%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWV836-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n004.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 : Wed Jul 20 21:36:11 EDT 2022
% Result : Unsatisfiable 1.30s 1.48s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 22 ( 19 unt; 0 nHn; 11 RR)
% Number of literals : 28 ( 11 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Compl__Un_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X,Y,tc_fun(Z,tc_bool)),tc_fun(Z,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(Z,tc_bool)),c_HOL_Ouminus__class_Ouminus(X,tc_fun(Z,tc_bool))),c_HOL_Ouminus__class_Ouminus(Y,tc_fun(Z,tc_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X,tc_bool)),Y),Z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X,tc_bool)),Z),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X,c_Orderings_Obot__class_Obot(tc_fun(Y,tc_bool)),tc_fun(Y,tc_bool)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_double__complement_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X,tc_fun(Y,tc_bool)),tc_fun(Y,tc_bool)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X,Y,tc_fun(Z,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(Y,X,tc_fun(Z,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X,Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(c_fequal(X,Y),Y) = c_Set_Oinsert(X,c_Orderings_Obot__class_Obot(tc_fun(Y,tc_bool)),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(427,plain,
c_fequal(X,Y) = c_Set_Oinsert(X,c_Orderings_Obot__class_Obot(tc_fun(Y,tc_bool)),Y),
inference('REWRITE',[status(thm)],[cls_singleton__conv2_0,cls_Collect__def_0,theory(equality)]) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(X,Y,Z) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X,c_Orderings_Obot__class_Obot(tc_fun(Z,tc_bool)),Z),Y,tc_fun(Z,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
cnf(460,plain,
c_Set_Oinsert(X,Y,Z) = c_Lattices_Oupper__semilattice__class_Osup(c_fequal(X,Z),Y,tc_fun(Z,tc_bool)),
inference('REWRITE',[status(thm)],[cls_insert__is__Un_0,427,theory(equality)]) ).
cnf(cls_hoare__derivs_Oinsert_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X,c_Set_Oinsert(Y,Z,tc_Hoare__Mirabelle_Otriple(U)),U)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X,Z,U)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X,c_Set_Oinsert(Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U),tc_bool)),tc_Hoare__Mirabelle_Otriple(U)),U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
cnf(480,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(Y,tc_Hoare__Mirabelle_Otriple(Z)),U,tc_fun(tc_Hoare__Mirabelle_Otriple(Z),tc_bool)),Z)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X,U,Z)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X,c_fequal(Y,tc_Hoare__Mirabelle_Otriple(Z)),Z) ),
inference('REWRITE',[status(thm)],[cls_hoare__derivs_Oinsert_0,cls_Un__empty__right_0,460,theory(equality)]) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(524,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference('REWRITE',[status(thm)],[cls_conjecture_3,cls_Un__empty__right_0,460,theory(equality)]) ).
cnf(cls_conjecture_4,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,v_tsa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(527,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),v_tsa,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference('REWRITE',[status(thm)],[cls_conjecture_5,460,theory(equality)]) ).
cnf(710,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Lattices_Oupper__semilattice__class_Osup(v_tsa,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference('PARAMODULATE',[status(thm)],[527,cls_Un__commute_0,theory(equality)]) ).
cnf(1084,plain,
c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X,tc_bool)),c_HOL_Ouminus__class_Ouminus(Y,tc_fun(X,tc_bool))),c_HOL_Ouminus__class_Ouminus(Z,tc_fun(X,tc_bool))),tc_fun(X,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(Y,Z,tc_fun(X,tc_bool)),
inference('PARAMODULATE',[status(thm)],[cls_double__complement_0,cls_Compl__Un_0,theory(equality)]) ).
cnf(1150,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_HOL_Ouminus__class_Ouminus(v_tsa,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),c_HOL_Ouminus__class_Ouminus(c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference('REWRITE',[status(thm)],[710,1084,theory(equality)]) ).
cnf(1198,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Hoare__Mirabelle_Otriple(Y),tc_bool)),c_HOL_Ouminus__class_Ouminus(c_fequal(Z,tc_Hoare__Mirabelle_Otriple(Y)),tc_fun(tc_Hoare__Mirabelle_Otriple(Y),tc_bool))),c_HOL_Ouminus__class_Ouminus(U,tc_fun(tc_Hoare__Mirabelle_Otriple(Y),tc_bool))),tc_fun(tc_Hoare__Mirabelle_Otriple(Y),tc_bool)),Y)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X,U,Y)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X,c_fequal(Z,tc_Hoare__Mirabelle_Otriple(Y)),Y) ),
inference('REWRITE',[status(thm)],[480,1084,theory(equality)]) ).
cnf(1693,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[1198,cls_conjecture_4,524]),1150,cls_Int__commute_0,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV836-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 21:21:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-15T21:21:39
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n004.cluster.edu at 2022-06-15T21:21:39
% 0.45/0.61 WARNING:
% 0.45/0.61 |c_Complete__Lattice_Ocomplete__lattice| is a 9-ary relation that occurs only negatively; disabling rows that contain it.
% 0.45/0.61 WARNING:
% 0.45/0.61 |class_OrderedGroup_Ogroup__add| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 0.45/0.61 WARNING:
% 0.45/0.61 |class_Ring__and__Field_Oordered__idom| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 0.45/0.61 WARNING:
% 0.45/0.61 |class_OrderedGroup_Opordered__ab__group__add| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 0.45/0.61 WARNING:
% 0.45/0.61 |class_Ring__and__Field_Oring| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 0.45/0.61 WARNING:
% 0.45/0.61 |class_OrderedGroup_Olordered__ab__group__add| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 0.45/0.61 WARNING:
% 0.45/0.61 |class_OrderedGroup_Oab__group__add| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 1.30/1.48
% 1.30/1.48
% 1.30/1.48 #||
% 1.30/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.30/1.48 % SZS output start Refutation
% See solution above
% 1.30/1.48 ||#
% 1.30/1.48
% 1.30/1.48 ; Summary of computation:
% 1.30/1.48 ; 4018 formulas have been input or derived (from 454 formulas).
% 1.30/1.48 ; 1693 (42%) were retained. Of these,
% 1.30/1.48 ; 489 (29%) were simplified or subsumed later,
% 1.30/1.48 ; 1204 (71%) are still being kept.
% 1.30/1.48 ;
% 1.30/1.48 ; Run time in seconds excluding printing time:
% 1.30/1.48 ; 0.120 12% Read assertion file (1 call)
% 1.30/1.48 ; 0.009 1% Assert (598 calls)
% 1.30/1.48 ; 0.210 21% Process new row (3,615 calls)
% 1.30/1.48 ; 0.067 7% Resolution (906 calls)
% 1.30/1.48 ; 0.031 3% Paramodulation (453 calls)
% 1.30/1.48 ; 0.000 0% Factoring (4 calls)
% 1.30/1.48 ; 0.054 5% Condensing (1,339 calls)
% 1.30/1.48 ; 0.073 7% Forward subsumption (1,339 calls)
% 1.30/1.48 ; 0.031 3% Backward subsumption (1,022 calls)
% 1.30/1.48 ; 0.006 1% Clause clause subsumption (2,403 calls)
% 1.30/1.48 ; 0.181 18% Forward simplification (3,357 calls)
% 1.30/1.48 ; 0.044 4% Backward simplification (1,603 calls)
% 1.30/1.48 ; 0.142 14% Ordering (11,499 calls)
% 1.30/1.48 ; 0.000 0% Sortal reasoning (32 calls)
% 1.30/1.48 ; 0.001 0% Purity testing (1 call)
% 1.30/1.48 ; 0.045 4% Other
% 1.30/1.48 ; 1.014 Total
% 1.30/1.48 ; 1.017 Real time
% 1.30/1.48 ;
% 1.30/1.48 ; Term-hash-array has 4,597 terms in all.
% 1.30/1.48 ; Feature-vector-row-index has 797 entries (797 at peak, 1,022 added, 225 deleted).
% 1.30/1.48 ; Feature-vector-row-index has 8,400 nodes (8,400 at peak, 10,473 added, 2,073 deleted).
% 1.30/1.48 ; Retrieved 2,530 possibly forward subsuming rows in 1,339 calls.
% 1.30/1.48 ; Retrieved 573 possibly backward subsumed rows in 1,022 calls.
% 1.30/1.48 ; Path-index has 3,622 entries (3,622 at peak, 4,787 added, 1,165 deleted).
% 1.30/1.48 ; Path-index has 13,121 nodes (13,121 at peak, 15,076 added, 1,955 deleted).
% 1.30/1.48 ; Trie-index has 3,622 entries (3,622 at peak, 4,787 added, 1,165 deleted).
% 1.30/1.48 ; Trie-index has 20,429 nodes (20,429 at peak, 28,529 added, 8,100 deleted).
% 1.30/1.48 ; Retrieved 19,964 generalization terms in 21,878 calls.
% 1.30/1.48 ; Retrieved 2,671 instance terms in 740 calls.
% 1.30/1.48 ; Retrieved 78,494 unifiable terms in 4,015 calls.
% 1.30/1.48 ;
% 1.30/1.48 ; The agenda of rows to process has 10 entries:
% 1.30/1.48 ; 2 with value 38 4 with value 41 4 with value 42
% 1.30/1.48 ; The agenda of input rows to give has 34 entries:
% 1.30/1.48 ; 6 with value 53 2 with value 66 1 with value 82
% 1.30/1.48 ; 2 with value 55 1 with value 69 1 with value 83
% 1.30/1.48 ; 1 with value 56 2 with value 70 2 with value 90
% 1.30/1.48 ; 1 with value 61 3 with value 71 3 with value 95
% 1.30/1.48 ; 1 with value 62 2 with value 72 1 with value 117
% 1.30/1.48 ; 3 with value 63 1 with value 73 1 with value 219
% 1.30/1.49 ; The agenda of rows to give has 789 entries:
% 1.30/1.49 ; 1 with value (4 5) 15 with value (4 40) 2 with value (4 74)
% 1.30/1.49 ; 7 with value (4 6) 12 with value (4 41) 10 with value (4 75)
% 1.30/1.49 ; 23 with value (4 7) 11 with value (4 42) 5 with value (4 76)
% 1.30/1.49 ; 3 with value (4 8) 8 with value (4 43) 3 with value (4 77)
% 1.30/1.49 ; 1 with value (4 9) 6 with value (4 44) 1 with value (4 78)
% 1.30/1.49 ; 2 with value (4 10) 22 with value (4 45) 7 with value (4 79)
% 1.30/1.49 ; 13 with value (4 11) 13 with value (4 46) 4 with value (4 80)
% 1.30/1.49 ; 2 with value (4 12) 16 with value (4 47) 1 with value (4 81)
% 1.30/1.49 ; 3 with value (4 13) 16 with value (4 48) 3 with value (4 82)
% 1.30/1.49 ; 7 with value (4 14) 21 with value (4 49) 4 with value (4 83)
% 1.30/1.49 ; 11 with value (4 15) 12 with value (4 50) 3 with value (4 84)
% 1.30/1.49 ; 4 with value (4 16) 7 with value (4 51) 3 with value (4 85)
% 1.30/1.49 ; 2 with value (4 17) 9 with value (4 52) 1 with value (4 86)
% 1.30/1.49 ; 15 with value (4 18) 14 with value (4 53) 4 with value (4 87)
% 1.30/1.49 ; 14 with value (4 19) 20 with value (4 54) 8 with value (4 88)
% 1.30/1.49 ; 4 with value (4 20) 15 with value (4 55) 1 with value (4 89)
% 1.30/1.49 ; 5 with value (4 21) 10 with value (4 56) 2 with value (4 90)
% 1.30/1.49 ; 21 with value (4 22) 5 with value (4 57) 2 with value (4 91)
% 1.30/1.49 ; 4 with value (4 23) 4 with value (4 58) 1 with value (4 92)
% 1.30/1.49 ; 24 with value (4 24) 4 with value (4 59) 2 with value (4 93)
% 1.30/1.49 ; 25 with value (4 25) 5 with value (4 60) 9 with value (4 94)
% 1.30/1.49 ; 6 with value (4 26) 5 with value (4 61) 8 with value (4 95)
% 1.30/1.49 ; 9 with value (4 27) 6 with value (4 62) 2 with value (4 96)
% 1.30/1.49 ; 13 with value (4 28) 10 with value (4 63) 3 with value (4 98)
% 1.30/1.49 ; 5 with value (4 29) 3 with value (4 64) 5 with value (4 99)
% 1.30/1.49 ; 12 with value (4 30) 4 with value (4 65) 2 with value (4 100)
% 1.30/1.49 ; 6 with value (4 31) 3 with value (4 66) 1 with value (4 105)
% 1.30/1.49 ; 10 with value (4 32) 6 with value (4 67) 1 with value (4 107)
% 1.30/1.49 ; 10 with value (4 33) 7 with value (4 68) 4 with value (4 108)
% 1.30/1.49 ; 14 with value (4 34) 6 with value (4 69) 4 with value (4 109)
% 1.30/1.49 ; 18 with value (4 35) 4 with value (4 70) 1 with value (4 110)
% 1.30/1.49 ; 10 with value (4 36) 7 with value (4 71) 1 with value (4 112)
% 1.30/1.49 ; 16 with value (4 37) 8 with value (4 72) 2 with value (4 113)
% 1.30/1.49 ; 19 with value (4 38) 3 with value (4 73) 1 with value (4 114)
% 1.30/1.49 ; 22 with value (4 39)
% 1.30/1.49 Evaluation took:
% 1.30/1.49 1.018 seconds of real time
% 1.30/1.49 0.964682 seconds of user run time
% 1.30/1.49 0.052916 seconds of system run time
% 1.30/1.49 [Run times include 0.087 seconds GC run time.]
% 1.30/1.49 0 calls to %EVAL
% 1.30/1.49 0 page faults and
% 1.30/1.49 79,270,072 bytes consed.
% 1.30/1.49 :PROOF-FOUND
% 1.30/1.49 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-15T21:21:40
% 1.30/1.49 :PROOF-FOUND
% 1.30/1.49 *
%------------------------------------------------------------------------------