%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL299-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Tue Sep 29 11:51:54 AM UTC 2026
% Result : Unsatisfiable 15.09s 3.49s
% Output : Refutation 16.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 30
% Syntax : Number of formulae : 156 ( 86 unt; 19 def)
% Number of atoms : 246 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 182 ( 92 ~; 87 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 140 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f6,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f7,axiom,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f8,axiom,
! [X0,X1] :
( theorem(X0)
| ~ theorem(implies(X1,X0))
| ~ theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f9,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f11,negated_conjecture,
~ theorem(equivalent(not(implies(not(p),q)),and(not(p),not(q)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f12,plain,
! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
inference(definition_unfolding,[],[f10,f9,f6,f6]) ).
fof(f13,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f14,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f15,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f16,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f17,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f18,plain,
! [X0,X1] :
( ~ theorem(or(not(X1),X0))
| theorem(X0)
| ~ theorem(X1) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f19,plain,
~ theorem(not(or(not(or(not(not(or(not(not(p)),q))),not(or(not(not(p)),not(not(q)))))),not(or(not(not(or(not(not(p)),not(not(q))))),not(or(not(not(p)),q))))))),
inference(definition_unfolding,[],[f11,f12,f6,f9]) ).
fof(f20,definition,
sF0 = not(p),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f21,plain,
not(p) = sF0,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF1 = not(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f23,plain,
not(sF0) = sF1,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF2 = or(sF1,q),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f25,plain,
or(sF1,q) = sF2,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF3 = not(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f27,plain,
not(sF2) = sF3,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF4 = not(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f29,plain,
not(sF3) = sF4,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF5 = not(q),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f31,plain,
not(q) = sF5,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF6 = not(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f33,plain,
not(sF5) = sF6,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF7 = or(sF1,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f35,plain,
or(sF1,sF6) = sF7,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF8 = not(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f37,plain,
not(sF7) = sF8,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF9 = or(sF4,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f39,plain,
or(sF4,sF8) = sF9,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF10 = not(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f41,plain,
not(sF9) = sF10,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF11 = not(sF8),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f43,plain,
not(sF8) = sF11,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF12 = or(sF11,sF3),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f45,plain,
or(sF11,sF3) = sF12,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF13 = not(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f47,plain,
not(sF12) = sF13,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF14 = or(sF10,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f49,plain,
or(sF10,sF13) = sF14,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF15 = not(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f51,plain,
not(sF14) = sF15,
inference(reorient_equations,[],[f50]) ).
fof(f52,plain,
~ theorem(sF15),
inference(definition_folding,[],[f19,f51,f49,f47,f45,f27,f25,f23,f21,f43,f37,f35,f33,f31,f23,f21,f41,f39,f37,f35,f33,f31,f23,f21,f29,f27,f25,f23,f21]) ).
fof(f54,plain,
! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(resolution,[],[f7,f17]) ).
fof(f55,plain,
! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(resolution,[],[f7,f16]) ).
fof(f63,plain,
! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(resolution,[],[f15,f7]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f18,f55]) ).
fof(f75,plain,
! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) ),
inference(resolution,[],[f18,f54]) ).
fof(f76,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f18,f63]) ).
fof(f85,plain,
! [X0] :
( ~ theorem(or(sF13,X0))
| theorem(X0)
| ~ theorem(sF12) ),
inference(superposition,[],[f18,f47]) ).
fof(f87,definition,
( spl16_1
<=> theorem(sF12) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f89,plain,
( ~ theorem(sF12)
| spl16_1 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl16_2
<=> ! [X0] :
( ~ theorem(or(sF13,X0))
| theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f92,plain,
( ! [X0] :
( ~ theorem(or(sF13,X0))
| theorem(X0) )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f85,f91,f87]) ).
fof(f159,plain,
! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))),
inference(resolution,[],[f74,f54]) ).
fof(f257,plain,
theorem(or(not(sF14),or(sF13,sF10))),
inference(superposition,[],[f63,f49]) ).
fof(f259,plain,
theorem(or(sF15,or(sF13,sF10))),
inference(forward_demodulation,[],[f257,f51]) ).
fof(f274,plain,
! [X0,X1] : theorem(or(not(X0),or(X1,X0))),
inference(resolution,[],[f14,f7]) ).
fof(f316,plain,
theorem(or(not(q),sF2)),
inference(superposition,[],[f274,f25]) ).
fof(f318,plain,
theorem(or(not(sF8),sF9)),
inference(superposition,[],[f274,f39]) ).
fof(f322,plain,
theorem(or(sF11,sF9)),
inference(forward_demodulation,[],[f318,f43]) ).
fof(f323,plain,
theorem(or(sF5,sF2)),
inference(forward_demodulation,[],[f316,f31]) ).
fof(f324,plain,
! [X0] : theorem(or(not(or(X0,X0)),X0)),
inference(resolution,[],[f13,f7]) ).
fof(f325,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[],[f324,f18]) ).
fof(f328,plain,
! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ),
inference(resolution,[],[f75,f18]) ).
fof(f331,plain,
! [X0] :
( theorem(or(not(sF2),or(sF1,X0)))
| ~ theorem(or(not(q),X0)) ),
inference(superposition,[],[f75,f25]) ).
fof(f345,plain,
! [X0] :
( theorem(or(sF3,or(sF1,X0)))
| ~ theorem(or(not(q),X0)) ),
inference(forward_demodulation,[],[f331,f27]) ).
fof(f348,plain,
! [X0] :
( theorem(or(sF3,or(sF1,X0)))
| ~ theorem(or(sF5,X0)) ),
inference(forward_demodulation,[],[f345,f31]) ).
fof(f349,plain,
! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X2,or(X1,X3))))
| theorem(or(X0,or(X1,or(X2,X3)))) ),
inference(resolution,[],[f328,f55]) ).
fof(f351,plain,
! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f328,f63]) ).
fof(f352,plain,
! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X3)))
| theorem(or(X0,or(X1,X2)))
| ~ theorem(or(not(X3),X2)) ),
inference(resolution,[],[f328,f75]) ).
fof(f353,plain,
! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) ),
inference(resolution,[],[f328,f274]) ).
fof(f354,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f328,f324]) ).
fof(f358,plain,
! [X0,X1] :
( ~ theorem(or(sF3,X0))
| theorem(or(X1,X0))
| ~ theorem(or(X1,sF2)) ),
inference(superposition,[],[f328,f27]) ).
fof(f360,plain,
! [X0,X1] :
( ~ theorem(or(sF6,X0))
| theorem(or(X1,X0))
| ~ theorem(or(X1,sF5)) ),
inference(superposition,[],[f328,f33]) ).
fof(f361,plain,
! [X0,X1] :
( ~ theorem(or(sF8,X0))
| theorem(or(X1,X0))
| ~ theorem(or(X1,sF7)) ),
inference(superposition,[],[f328,f37]) ).
fof(f363,plain,
! [X0,X1] :
( ~ theorem(or(sF10,X0))
| theorem(or(X1,X0))
| ~ theorem(or(X1,sF9)) ),
inference(superposition,[],[f328,f41]) ).
fof(f369,plain,
! [X0] : theorem(or(not(X0),X0)),
inference(resolution,[],[f354,f274]) ).
fof(f375,plain,
! [X0,X1] : theorem(or(not(X0),or(X0,X1))),
inference(resolution,[],[f351,f274]) ).
fof(f387,plain,
! [X0] : theorem(or(X0,not(X0))),
inference(resolution,[],[f369,f76]) ).
fof(f404,plain,
theorem(or(sF0,sF1)),
inference(superposition,[],[f387,f23]) ).
fof(f407,plain,
theorem(or(sF5,sF6)),
inference(superposition,[],[f387,f33]) ).
fof(f414,plain,
theorem(or(sF13,or(sF15,sF10))),
inference(resolution,[],[f259,f74]) ).
fof(f418,plain,
! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) ),
inference(resolution,[],[f159,f18]) ).
fof(f459,plain,
! [X0,X1] :
( theorem(or(not(or(sF1,X0)),or(X1,X0)))
| ~ theorem(or(X1,sF0)) ),
inference(superposition,[],[f418,f23]) ).
fof(f475,plain,
! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f353,f351]) ).
fof(f484,plain,
! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) ),
inference(resolution,[],[f352,f63]) ).
fof(f487,plain,
! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(X1,X2))),or(X1,X3)))
| ~ theorem(or(not(or(X0,X2)),X3)) ),
inference(resolution,[],[f352,f55]) ).
fof(f504,plain,
theorem(or(sF13,or(sF10,sF15))),
inference(resolution,[],[f414,f351]) ).
fof(f515,plain,
! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1)))),
inference(resolution,[],[f349,f63]) ).
fof(f527,plain,
! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X0,X2)) ),
inference(resolution,[],[f484,f18]) ).
fof(f531,plain,
! [X0,X1] :
( theorem(or(not(or(X0,X1)),X1))
| ~ theorem(or(not(X0),X1)) ),
inference(resolution,[],[f484,f354]) ).
fof(f552,plain,
! [X2,X3,X0,X1] :
( ~ theorem(or(not(or(X0,X1)),X2))
| theorem(or(X3,X2))
| ~ theorem(or(X0,or(X3,X1))) ),
inference(resolution,[],[f487,f18]) ).
fof(f582,plain,
! [X0] :
( ~ theorem(or(X0,sF1))
| theorem(or(X0,sF2)) ),
inference(superposition,[],[f475,f25]) ).
fof(f584,plain,
! [X0] :
( ~ theorem(or(X0,sF4))
| theorem(or(X0,sF9)) ),
inference(superposition,[],[f475,f39]) ).
fof(f599,plain,
( theorem(or(sF3,sF7))
| ~ theorem(or(sF5,sF6)) ),
inference(superposition,[],[f348,f35]) ).
fof(f600,plain,
theorem(or(sF3,sF7)),
inference(forward_subsumption_resolution,[],[f599,f407]) ).
fof(f654,plain,
! [X0] :
( theorem(or(X0,not(sF3)))
| ~ theorem(or(X0,sF2)) ),
inference(resolution,[],[f358,f387]) ).
fof(f657,plain,
! [X0] :
( ~ theorem(or(X0,sF2))
| theorem(or(X0,sF4)) ),
inference(forward_demodulation,[],[f654,f29]) ).
fof(f685,plain,
! [X0] :
( theorem(or(X0,not(sF8)))
| ~ theorem(or(X0,sF7)) ),
inference(resolution,[],[f361,f387]) ).
fof(f688,plain,
! [X0] :
( ~ theorem(or(X0,sF7))
| theorem(or(X0,sF11)) ),
inference(forward_demodulation,[],[f685,f43]) ).
fof(f691,plain,
theorem(or(sF3,sF11)),
inference(resolution,[],[f688,f600]) ).
fof(f694,plain,
theorem(or(sF11,sF3)),
inference(resolution,[],[f691,f76]) ).
fof(f695,plain,
theorem(sF12),
inference(forward_demodulation,[],[f694,f45]) ).
fof(f696,plain,
( $false
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f695,f89]) ).
fof(f697,plain,
spl16_1,
inference(avatar_contradiction_clause,[],[f696]) ).
fof(f699,plain,
( theorem(or(sF10,sF15))
| ~ spl16_2 ),
inference(resolution,[],[f92,f504]) ).
fof(f705,plain,
( ! [X0] :
( ~ theorem(or(X0,sF9))
| theorem(or(X0,sF15)) )
| ~ spl16_2 ),
inference(resolution,[],[f699,f363]) ).
fof(f709,plain,
( theorem(or(sF11,sF15))
| ~ spl16_2 ),
inference(resolution,[],[f705,f322]) ).
fof(f725,plain,
theorem(or(sF5,sF4)),
inference(resolution,[],[f323,f657]) ).
fof(f749,plain,
theorem(or(not(sF4),sF9)),
inference(superposition,[],[f375,f39]) ).
fof(f1049,plain,
! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X2,X1))
| ~ theorem(or(not(X0),X1)) ),
inference(resolution,[],[f531,f552]) ).
fof(f1265,plain,
theorem(or(sF5,sF9)),
inference(resolution,[],[f584,f725]) ).
fof(f1266,plain,
( theorem(or(sF5,sF15))
| ~ spl16_2 ),
inference(resolution,[],[f1265,f705]) ).
fof(f1268,plain,
( theorem(or(sF15,sF5))
| ~ spl16_2 ),
inference(resolution,[],[f1266,f76]) ).
fof(f1295,plain,
! [X2,X0,X1] :
( ~ theorem(or(or(X0,X2),X1))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f515,f18]) ).
fof(f1891,plain,
( theorem(or(not(sF4),sF15))
| ~ spl16_2 ),
inference(resolution,[],[f749,f705]) ).
fof(f1894,plain,
( ! [X0] :
( ~ theorem(or(sF4,X0))
| theorem(or(X0,sF15)) )
| ~ spl16_2 ),
inference(resolution,[],[f1891,f527]) ).
fof(f2696,plain,
theorem(or(sF0,sF2)),
inference(resolution,[],[f404,f582]) ).
fof(f2710,plain,
theorem(or(sF0,sF4)),
inference(resolution,[],[f2696,f657]) ).
fof(f2714,plain,
theorem(or(sF4,sF0)),
inference(resolution,[],[f2710,f76]) ).
fof(f3108,definition,
( spl16_121
<=> theorem(or(sF15,sF15)) ),
introduced(definition,[new_symbols(definition,[spl16_121])],[avatar_definition]) ).
fof(f3110,plain,
( theorem(or(sF15,sF15))
| ~ spl16_121 ),
inference(avatar_component_clause,[],[f3108]) ).
fof(f3952,plain,
! [X0] :
( theorem(or(not(sF7),or(X0,sF6)))
| ~ theorem(or(X0,sF0)) ),
inference(superposition,[],[f459,f35]) ).
fof(f3968,plain,
! [X0] :
( theorem(or(sF8,or(X0,sF6)))
| ~ theorem(or(X0,sF0)) ),
inference(forward_demodulation,[],[f3952,f37]) ).
fof(f4001,plain,
! [X0] :
( theorem(or(X0,or(sF8,sF6)))
| ~ theorem(or(X0,sF0)) ),
inference(resolution,[],[f3968,f74]) ).
fof(f4350,plain,
( ~ theorem(or(sF4,sF0))
| theorem(or(or(sF8,sF6),sF15))
| ~ spl16_2 ),
inference(resolution,[],[f4001,f1894]) ).
fof(f4365,plain,
( theorem(or(or(sF8,sF6),sF15))
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f4350,f2714]) ).
fof(f4396,plain,
( theorem(or(sF8,or(sF15,sF6)))
| ~ spl16_2 ),
inference(resolution,[],[f4365,f1295]) ).
fof(f4401,plain,
( theorem(or(sF8,or(sF6,sF15)))
| ~ spl16_2 ),
inference(resolution,[],[f4396,f351]) ).
fof(f4406,plain,
( theorem(or(sF6,sF15))
| ~ theorem(or(not(sF8),sF15))
| ~ spl16_2 ),
inference(resolution,[],[f4401,f1049]) ).
fof(f4411,plain,
( ~ theorem(or(sF11,sF15))
| theorem(or(sF6,sF15))
| ~ spl16_2 ),
inference(forward_demodulation,[],[f4406,f43]) ).
fof(f4412,plain,
( theorem(or(sF6,sF15))
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f4411,f709]) ).
fof(f4413,plain,
( ! [X0] :
( ~ theorem(or(X0,sF5))
| theorem(or(X0,sF15)) )
| ~ spl16_2 ),
inference(resolution,[],[f4412,f360]) ).
fof(f4429,plain,
( theorem(or(sF15,sF15))
| ~ spl16_2 ),
inference(resolution,[],[f4413,f1268]) ).
fof(f4430,plain,
( spl16_121
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f4429,f91,f3108]) ).
fof(f4438,plain,
( theorem(sF15)
| ~ spl16_121 ),
inference(resolution,[],[f3110,f325]) ).
fof(f4440,plain,
( $false
| ~ spl16_121 ),
inference(forward_subsumption_resolution,[],[f4438,f52]) ).
fof(f4441,plain,
~ spl16_121,
inference(avatar_contradiction_clause,[],[f4440]) ).
cnf(s1,plain,
( ~ spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f93]) ).
cnf(s15,plain,
spl16_1,
inference(sat_conversion,[],[f697]) ).
cnf(s171,plain,
( ~ spl16_2
| spl16_121 ),
inference(sat_conversion,[],[f4430]) ).
cnf(s174,plain,
~ spl16_121,
inference(sat_conversion,[],[f4441]) ).
cnf(s176,plain,
~ spl16_2,
inference(rat,[],[s171,s174]) ).
cnf(s179,plain,
$false,
inference(rat,[],[s1,s176,s15]) ).
fof(f4443,plain,
$false,
inference(avatar_sat_refutation,[],[s179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL299-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 % Computer : n015.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sun Sep 27 15:36:31 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.53 Running first-order theorem proving
% 0.27/0.53 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.09/3.49 % (1795432)Input is clausal, will run a generic CNF schedule.
% 15.09/3.49 % (1795438)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3131027444:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 15.09/3.49 % (1795441)lrs+10_1_sil=8000:sp=occurrence:random_seed=3062238532:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 15.09/3.49 % (1795439)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4283841965:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 15.09/3.49 % (1795440)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3964734321:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 15.09/3.49 % (1795443)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=384783720:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 15.09/3.49 % (1795442)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4179399085:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 15.09/3.49 % (1795444)dis-21_1_sil=8000:lcm=predicate:random_seed=1037735543:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 15.09/3.49 % (1795441)Instruction limit reached!
% 15.09/3.49 % (1795441)------------------------------
% 15.09/3.49 % (1795441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795441)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795441)Termination reason: Instruction limit
% 15.09/3.49 % (1795441)Termination phase: Saturation
% 15.09/3.49 % (1795441)Time elapsed: 0.106 s
% 15.09/3.49 % (1795441)Peak memory usage: 89 MB
% 15.09/3.49 % (1795441)Instructions burned: 107 (million)
% 15.09/3.49 % (1795444)Instruction limit reached!
% 15.09/3.49 % (1795444)------------------------------
% 15.09/3.49 % (1795444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795444)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795444)Termination reason: Instruction limit
% 15.09/3.49 % (1795444)Termination phase: Saturation
% 15.09/3.49 % (1795444)Time elapsed: 0.095 s
% 15.09/3.49 % (1795444)Peak memory usage: 87 MB
% 15.09/3.49 % (1795444)Instructions burned: 117 (million)
% 15.09/3.49 % (1795442)Instruction limit reached!
% 15.09/3.49 % (1795442)------------------------------
% 15.09/3.49 % (1795442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795442)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795442)Termination reason: Instruction limit
% 15.09/3.49 % (1795442)Termination phase: Saturation
% 15.09/3.49 % (1795442)Time elapsed: 0.112 s
% 15.09/3.49 % (1795442)Peak memory usage: 89 MB
% 15.09/3.49 % (1795442)Instructions burned: 114 (million)
% 15.09/3.49 % (1795443)Instruction limit reached!
% 15.09/3.49 % (1795443)------------------------------
% 15.09/3.49 % (1795443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795443)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795443)Termination reason: Instruction limit
% 15.09/3.49 % (1795443)Termination phase: Saturation
% 15.09/3.49 % (1795443)Time elapsed: 0.174 s
% 15.09/3.49 % (1795443)Peak memory usage: 89 MB
% 15.09/3.49 % (1795443)Instructions burned: 181 (million)
% 15.09/3.49 % (1795452)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=466901378:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 15.09/3.49 % (1795453)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=11327484:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 15.09/3.49 % (1795452)Refutation not found, incomplete strategy
% 15.09/3.49 % (1795452)------------------------------
% 15.09/3.49 % (1795452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795453)Refutation not found, incomplete strategy
% 15.09/3.49 % (1795453)------------------------------
% 15.09/3.49 % (1795453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795453)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795453)Termination reason: Refutation not found, incomplete strategy
% 15.09/3.49 % (1795453)Time elapsed: 0.002 s
% 15.09/3.49 % (1795452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795452)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795453)Peak memory usage: 87 MB
% 15.09/3.49 % (1795452)Termination reason: Refutation not found, incomplete strategy
% 15.09/3.49 % (1795452)Time elapsed: 0.002 s
% 15.09/3.49 % (1795452)Peak memory usage: 88 MB
% 15.09/3.49 % (1795454)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1506702082:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 15.09/3.49 % (1795454)Refutation not found, incomplete strategy
% 15.09/3.49 % (1795454)------------------------------
% 15.09/3.49 % (1795454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795454)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795454)Termination reason: Refutation not found, incomplete strategy
% 15.09/3.49 % (1795454)Time elapsed: 0.003 s
% 15.09/3.49 % (1795454)Peak memory usage: 88 MB
% 15.09/3.49 % (1795454)Instructions burned: 1 (million)
% 15.09/3.49 % (1795455)lrs+10_64_to=lpo:sil=8000:random_seed=3741378851:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 15.09/3.49 % (1795455)Instruction limit reached!
% 15.09/3.49 % (1795455)------------------------------
% 15.09/3.49 % (1795455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795455)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795455)Termination reason: Instruction limit
% 15.09/3.49 % (1795455)Termination phase: Saturation
% 15.09/3.49 % (1795455)Time elapsed: 0.119 s
% 15.09/3.49 % (1795455)Peak memory usage: 89 MB
% 15.09/3.49 % (1795455)Instructions burned: 126 (million)
% 15.09/3.49 % (1795452)------------------------------
% 15.09/3.49 % (1795452)------------------------------
% 15.09/3.49 % (1795454)------------------------------
% 15.09/3.49 % (1795454)------------------------------
% 15.09/3.49 % (1795453)------------------------------
% 15.09/3.49 % (1795453)------------------------------
% 15.09/3.49 % (1795460)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=115715194:avsq=on:i=194:fgj=on:bd=preordered_2992 on theBenchmark for (2992ds/194Mi)
% 15.09/3.49 % (1795461)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=443933842:i=157:gtg=all_2990 on theBenchmark for (2990ds/157Mi)
% 15.09/3.49 % (1795460)Instruction limit reached!
% 15.09/3.49 % (1795460)------------------------------
% 15.09/3.49 % (1795460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795460)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795460)Termination reason: Instruction limit
% 15.09/3.49 % (1795460)Termination phase: Saturation
% 15.09/3.49 % (1795460)Time elapsed: 0.197 s
% 15.09/3.49 % (1795460)Peak memory usage: 90 MB
% 15.09/3.49 % (1795460)Instructions burned: 194 (million)
% 15.09/3.49 % (1795462)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3971010514:i=3394:sd=4:ss=included:sgt=64_2990 on theBenchmark for (2990ds/3394Mi)
% 15.09/3.49 % (1795463)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3204115797:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2990 on theBenchmark for (2990ds/106Mi)
% 15.09/3.49 % (1795461)Instruction limit reached!
% 15.09/3.49 % (1795461)------------------------------
% 15.09/3.49 % (1795461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795461)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795461)Termination reason: Instruction limit
% 15.09/3.49 % (1795461)Termination phase: Saturation
% 15.09/3.49 % (1795461)Time elapsed: 0.087 s
% 15.09/3.49 % (1795461)Peak memory usage: 91 MB
% 15.09/3.49 % (1795461)Instructions burned: 158 (million)
% 15.09/3.49 % (1795463)Instruction limit reached!
% 15.09/3.49 % (1795463)------------------------------
% 15.09/3.49 % (1795463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795463)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795463)Termination reason: Instruction limit
% 15.09/3.49 % (1795463)Termination phase: Saturation
% 15.09/3.49 % (1795463)Time elapsed: 0.094 s
% 15.09/3.49 % (1795463)Peak memory usage: 89 MB
% 15.09/3.49 % (1795463)Instructions burned: 106 (million)
% 15.09/3.49 % (1795469)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3626040400:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2987 on theBenchmark for (2987ds/242Mi)
% 15.09/3.49 % (1795467)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3393165021:i=107_2988 on theBenchmark for (2988ds/107Mi)
% 15.09/3.49 % (1795467)Refutation not found, incomplete strategy
% 15.09/3.49 % (1795467)------------------------------
% 15.09/3.49 % (1795467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795467)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795467)Termination reason: Refutation not found, incomplete strategy
% 15.09/3.49 % (1795467)Time elapsed: 0.002 s
% 15.09/3.49 % (1795467)Peak memory usage: 87 MB
% 15.09/3.49 % (1795469)Instruction limit reached!
% 15.09/3.49 % (1795469)------------------------------
% 15.09/3.49 % (1795469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795469)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795469)Termination reason: Instruction limit
% 15.09/3.49 % (1795469)Termination phase: Saturation
% 15.09/3.49 % (1795469)Time elapsed: 0.121 s
% 15.09/3.49 % (1795469)Peak memory usage: 91 MB
% 15.09/3.49 % (1795469)Instructions burned: 243 (million)
% 15.09/3.49 % (1795470)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=690096430:cond=fast:i=5208:av=off_2987 on theBenchmark for (2987ds/5208Mi)
% 15.09/3.49 % (1795473)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1114956456:i=134:sd=2:doe=on:ss=axioms:sgt=14_2985 on theBenchmark for (2985ds/134Mi)
% 15.09/3.49 % (1795473)Instruction limit reached!
% 15.09/3.49 % (1795473)------------------------------
% 15.09/3.49 % (1795473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795473)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795473)Termination reason: Instruction limit
% 15.09/3.49 % (1795473)Termination phase: Saturation
% 15.09/3.49 % (1795473)Time elapsed: 0.072 s
% 15.09/3.49 % (1795473)Peak memory usage: 90 MB
% 15.09/3.49 % (1795473)Instructions burned: 134 (million)
% 15.09/3.49 % (1795438)First to succeed.
% 15.09/3.49 % (1795438)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1795432"
% 15.09/3.49 % (1795467)------------------------------
% 15.09/3.49 % (1795467)------------------------------
% 15.09/3.49 % (1795476)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2817857304:i=499:bd=all_2982 on theBenchmark for (2982ds/499Mi)
% 15.09/3.49 % (1795477)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=2717188808:i=191:fgj=on:bd=all_2981 on theBenchmark for (2981ds/191Mi)
% 15.09/3.49 % (1795476)Instruction limit reached!
% 15.09/3.49 % (1795476)------------------------------
% 15.09/3.49 % (1795476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.09/3.49 % (1795476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/3.49 % (1795476)CaDiCaL version: 2.1.3
% 15.09/3.49 % (1795476)Termination reason: Instruction limit
% 15.09/3.49 % (1795476)Termination phase: Saturation
% 15.09/3.49 % (1795476)Time elapsed: 0.247 s
% 15.09/3.49 % (1795476)Peak memory usage: 94 MB
% 15.09/3.49 % (1795476)Instructions burned: 501 (million)
% 15.09/3.49 % (1795438)Refutation found. Thanks to Tanya!
% 15.09/3.49 % SZS status Unsatisfiable for theBenchmark
% 15.09/3.49 % SZS output start Proof for theBenchmark
% See solution above
% 16.72/3.87 % (1795438)------------------------------
% 16.72/3.87 % (1795438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.72/3.87 % (1795438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.72/3.87 % (1795438)CaDiCaL version: 2.1.3
% 16.72/3.87 % (1795438)Termination reason: Refutation
% 16.72/3.87 % (1795438)Time elapsed: 1.606 s
% 16.72/3.87 % (1795438)Peak memory usage: 137 MB
% 16.72/3.87 % (1795438)Instructions burned: 1825 (million)
% 16.72/3.87 % (1795438)------------------------------
% 16.72/3.87 % (1795438)------------------------------
% 16.72/3.87 % (1795432)Success in time 2.21 s
% 16.72/3.87 % Vampire exiting
%------------------------------------------------------------------------------