TSTP Solution File: NUM854+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM854+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 : 300s
% DateTime : Thu Aug 31 11:33:17 EDT 2023
% Result : Theorem 0.46s 1.17s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f167)
% Comments :
%------------------------------------------------------------------------------
fof(f158,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK0(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK1(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK2(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f165,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK3(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
cnf(c_49,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[],[f167]) ).
cnf(c_51,plain,
greater(vd508,vd509),
inference(cnf_transformation,[],[f169]) ).
cnf(c_57,plain,
vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(cnf_transformation,[],[f176]) ).
cnf(c_58,plain,
vplus(vmul(X0,X1),vmul(X0,X2)) = vmul(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f177]) ).
cnf(c_59,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f178]) ).
cnf(c_90,plain,
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_97,plain,
greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f253]) ).
cnf(c_105,plain,
vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f225]) ).
cnf(c_1462,plain,
less(vd509,vd508),
inference(superposition,[status(thm)],[c_51,c_90]) ).
cnf(c_1554,plain,
greater(vmul(X0,vplus(X1,X2)),vmul(X0,X1)),
inference(superposition,[status(thm)],[c_58,c_97]) ).
fof(f43,axiom,
! [X77,X78] :
( less(X78,X77)
<=> ? [X79] : vplus(X78,X79) = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f252,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f216]) ).
fof(f44,axiom,
! [X80,X81] :
( greater(X81,X80)
<=> ? [X82] : vplus(X80,X82) = X81 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f253,plain,
! [X2,X0] : greater(vplus(X0,X2),X0),
inference(equality_resolution,[],[f218]) ).
fof(f53,axiom,
! [X96] : vplus(v1,X96) = vsucc(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f235,plain,
! [X0] : v1 != vsucc(X0),
inference(cnf_transformation,[],[f116]) ).
fof(f99,plain,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : vplus(X1,X2) = X0 ),
inference(rectify,[],[f43]) ).
fof(f100,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f44]) ).
fof(f109,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f53]) ).
fof(f111,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
inference(rectify,[],[f55]) ).
fof(f112,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f56]) ).
fof(f113,plain,
! [X0] : vsucc(X0) != X0,
inference(rectify,[],[f57]) ).
fof(f114,plain,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
inference(rectify,[],[f58]) ).
fof(f115,plain,
! [X0,X1] :
( vsucc(X0) = vsucc(X1)
=> X0 = X1 ),
inference(rectify,[],[f59]) ).
fof(f116,plain,
! [X0] : v1 != vsucc(X0),
inference(rectify,[],[f60]) ).
fof(f149,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f112]) ).
fof(f150,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f114]) ).
fof(f151,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(ennf_transformation,[],[f115]) ).
fof(f156,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : vplus(X1,X2) = X0
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f157,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f156]) ).
fof(f159,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( vplus(X1,sK0(X0,X1)) = X0
| ~ less(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f157,f158]) ).
fof(f160,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f161,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f160]) ).
fof(f163,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f161,f162]) ).
fof(f45,axiom,
! [X83,X84] :
( ? [X86] : vplus(X83,X86) = X84
| ? [X85] : vplus(X84,X85) = X83
| X83 = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f217,plain,
! [X0,X1] :
( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f45]) ).
fof(f166,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| vplus(X1,sK3(X0,X1)) = X0
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f101,f165,f164]) ).
fof(f46,axiom,
! [X83,X84] :
( ~ ? [X86] : vplus(X83,X86) = X84
| X83 != X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f219,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| vplus(X1,sK3(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f166]) ).
fof(f102,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f46]) ).
fof(f145,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f102]) ).
fof(f215,plain,
! [X0,X1] :
( vplus(X1,sK0(X0,X1)) = X0
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f216,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f218,plain,
! [X2,X0,X1] :
( greater(X1,X0)
| vplus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f163]) ).
fof(f220,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f47,axiom,
! [X83,X84] :
( ~ ? [X86] : vplus(X83,X86) = X84
| ~ ? [X85] : vplus(X84,X85) = X83 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f254,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f220]) ).
fof(f103,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f47]) ).
fof(f146,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f103]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f48,axiom,
! [X83,X84] :
( ~ ? [X85] : vplus(X84,X85) = X83
| X83 != X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f255,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f221]) ).
fof(f104,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X1,X2) = X0
| X0 != X1 ),
inference(rectify,[],[f48]) ).
fof(f147,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| X0 != X1 ),
inference(ennf_transformation,[],[f104]) ).
fof(f222,plain,
! [X2,X0,X1] :
( vplus(X1,X2) != X0
| X0 != X1 ),
inference(cnf_transformation,[],[f147]) ).
fof(f49,axiom,
! [X87,X88] :
( X87 != X88
=> ! [X89] : vplus(X89,X87) != vplus(X89,X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f256,plain,
! [X2,X1] : vplus(X1,X2) != X1,
inference(equality_resolution,[],[f222]) ).
fof(f105,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f49]) ).
fof(f148,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f105]) ).
fof(f50,axiom,
! [X90,X91] : vplus(X90,X91) != X91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f223,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f106,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f50]) ).
fof(f51,axiom,
! [X92,X93] : vplus(X93,X92) = vplus(X92,X93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f224,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f106]) ).
fof(f107,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f51]) ).
fof(f52,axiom,
! [X94,X95] : vplus(vsucc(X94),X95) = vsucc(vplus(X94,X95)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f225,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f107]) ).
fof(f108,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(rectify,[],[f52]) ).
fof(f226,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[],[f108]) ).
fof(f227,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f109]) ).
fof(f54,axiom,
! [X97,X98,X99] : vplus(vplus(X97,X98),X99) = vplus(X97,vplus(X98,X99)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f238,plain,
! [X0,X1] : vplus(vplus(v1,X0),X1) = vplus(v1,vplus(X0,X1)),
inference(definition_unfolding,[],[f226,f227,f227]) ).
fof(f110,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f54]) ).
fof(f228,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f110]) ).
fof(f229,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f111]) ).
fof(f56,axiom,
! [X102] :
( v1 != X102
=> vsucc(vskolem2(X102)) = X102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f240,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f229,f227,f227]) ).
fof(f230,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f111]) ).
fof(f55,axiom,
! [X100,X101] :
( vplus(X100,v1) = vsucc(X100)
& vplus(X100,vsucc(X101)) = vsucc(vplus(X100,X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f239,plain,
! [X0] : vplus(v1,X0) = vplus(X0,v1),
inference(definition_unfolding,[],[f230,f227]) ).
fof(f231,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f149]) ).
fof(f57,axiom,
! [X103] : vsucc(X103) != X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f241,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f231,f227]) ).
fof(f232,plain,
! [X0] : vsucc(X0) != X0,
inference(cnf_transformation,[],[f113]) ).
fof(f58,axiom,
! [X104,X105] :
( X104 != X105
=> vsucc(X104) != vsucc(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f242,plain,
! [X0] : vplus(v1,X0) != X0,
inference(definition_unfolding,[],[f232,f227]) ).
fof(f233,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f150]) ).
fof(f59,axiom,
! [X106,X107] :
( vsucc(X106) = vsucc(X107)
=> X106 = X107 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof(f243,plain,
! [X0,X1] :
( vplus(v1,X0) != vplus(v1,X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f233,f227,f227]) ).
fof(f234,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f60,axiom,
! [X108] : v1 != vsucc(X108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f244,plain,
! [X0,X1] :
( X0 = X1
| vplus(v1,X0) != vplus(v1,X1) ),
inference(definition_unfolding,[],[f234,f227,f227]) ).
cnf(c_96,plain,
( ~ less(X0,X1)
| vplus(X0,sK0(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_107,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f228]) ).
cnf(c_144,negated_conjecture,
~ greater(vmul(vd511,vd508),vmul(vd511,vd509)),
inference(theory_normalisation,[status(thm)],[c_49,c_107,c_105,c_57,c_59]) ).
cnf(c_3025,plain,
vplus(vd509,sK0(vd508,vd509)) = vd508,
inference(superposition,[status(thm)],[c_1462,c_96]) ).
cnf(c_8671,plain,
greater(vmul(X0,vd508),vmul(X0,vd509)),
inference(superposition,[status(thm)],[c_3025,c_1554]) ).
cnf(c_8755,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_144,c_8671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM854+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 14:54:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.46/1.17 % SZS status Started for theBenchmark.p
% 0.46/1.17 % SZS status Theorem for theBenchmark.p
% 0.46/1.17
% 0.46/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.46/1.17
% 0.46/1.17 ------ iProver source info
% 0.46/1.17
% 0.46/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.46/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.46/1.17 git: non_committed_changes: false
% 0.46/1.17 git: last_make_outside_of_git: false
% 0.46/1.17
% 0.46/1.17 ------ Parsing...
% 0.46/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.17
% 0.46/1.17 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.46/1.17
% 0.46/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.17
% 0.46/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.46/1.17 ------ Proving...
% 0.46/1.17 ------ Problem Properties
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 clauses 55
% 0.46/1.17 conjectures 1
% 0.46/1.17 EPR 21
% 0.46/1.17 Horn 50
% 0.46/1.17 unary 20
% 0.46/1.17 binary 23
% 0.46/1.17 lits 102
% 0.46/1.17 lits eq 26
% 0.46/1.17 fd_pure 0
% 0.46/1.17 fd_pseudo 0
% 0.46/1.17 fd_cond 0
% 0.46/1.17 fd_pseudo_cond 6
% 0.46/1.17 AC symbols 2
% 0.46/1.17
% 0.46/1.17 ------ Schedule dynamic 5 is on
% 0.46/1.17
% 0.46/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 ------
% 0.46/1.17 Current options:
% 0.46/1.17 ------
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 ------ Proving...
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 % SZS status Theorem for theBenchmark.p
% 0.46/1.17
% 0.46/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.79/1.17
% 0.79/1.17
%------------------------------------------------------------------------------