(skolemFOFtoCNF_A_5) = empty_set,
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_7,plain,
( relation_rng(skolemFOFtoCNF_A_5) != empty_set
| ~ empty(empty_set)
| empty(relation_rng(skolemFOFtoCNF_A_5)) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_rng(skolemFOFtoCNF_A_5)) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_8,plain,
( ~ empty(empty_set)
| empty(relation_rng(skolemFOFtoCNF_A_5)) ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_5),empty_set) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
( ~ empty(empty_set)
| ~ relation(skolemFOFtoCNF_A_5)
| empty(skolemFOFtoCNF_A_5) ),
inference(resolve,[$cnf( empty(relation_rng(skolemFOFtoCNF_A_5)) )],[refute_1_8,refute_1_5]) ).
cnf(refute_1_10,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_11,plain,
( ~ relation(skolemFOFtoCNF_A_5)
| empty(skolemFOFtoCNF_A_5) ),
inference(resolve,[$cnf( empty(empty_set) )],[refute_1_10,refute_1_9]) ).
cnf(refute_1_12,plain,
relation(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_13,plain,
empty(skolemFOFtoCNF_A_5),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_5) )],[refute_1_12,refute_1_11]) ).
cnf(refute_1_14,plain,
skolemFOFtoCNF_A_5 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_5) )],[refute_1_13,refute_1_3]) ).
cnf(refute_1_15,plain,
relation_dom(skolemFOFtoCNF_A_5) = relation_dom(skolemFOFtoCNF_A_5),
introduced(tautology,[refl,[$fot(relation_dom(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_1_16,plain,
( relation_dom(skolemFOFtoCNF_A_5) != relation_dom(skolemFOFtoCNF_A_5)
| skolemFOFtoCNF_A_5 != empty_set
| relation_dom(skolemFOFtoCNF_A_5) = relation_dom(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),relation_dom(skolemFOFtoCNF_A_5)) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_1_17,plain,
( skolemFOFtoCNF_A_5 != empty_set
| relation_dom(skolemFOFtoCNF_A_5) = relation_dom(empty_set) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),relation_dom(skolemFOFtoCNF_A_5)) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
relation_dom(skolemFOFtoCNF_A_5) = relation_dom(empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_5,empty_set) )],[refute_1_14,refute_1_17]) ).
cnf(refute_1_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_23,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
( relation_dom(empty_set) != empty_set
| relation_dom(skolemFOFtoCNF_A_5) != relation_dom(empty_set)
| relation_dom(skolemFOFtoCNF_A_5) = empty_set ),
inference(subst,[],[refute_1_23:[bind(X,$fot(relation_dom(skolemFOFtoCNF_A_5))),bind(Y,$fot(relation_dom(empty_set))),bind(Z,$fot(empty_set))]]) ).
cnf(refute_1_25,plain,
( relation_dom(empty_set) != empty_set
| relation_dom(skolemFOFtoCNF_A_5) = empty_set ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),relation_dom(empty_set)) )],[refute_1_18,refute_1_24]) ).
cnf(refute_1_26,plain,
relation_dom(skolemFOFtoCNF_A_5) = empty_set,
inference(resolve,[$cnf( $equal(relation_dom(empty_set),empty_set) )],[refute_1_1,refute_1_25]) ).
cnf(refute_1_27,plain,
( empty_set != empty_set
| relation_dom(skolemFOFtoCNF_A_5) != empty_set
| relation_dom(skolemFOFtoCNF_A_5) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_28,plain,
( empty_set != empty_set
| relation_dom(skolemFOFtoCNF_A_5) = empty_set ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),empty_set) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),empty_set) )],[refute_1_28,refute_1_0]) ).
cnf(refute_1_30,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_1_31,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_1_30,refute_1_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 11:22:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------