TSTP Solution File: GEO558+1 by PyRes---1.3
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- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : GEO558+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n017.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 : Sat Jul 16 06:00:55 EDT 2022
% Result : Theorem 68.51s 68.75s
% Output : Refutation 68.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO558+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33 % Computer : n017.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 : Sat Jun 18 16:28:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 68.51/68.75 # Version: 1.3
% 68.51/68.75 # SZS status Theorem
% 68.51/68.75 # SZS output start CNFRefutation
% 68.51/68.75 fof(exemplo6GDDFULL012018,conjecture,(![A]:(![C]:(![K]:(![O]:(![N]:(![B]:(![G]:(![O1]:(![M]:(![NWPNT1]:(![NWPNT2]:(![NWPNT3]:((((((((circle(O,A,C,K)&circle(O,A,N,NWPNT1))&coll(B,A,K))&coll(B,C,N))&circle(G,A,C,B))&circle(O1,K,N,B))&circle(G,A,M,NWPNT2))&circle(O1,K,M,NWPNT3))=>perp(B,M,M,O)))))))))))))),input).
% 68.51/68.75 fof(c11,negated_conjecture,(~(![A]:(![C]:(![K]:(![O]:(![N]:(![B]:(![G]:(![O1]:(![M]:(![NWPNT1]:(![NWPNT2]:(![NWPNT3]:((((((((circle(O,A,C,K)&circle(O,A,N,NWPNT1))&coll(B,A,K))&coll(B,C,N))&circle(G,A,C,B))&circle(O1,K,N,B))&circle(G,A,M,NWPNT2))&circle(O1,K,M,NWPNT3))=>perp(B,M,M,O))))))))))))))),inference(assume_negation,status(cth),[exemplo6GDDFULL012018])).
% 68.51/68.75 fof(c12,negated_conjecture,(?[A]:(?[C]:(?[K]:(?[O]:(?[N]:(?[B]:(?[G]:(?[O1]:(?[M]:(?[NWPNT1]:(?[NWPNT2]:(?[NWPNT3]:((((((((circle(O,A,C,K)&circle(O,A,N,NWPNT1))&coll(B,A,K))&coll(B,C,N))&circle(G,A,C,B))&circle(O1,K,N,B))&circle(G,A,M,NWPNT2))&circle(O1,K,M,NWPNT3))&~perp(B,M,M,O)))))))))))))),inference(fof_nnf,status(thm),[c11])).
% 68.51/68.75 fof(c13,negated_conjecture,(?[A]:(?[C]:(?[K]:(?[O]:(?[N]:(?[B]:(?[G]:(?[O1]:(?[M]:((((((((circle(O,A,C,K)&(?[NWPNT1]:circle(O,A,N,NWPNT1)))&coll(B,A,K))&coll(B,C,N))&circle(G,A,C,B))&circle(O1,K,N,B))&(?[NWPNT2]:circle(G,A,M,NWPNT2)))&(?[NWPNT3]:circle(O1,K,M,NWPNT3)))&~perp(B,M,M,O))))))))))),inference(shift_quantors,status(thm),[c12])).
% 68.51/68.75 fof(c14,negated_conjecture,(?[X2]:(?[X3]:(?[X4]:(?[X5]:(?[X6]:(?[X7]:(?[X8]:(?[X9]:(?[X10]:((((((((circle(X5,X2,X3,X4)&(?[X11]:circle(X5,X2,X6,X11)))&coll(X7,X2,X4))&coll(X7,X3,X6))&circle(X8,X2,X3,X7))&circle(X9,X4,X6,X7))&(?[X12]:circle(X8,X2,X10,X12)))&(?[X13]:circle(X9,X4,X10,X13)))&~perp(X7,X10,X10,X5))))))))))),inference(variable_rename,status(thm),[c13])).
% 68.51/68.75 fof(c15,negated_conjecture,((((((((circle(skolem0004,skolem0001,skolem0002,skolem0003)&circle(skolem0004,skolem0001,skolem0005,skolem0010))&coll(skolem0006,skolem0001,skolem0003))&coll(skolem0006,skolem0002,skolem0005))&circle(skolem0007,skolem0001,skolem0002,skolem0006))&circle(skolem0008,skolem0003,skolem0005,skolem0006))&circle(skolem0007,skolem0001,skolem0009,skolem0011))&circle(skolem0008,skolem0003,skolem0009,skolem0012))&~perp(skolem0006,skolem0009,skolem0009,skolem0004)),inference(skolemize,status(esa),[c14])).
% 68.51/68.75 cnf(c24,negated_conjecture,~perp(skolem0006,skolem0009,skolem0009,skolem0004),inference(split_conjunct,status(thm),[c15])).
% 68.51/68.75 fof(ruleD74,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:((eqangle(A,B,C,D,P,Q,U,V)&perp(P,Q,U,V))=>perp(A,B,C,D)))))))))),input).
% 68.51/68.75 fof(c160,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:((~eqangle(A,B,C,D,P,Q,U,V)|~perp(P,Q,U,V))|perp(A,B,C,D)))))))))),inference(fof_nnf,status(thm),[ruleD74])).
% 68.51/68.75 fof(c161,axiom,(![A]:(![B]:(![C]:(![D]:((![P]:(![Q]:(![U]:(![V]:(~eqangle(A,B,C,D,P,Q,U,V)|~perp(P,Q,U,V))))))|perp(A,B,C,D)))))),inference(shift_quantors,status(thm),[c160])).
% 68.51/68.75 fof(c163,axiom,(![X129]:(![X130]:(![X131]:(![X132]:(![X133]:(![X134]:(![X135]:(![X136]:((~eqangle(X129,X130,X131,X132,X133,X134,X135,X136)|~perp(X133,X134,X135,X136))|perp(X129,X130,X131,X132)))))))))),inference(shift_quantors,status(thm),[fof(c162,axiom,(![X129]:(![X130]:(![X131]:(![X132]:((![X133]:(![X134]:(![X135]:(![X136]:(~eqangle(X129,X130,X131,X132,X133,X134,X135,X136)|~perp(X133,X134,X135,X136))))))|perp(X129,X130,X131,X132)))))),inference(variable_rename,status(thm),[c161])).])).
% 68.51/68.75 cnf(c164,axiom,~eqangle(X929,X931,X930,X934,X936,X933,X935,X932)|~perp(X936,X933,X935,X932)|perp(X929,X931,X930,X934),inference(split_conjunct,status(thm),[c163])).
% 68.51/68.75 fof(ruleD40,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(para(A,B,C,D)=>eqangle(A,B,P,Q,C,D,P,Q)))))))),input).
% 68.51/68.75 fof(c282,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q)))))))),inference(fof_nnf,status(thm),[ruleD40])).
% 68.51/68.75 fof(c283,axiom,(![A]:(![B]:(![C]:(![D]:(~para(A,B,C,D)|(![P]:(![Q]:eqangle(A,B,P,Q,C,D,P,Q)))))))),inference(shift_quantors,status(thm),[c282])).
% 68.51/68.75 fof(c285,axiom,(![X294]:(![X295]:(![X296]:(![X297]:(![X298]:(![X299]:(~para(X294,X295,X296,X297)|eqangle(X294,X295,X298,X299,X296,X297,X298,X299)))))))),inference(shift_quantors,status(thm),[fof(c284,axiom,(![X294]:(![X295]:(![X296]:(![X297]:(~para(X294,X295,X296,X297)|(![X298]:(![X299]:eqangle(X294,X295,X298,X299,X296,X297,X298,X299)))))))),inference(variable_rename,status(thm),[c283])).])).
% 68.51/68.75 cnf(c286,axiom,~para(X1085,X1082,X1081,X1083)|eqangle(X1085,X1082,X1086,X1084,X1081,X1083,X1086,X1084),inference(split_conjunct,status(thm),[c285])).
% 68.51/68.75 fof(ruleD4,axiom,(![A]:(![B]:(![C]:(![D]:(para(A,B,C,D)=>para(A,B,D,C)))))),input).
% 68.51/68.75 fof(c398,axiom,(![A]:(![B]:(![C]:(![D]:(~para(A,B,C,D)|para(A,B,D,C)))))),inference(fof_nnf,status(thm),[ruleD4])).
% 68.51/68.75 fof(c399,axiom,(![X521]:(![X522]:(![X523]:(![X524]:(~para(X521,X522,X523,X524)|para(X521,X522,X524,X523)))))),inference(variable_rename,status(thm),[c398])).
% 68.51/68.75 cnf(c400,axiom,~para(X678,X679,X680,X681)|para(X678,X679,X681,X680),inference(split_conjunct,status(thm),[c399])).
% 68.51/68.75 fof(ruleD39,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(eqangle(A,B,P,Q,C,D,P,Q)=>para(A,B,C,D)))))))),input).
% 68.51/68.75 fof(c287,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(~eqangle(A,B,P,Q,C,D,P,Q)|para(A,B,C,D)))))))),inference(fof_nnf,status(thm),[ruleD39])).
% 68.51/68.75 fof(c288,axiom,(![A]:(![B]:(![C]:(![D]:((![P]:(![Q]:~eqangle(A,B,P,Q,C,D,P,Q)))|para(A,B,C,D)))))),inference(shift_quantors,status(thm),[c287])).
% 68.51/68.75 fof(c290,axiom,(![X300]:(![X301]:(![X302]:(![X303]:(![X304]:(![X305]:(~eqangle(X300,X301,X304,X305,X302,X303,X304,X305)|para(X300,X301,X302,X303)))))))),inference(shift_quantors,status(thm),[fof(c289,axiom,(![X300]:(![X301]:(![X302]:(![X303]:((![X304]:(![X305]:~eqangle(X300,X301,X304,X305,X302,X303,X304,X305)))|para(X300,X301,X302,X303)))))),inference(variable_rename,status(thm),[c288])).])).
% 68.51/68.75 cnf(c291,axiom,~eqangle(X1092,X1088,X1093,X1089,X1090,X1091,X1093,X1089)|para(X1092,X1088,X1090,X1091),inference(split_conjunct,status(thm),[c290])).
% 68.51/68.75 fof(ruleD19,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(eqangle(A,B,C,D,P,Q,U,V)=>eqangle(C,D,A,B,U,V,P,Q)))))))))),input).
% 68.51/68.75 fof(c351,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(~eqangle(A,B,C,D,P,Q,U,V)|eqangle(C,D,A,B,U,V,P,Q)))))))))),inference(fof_nnf,status(thm),[ruleD19])).
% 68.51/68.75 fof(c352,axiom,(![X446]:(![X447]:(![X448]:(![X449]:(![X450]:(![X451]:(![X452]:(![X453]:(~eqangle(X446,X447,X448,X449,X450,X451,X452,X453)|eqangle(X448,X449,X446,X447,X452,X453,X450,X451)))))))))),inference(variable_rename,status(thm),[c351])).
% 68.51/68.75 cnf(c353,axiom,~eqangle(X1239,X1240,X1243,X1245,X1244,X1238,X1242,X1241)|eqangle(X1243,X1245,X1239,X1240,X1242,X1241,X1244,X1238),inference(split_conjunct,status(thm),[c352])).
% 68.51/68.75 fof(ruleD8,axiom,(![A]:(![B]:(![C]:(![D]:(perp(A,B,C,D)=>perp(C,D,A,B)))))),input).
% 68.51/68.75 fof(c386,axiom,(![A]:(![B]:(![C]:(![D]:(~perp(A,B,C,D)|perp(C,D,A,B)))))),inference(fof_nnf,status(thm),[ruleD8])).
% 68.51/68.75 fof(c387,axiom,(![X503]:(![X504]:(![X505]:(![X506]:(~perp(X503,X504,X505,X506)|perp(X505,X506,X503,X504)))))),inference(variable_rename,status(thm),[c386])).
% 68.51/68.75 cnf(c388,axiom,~perp(X650,X653,X652,X651)|perp(X652,X651,X650,X653),inference(split_conjunct,status(thm),[c387])).
% 68.51/68.75 cnf(c21,negated_conjecture,circle(skolem0008,skolem0003,skolem0005,skolem0006),inference(split_conjunct,status(thm),[c15])).
% 68.51/68.75 fof(ruleX11,axiom,(![A]:(![B]:(![C]:(![O]:(?[P]:(circle(O,A,B,C)=>perp(P,A,A,O))))))),input).
% 68.51/68.75 fof(c73,axiom,(![A]:(![B]:(![C]:(![O]:(?[P]:(~circle(O,A,B,C)|perp(P,A,A,O))))))),inference(fof_nnf,status(thm),[ruleX11])).
% 68.51/68.75 fof(c74,axiom,(![A]:(![B]:(![C]:(![O]:(~circle(O,A,B,C)|(?[P]:perp(P,A,A,O))))))),inference(shift_quantors,status(thm),[c73])).
% 68.51/68.75 fof(c75,axiom,(![X56]:(![X57]:(![X58]:(![X59]:(~circle(X59,X56,X57,X58)|(?[X60]:perp(X60,X56,X56,X59))))))),inference(variable_rename,status(thm),[c74])).
% 68.51/68.75 fof(c76,axiom,(![X56]:(![X57]:(![X58]:(![X59]:(~circle(X59,X56,X57,X58)|perp(skolem0021(X56,X57,X58,X59),X56,X56,X59)))))),inference(skolemize,status(esa),[c75])).
% 68.51/68.75 cnf(c77,axiom,~circle(X791,X792,X793,X790)|perp(skolem0021(X792,X793,X790,X791),X792,X792,X791),inference(split_conjunct,status(thm),[c76])).
% 68.51/68.75 cnf(c589,plain,perp(skolem0021(skolem0003,skolem0005,skolem0006,skolem0008),skolem0003,skolem0003,skolem0008),inference(resolution,status(thm),[c77, c21])).
% 68.51/68.75 cnf(c1518,plain,perp(skolem0003,skolem0008,skolem0021(skolem0003,skolem0005,skolem0006,skolem0008),skolem0003),inference(resolution,status(thm),[c589, c388])).
% 68.51/68.75 fof(ruleD9,axiom,(![A]:(![B]:(![C]:(![D]:(![E]:(![F]:((perp(A,B,C,D)&perp(C,D,E,F))=>para(A,B,E,F)))))))),input).
% 68.51/68.75 fof(c383,axiom,(![A]:(![B]:(![C]:(![D]:(![E]:(![F]:((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F)))))))),inference(fof_nnf,status(thm),[ruleD9])).
% 68.51/68.75 fof(c384,axiom,(![X497]:(![X498]:(![X499]:(![X500]:(![X501]:(![X502]:((~perp(X497,X498,X499,X500)|~perp(X499,X500,X501,X502))|para(X497,X498,X501,X502)))))))),inference(variable_rename,status(thm),[c383])).
% 68.51/68.75 cnf(c385,axiom,~perp(X1280,X1279,X1282,X1281)|~perp(X1282,X1281,X1283,X1278)|para(X1280,X1279,X1283,X1278),inference(split_conjunct,status(thm),[c384])).
% 68.51/68.75 cnf(c1528,plain,~perp(X2655,X2656,skolem0021(skolem0003,skolem0005,skolem0006,skolem0008),skolem0003)|para(X2655,X2656,skolem0003,skolem0008),inference(resolution,status(thm),[c589, c385])).
% 68.51/68.75 cnf(c3260,plain,para(skolem0003,skolem0008,skolem0003,skolem0008),inference(resolution,status(thm),[c1528, c1518])).
% 68.51/68.75 cnf(c3264,plain,eqangle(skolem0003,skolem0008,X3051,X3050,skolem0003,skolem0008,X3051,X3050),inference(resolution,status(thm),[c3260, c286])).
% 68.51/68.75 cnf(c6063,plain,eqangle(X4338,X4337,skolem0003,skolem0008,X4338,X4337,skolem0003,skolem0008),inference(resolution,status(thm),[c3264, c353])).
% 68.51/68.75 cnf(c9532,plain,para(X4340,X4339,X4340,X4339),inference(resolution,status(thm),[c6063, c291])).
% 68.51/68.75 cnf(c9542,plain,para(X4358,X4357,X4357,X4358),inference(resolution,status(thm),[c9532, c400])).
% 68.51/68.75 cnf(c10593,plain,eqangle(X6001,X5999,X6000,X5998,X5999,X6001,X6000,X5998),inference(resolution,status(thm),[c9542, c286])).
% 68.51/68.75 cnf(c16303,plain,~perp(X7090,X7091,X7089,X7092)|perp(X7091,X7090,X7089,X7092),inference(resolution,status(thm),[c10593, c164])).
% 68.51/68.75 fof(ruleD41,axiom,(![A]:(![B]:(![P]:(![Q]:(cyclic(A,B,P,Q)=>eqangle(P,A,P,B,Q,A,Q,B)))))),input).
% 68.51/68.75 fof(c279,axiom,(![A]:(![B]:(![P]:(![Q]:(~cyclic(A,B,P,Q)|eqangle(P,A,P,B,Q,A,Q,B)))))),inference(fof_nnf,status(thm),[ruleD41])).
% 68.51/68.75 fof(c280,axiom,(![X290]:(![X291]:(![X292]:(![X293]:(~cyclic(X290,X291,X292,X293)|eqangle(X292,X290,X292,X291,X293,X290,X293,X291)))))),inference(variable_rename,status(thm),[c279])).
% 68.51/68.75 cnf(c281,axiom,~cyclic(X1079,X1076,X1078,X1077)|eqangle(X1078,X1079,X1078,X1076,X1077,X1079,X1077,X1076),inference(split_conjunct,status(thm),[c280])).
% 68.51/68.75 fof(ruleD16,axiom,(![A]:(![B]:(![C]:(![D]:(cyclic(A,B,C,D)=>cyclic(B,A,C,D)))))),input).
% 68.51/68.75 fof(c360,axiom,(![A]:(![B]:(![C]:(![D]:(~cyclic(A,B,C,D)|cyclic(B,A,C,D)))))),inference(fof_nnf,status(thm),[ruleD16])).
% 68.51/68.75 fof(c361,axiom,(![X467]:(![X468]:(![X469]:(![X470]:(~cyclic(X467,X468,X469,X470)|cyclic(X468,X467,X469,X470)))))),inference(variable_rename,status(thm),[c360])).
% 68.51/68.75 cnf(c362,axiom,~cyclic(X639,X640,X638,X641)|cyclic(X640,X639,X638,X641),inference(split_conjunct,status(thm),[c361])).
% 68.51/68.75 fof(ruleD15,axiom,(![A]:(![B]:(![C]:(![D]:(cyclic(A,B,C,D)=>cyclic(A,C,B,D)))))),input).
% 68.51/68.75 fof(c363,axiom,(![A]:(![B]:(![C]:(![D]:(~cyclic(A,B,C,D)|cyclic(A,C,B,D)))))),inference(fof_nnf,status(thm),[ruleD15])).
% 68.51/68.75 fof(c364,axiom,(![X471]:(![X472]:(![X473]:(![X474]:(~cyclic(X471,X472,X473,X474)|cyclic(X471,X473,X472,X474)))))),inference(variable_rename,status(thm),[c363])).
% 68.51/68.75 cnf(c365,axiom,~cyclic(X645,X643,X642,X644)|cyclic(X645,X642,X643,X644),inference(split_conjunct,status(thm),[c364])).
% 68.51/68.75 fof(ruleD1,axiom,(![A]:(![B]:(![C]:(coll(A,B,C)=>coll(A,C,B))))),input).
% 68.51/68.75 fof(c407,axiom,(![A]:(![B]:(![C]:(~coll(A,B,C)|coll(A,C,B))))),inference(fof_nnf,status(thm),[ruleD1])).
% 68.51/68.75 fof(c408,axiom,(![X532]:(![X533]:(![X534]:(~coll(X532,X533,X534)|coll(X532,X534,X533))))),inference(variable_rename,status(thm),[c407])).
% 68.51/68.75 cnf(c409,axiom,~coll(X576,X575,X577)|coll(X576,X577,X575),inference(split_conjunct,status(thm),[c408])).
% 68.51/68.75 fof(ruleD2,axiom,(![A]:(![B]:(![C]:(coll(A,B,C)=>coll(B,A,C))))),input).
% 68.51/68.75 fof(c404,axiom,(![A]:(![B]:(![C]:(~coll(A,B,C)|coll(B,A,C))))),inference(fof_nnf,status(thm),[ruleD2])).
% 68.51/68.75 fof(c405,axiom,(![X529]:(![X530]:(![X531]:(~coll(X529,X530,X531)|coll(X530,X529,X531))))),inference(variable_rename,status(thm),[c404])).
% 68.51/68.75 cnf(c406,axiom,~coll(X565,X566,X564)|coll(X566,X565,X564),inference(split_conjunct,status(thm),[c405])).
% 68.51/68.75 fof(ruleD66,axiom,(![A]:(![B]:(![C]:(para(A,B,A,C)=>coll(A,B,C))))),input).
% 68.51/68.75 fof(c190,axiom,(![A]:(![B]:(![C]:(~para(A,B,A,C)|coll(A,B,C))))),inference(fof_nnf,status(thm),[ruleD66])).
% 68.51/68.75 fof(c191,axiom,(![X168]:(![X169]:(![X170]:(~para(X168,X169,X168,X170)|coll(X168,X169,X170))))),inference(variable_rename,status(thm),[c190])).
% 68.51/68.75 cnf(c192,axiom,~para(X611,X612,X611,X613)|coll(X611,X612,X613),inference(split_conjunct,status(thm),[c191])).
% 68.51/68.75 cnf(c9545,plain,coll(X4342,X4341,X4341),inference(resolution,status(thm),[c9532, c192])).
% 68.51/68.75 cnf(c9755,plain,coll(X4345,X4346,X4345),inference(resolution,status(thm),[c9545, c406])).
% 68.51/68.75 cnf(c10012,plain,coll(X4350,X4350,X4349),inference(resolution,status(thm),[c9755, c409])).
% 68.51/68.75 fof(ruleD3,axiom,(![A]:(![B]:(![C]:(![D]:((coll(A,B,C)&coll(A,B,D))=>coll(C,D,A)))))),input).
% 68.51/68.75 fof(c401,axiom,(![A]:(![B]:(![C]:(![D]:((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A)))))),inference(fof_nnf,status(thm),[ruleD3])).
% 68.51/68.75 fof(c402,axiom,(![X525]:(![X526]:(![X527]:(![X528]:((~coll(X525,X526,X527)|~coll(X525,X526,X528))|coll(X527,X528,X525)))))),inference(variable_rename,status(thm),[c401])).
% 68.51/68.75 cnf(c403,axiom,~coll(X688,X690,X691)|~coll(X688,X690,X689)|coll(X691,X689,X688),inference(split_conjunct,status(thm),[c402])).
% 68.51/68.75 cnf(c10494,plain,~coll(X5854,X5854,X5853)|coll(X5853,X5852,X5854),inference(resolution,status(thm),[c10012, c403])).
% 68.51/68.75 cnf(c16117,plain,coll(X5864,X5865,X5863),inference(resolution,status(thm),[c10494, c10012])).
% 68.51/68.75 fof(ruleD42b,axiom,(![A]:(![B]:(![P]:(![Q]:((eqangle(P,A,P,B,Q,A,Q,B)&coll(P,Q,B))=>cyclic(A,B,P,Q)))))),input).
% 68.51/68.75 fof(c272,axiom,(![A]:(![B]:(![P]:(![Q]:((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q)))))),inference(fof_nnf,status(thm),[ruleD42b])).
% 68.51/68.75 fof(c273,axiom,(![X282]:(![X283]:(![X284]:(![X285]:((~eqangle(X284,X282,X284,X283,X285,X282,X285,X283)|~coll(X284,X285,X283))|cyclic(X282,X283,X284,X285)))))),inference(variable_rename,status(thm),[c272])).
% 68.51/68.75 cnf(c274,axiom,~eqangle(X1069,X1068,X1069,X1070,X1067,X1068,X1067,X1070)|~coll(X1069,X1067,X1070)|cyclic(X1068,X1070,X1069,X1067),inference(split_conjunct,status(thm),[c273])).
% 68.51/68.75 cnf(c9544,plain,eqangle(X5611,X5613,X5612,X5610,X5611,X5613,X5612,X5610),inference(resolution,status(thm),[c9532, c286])).
% 68.51/68.75 cnf(c15777,plain,~coll(X6210,X6210,X6212)|cyclic(X6211,X6212,X6210,X6210),inference(resolution,status(thm),[c9544, c274])).
% 68.51/68.75 cnf(c16645,plain,cyclic(X6214,X6215,X6213,X6213),inference(resolution,status(thm),[c15777, c16117])).
% 68.51/68.75 cnf(c16649,plain,cyclic(X6216,X6218,X6217,X6218),inference(resolution,status(thm),[c16645, c365])).
% 68.51/68.75 cnf(c16659,plain,cyclic(X6232,X6231,X6233,X6232),inference(resolution,status(thm),[c16649, c362])).
% 68.51/68.75 cnf(c16666,plain,eqangle(X6295,X6296,X6295,X6294,X6296,X6296,X6296,X6294),inference(resolution,status(thm),[c16659, c281])).
% 68.51/68.75 cnf(c16723,plain,~perp(X10825,X10825,X10825,X10823)|perp(X10824,X10825,X10824,X10823),inference(resolution,status(thm),[c16666, c164])).
% 68.51/68.75 fof(ruleD10,axiom,(![A]:(![B]:(![C]:(![D]:(![E]:(![F]:((para(A,B,C,D)&perp(C,D,E,F))=>perp(A,B,E,F)))))))),input).
% 68.51/68.75 fof(c380,axiom,(![A]:(![B]:(![C]:(![D]:(![E]:(![F]:((~para(A,B,C,D)|~perp(C,D,E,F))|perp(A,B,E,F)))))))),inference(fof_nnf,status(thm),[ruleD10])).
% 68.51/68.75 fof(c381,axiom,(![X491]:(![X492]:(![X493]:(![X494]:(![X495]:(![X496]:((~para(X491,X492,X493,X494)|~perp(X493,X494,X495,X496))|perp(X491,X492,X495,X496)))))))),inference(variable_rename,status(thm),[c380])).
% 68.51/68.75 cnf(c382,axiom,~para(X1275,X1272,X1273,X1277)|~perp(X1273,X1277,X1274,X1276)|perp(X1275,X1272,X1274,X1276),inference(split_conjunct,status(thm),[c381])).
% 68.51/68.75 fof(ruleD7,axiom,(![A]:(![B]:(![C]:(![D]:(perp(A,B,C,D)=>perp(A,B,D,C)))))),input).
% 68.51/68.75 fof(c389,axiom,(![A]:(![B]:(![C]:(![D]:(~perp(A,B,C,D)|perp(A,B,D,C)))))),inference(fof_nnf,status(thm),[ruleD7])).
% 68.51/68.75 fof(c390,axiom,(![X507]:(![X508]:(![X509]:(![X510]:(~perp(X507,X508,X509,X510)|perp(X507,X508,X510,X509)))))),inference(variable_rename,status(thm),[c389])).
% 68.51/68.75 cnf(c391,axiom,~perp(X655,X654,X657,X656)|perp(X655,X654,X656,X657),inference(split_conjunct,status(thm),[c390])).
% 68.51/68.75 cnf(c17,negated_conjecture,circle(skolem0004,skolem0001,skolem0005,skolem0010),inference(split_conjunct,status(thm),[c15])).
% 68.51/68.75 cnf(c594,plain,perp(skolem0021(skolem0001,skolem0005,skolem0010,skolem0004),skolem0001,skolem0001,skolem0004),inference(resolution,status(thm),[c77, c17])).
% 68.51/68.75 cnf(c1633,plain,perp(skolem0001,skolem0004,skolem0021(skolem0001,skolem0005,skolem0010,skolem0004),skolem0001),inference(resolution,status(thm),[c594, c388])).
% 68.51/68.75 cnf(c2424,plain,perp(skolem0001,skolem0004,skolem0001,skolem0021(skolem0001,skolem0005,skolem0010,skolem0004)),inference(resolution,status(thm),[c1633, c391])).
% 68.51/68.75 cnf(c2582,plain,perp(skolem0001,skolem0021(skolem0001,skolem0005,skolem0010,skolem0004),skolem0001,skolem0004),inference(resolution,status(thm),[c2424, c388])).
% 68.51/68.75 cnf(c2790,plain,~para(X4872,X4873,skolem0001,skolem0021(skolem0001,skolem0005,skolem0010,skolem0004))|perp(X4872,X4873,skolem0001,skolem0004),inference(resolution,status(thm),[c2582, c382])).
% 68.51/68.75 fof(ruleD11,axiom,(![A]:(![B]:(![M]:(midp(M,B,A)=>midp(M,A,B))))),input).
% 68.51/68.75 fof(c377,axiom,(![A]:(![B]:(![M]:(~midp(M,B,A)|midp(M,A,B))))),inference(fof_nnf,status(thm),[ruleD11])).
% 68.51/68.75 fof(c378,axiom,(![X488]:(![X489]:(![X490]:(~midp(X490,X489,X488)|midp(X490,X488,X489))))),inference(variable_rename,status(thm),[c377])).
% 68.51/68.75 cnf(c379,axiom,~midp(X554,X553,X555)|midp(X554,X555,X553),inference(split_conjunct,status(thm),[c378])).
% 68.51/68.75 fof(ruleD67,axiom,(![A]:(![B]:(![C]:((cong(A,B,A,C)&coll(A,B,C))=>midp(A,B,C))))),input).
% 68.51/68.75 fof(c187,axiom,(![A]:(![B]:(![C]:((~cong(A,B,A,C)|~coll(A,B,C))|midp(A,B,C))))),inference(fof_nnf,status(thm),[ruleD67])).
% 68.51/68.75 fof(c188,axiom,(![X165]:(![X166]:(![X167]:((~cong(X165,X166,X165,X167)|~coll(X165,X166,X167))|midp(X165,X166,X167))))),inference(variable_rename,status(thm),[c187])).
% 68.51/68.75 cnf(c189,axiom,~cong(X961,X960,X961,X959)|~coll(X961,X960,X959)|midp(X961,X960,X959),inference(split_conjunct,status(thm),[c188])).
% 68.51/68.75 fof(ruleD23,axiom,(![A]:(![B]:(![C]:(![D]:(cong(A,B,C,D)=>cong(A,B,D,C)))))),input).
% 68.51/68.75 fof(c339,axiom,(![A]:(![B]:(![C]:(![D]:(~cong(A,B,C,D)|cong(A,B,D,C)))))),inference(fof_nnf,status(thm),[ruleD23])).
% 68.51/68.75 fof(c340,axiom,(![X414]:(![X415]:(![X416]:(![X417]:(~cong(X414,X415,X416,X417)|cong(X414,X415,X417,X416)))))),inference(variable_rename,status(thm),[c339])).
% 68.51/68.75 cnf(c341,axiom,~cong(X619,X620,X621,X618)|cong(X619,X620,X618,X621),inference(split_conjunct,status(thm),[c340])).
% 68.51/68.75 fof(ruleD43,axiom,(![A]:(![B]:(![C]:(![P]:(![Q]:(![R]:((((cyclic(A,B,C,P)&cyclic(A,B,C,Q))&cyclic(A,B,C,R))&eqangle(C,A,C,B,R,P,R,Q))=>cong(A,B,P,Q)))))))),input).
% 68.51/68.75 fof(c267,axiom,(![A]:(![B]:(![C]:(![P]:(![Q]:(![R]:((((~cyclic(A,B,C,P)|~cyclic(A,B,C,Q))|~cyclic(A,B,C,R))|~eqangle(C,A,C,B,R,P,R,Q))|cong(A,B,P,Q)))))))),inference(fof_nnf,status(thm),[ruleD43])).
% 68.51/68.75 fof(c268,axiom,(![A]:(![B]:(![C]:(![P]:(![Q]:((![R]:(((~cyclic(A,B,C,P)|~cyclic(A,B,C,Q))|~cyclic(A,B,C,R))|~eqangle(C,A,C,B,R,P,R,Q)))|cong(A,B,P,Q))))))),inference(shift_quantors,status(thm),[c267])).
% 68.51/68.75 fof(c270,axiom,(![X276]:(![X277]:(![X278]:(![X279]:(![X280]:(![X281]:((((~cyclic(X276,X277,X278,X279)|~cyclic(X276,X277,X278,X280))|~cyclic(X276,X277,X278,X281))|~eqangle(X278,X276,X278,X277,X281,X279,X281,X280))|cong(X276,X277,X279,X280)))))))),inference(shift_quantors,status(thm),[fof(c269,axiom,(![X276]:(![X277]:(![X278]:(![X279]:(![X280]:((![X281]:(((~cyclic(X276,X277,X278,X279)|~cyclic(X276,X277,X278,X280))|~cyclic(X276,X277,X278,X281))|~eqangle(X278,X276,X278,X277,X281,X279,X281,X280)))|cong(X276,X277,X279,X280))))))),inference(variable_rename,status(thm),[c268])).])).
% 68.51/68.75 cnf(c271,axiom,~cyclic(X1061,X1066,X1062,X1064)|~cyclic(X1061,X1066,X1062,X1065)|~cyclic(X1061,X1066,X1062,X1063)|~eqangle(X1062,X1061,X1062,X1066,X1063,X1064,X1063,X1065)|cong(X1061,X1066,X1064,X1065),inference(split_conjunct,status(thm),[c270])).
% 68.51/68.75 fof(ruleD20,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(eqangle(A,B,C,D,P,Q,U,V)=>eqangle(P,Q,U,V,A,B,C,D)))))))))),input).
% 68.51/68.75 fof(c348,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(~eqangle(A,B,C,D,P,Q,U,V)|eqangle(P,Q,U,V,A,B,C,D)))))))))),inference(fof_nnf,status(thm),[ruleD20])).
% 68.51/68.75 fof(c349,axiom,(![X438]:(![X439]:(![X440]:(![X441]:(![X442]:(![X443]:(![X444]:(![X445]:(~eqangle(X438,X439,X440,X441,X442,X443,X444,X445)|eqangle(X442,X443,X444,X445,X438,X439,X440,X441)))))))))),inference(variable_rename,status(thm),[c348])).
% 68.51/68.75 cnf(c350,axiom,~eqangle(X1232,X1233,X1235,X1229,X1234,X1236,X1230,X1231)|eqangle(X1234,X1236,X1230,X1231,X1232,X1233,X1235,X1229),inference(split_conjunct,status(thm),[c349])).
% 68.51/68.75 fof(ruleD21,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(eqangle(A,B,C,D,P,Q,U,V)=>eqangle(A,B,P,Q,C,D,U,V)))))))))),input).
% 68.51/68.75 fof(c345,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(~eqangle(A,B,C,D,P,Q,U,V)|eqangle(A,B,P,Q,C,D,U,V)))))))))),inference(fof_nnf,status(thm),[ruleD21])).
% 68.51/68.75 fof(c346,axiom,(![X430]:(![X431]:(![X432]:(![X433]:(![X434]:(![X435]:(![X436]:(![X437]:(~eqangle(X430,X431,X432,X433,X434,X435,X436,X437)|eqangle(X430,X431,X434,X435,X432,X433,X436,X437)))))))))),inference(variable_rename,status(thm),[c345])).
% 68.51/68.75 cnf(c347,axiom,~eqangle(X1223,X1227,X1222,X1228,X1226,X1224,X1221,X1225)|eqangle(X1223,X1227,X1226,X1224,X1222,X1228,X1221,X1225),inference(split_conjunct,status(thm),[c346])).
% 68.51/68.75 cnf(c16305,plain,eqangle(X6043,X6042,X6042,X6043,X6041,X6044,X6041,X6044),inference(resolution,status(thm),[c10593, c347])).
% 68.51/68.75 cnf(c16390,plain,eqangle(X6100,X6099,X6100,X6099,X6098,X6101,X6101,X6098),inference(resolution,status(thm),[c16305, c350])).
% 68.51/68.75 cnf(c16457,plain,~cyclic(X7188,X7188,X7187,X7189)|cong(X7188,X7188,X7189,X7189),inference(resolution,status(thm),[c16390, c271])).
% 68.51/68.75 cnf(c17263,plain,cong(X7190,X7190,X7190,X7190),inference(resolution,status(thm),[c16457, c16649])).
% 68.51/68.75 cnf(c17283,plain,~coll(X7212,X7212,X7212)|midp(X7212,X7212,X7212),inference(resolution,status(thm),[c17263, c189])).
% 68.51/68.75 cnf(c17363,plain,midp(X7213,X7213,X7213),inference(resolution,status(thm),[c17283, c16117])).
% 68.51/68.75 fof(ruleD52,axiom,(![A]:(![B]:(![C]:(![M]:((perp(A,B,B,C)&midp(M,A,C))=>cong(A,M,B,M)))))),input).
% 68.51/68.75 fof(c239,axiom,(![A]:(![B]:(![C]:(![M]:((~perp(A,B,B,C)|~midp(M,A,C))|cong(A,M,B,M)))))),inference(fof_nnf,status(thm),[ruleD52])).
% 68.51/68.75 fof(c240,axiom,(![X236]:(![X237]:(![X238]:(![X239]:((~perp(X236,X237,X237,X238)|~midp(X239,X236,X238))|cong(X236,X239,X237,X239)))))),inference(variable_rename,status(thm),[c239])).
% 68.51/68.75 cnf(c241,axiom,~perp(X1021,X1024,X1024,X1023)|~midp(X1022,X1021,X1023)|cong(X1021,X1022,X1024,X1022),inference(split_conjunct,status(thm),[c240])).
% 68.51/68.75 fof(ruleD18,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(eqangle(A,B,C,D,P,Q,U,V)=>eqangle(B,A,C,D,P,Q,U,V)))))))))),input).
% 68.51/68.75 fof(c354,axiom,(![A]:(![B]:(![C]:(![D]:(![P]:(![Q]:(![U]:(![V]:(~eqangle(A,B,C,D,P,Q,U,V)|eqangle(B,A,C,D,P,Q,U,V)))))))))),inference(fof_nnf,status(thm),[ruleD18])).
% 68.51/68.75 fof(c355,axiom,(![X454]:(![X455]:(![X456]:(![X457]:(![X458]:(![X459]:(![X460]:(![X461]:(~eqangle(X454,X455,X456,X457,X458,X459,X460,X461)|eqangle(X455,X454,X456,X457,X458,X459,X460,X461)))))))))),inference(variable_rename,status(thm),[c354])).
% 68.51/68.75 cnf(c356,axiom,~eqangle(X1250,X1249,X1252,X1251,X1248,X1254,X1253,X1247)|eqangle(X1249,X1250,X1252,X1251,X1248,X1254,X1253,X1247),inference(split_conjunct,status(thm),[c355])).
% 68.51/68.75 cnf(c16454,plain,eqangle(X6131,X6133,X6133,X6131,X6132,X6134,X6134,X6132),inference(resolution,status(thm),[c16390, c356])).
% 68.51/68.75 cnf(c16535,plain,~perp(X7298,X7296,X7296,X7298)|perp(X7295,X7297,X7297,X7295),inference(resolution,status(thm),[c16454, c164])).
% 68.51/68.75 fof(ruleD14,axiom,(![A]:(![B]:(![C]:(![D]:(cyclic(A,B,C,D)=>cyclic(A,B,D,C)))))),input).
% 68.51/68.75 fof(c366,axiom,(![A]:(![B]:(![C]:(![D]:(~cyclic(A,B,C,D)|cyclic(A,B,D,C)))))),inference(fof_nnf,status(thm),[ruleD14])).
% 68.51/68.75 fof(c367,axiom,(![X475]:(![X476]:(![X477]:(![X478]:(~cyclic(X475,X476,X477,X478)|cyclic(X475,X476,X478,X477)))))),inference(variable_rename,status(thm),[c366])).
% 68.51/68.75 cnf(c368,axiom,~cyclic(X646,X648,X647,X649)|cyclic(X646,X648,X649,X647),inference(split_conjunct,status(thm),[c367])).
% 68.51/68.75 cnf(c16673,plain,cyclic(X6246,X6247,X6246,X6248),inference(resolution,status(thm),[c16659, c368])).
% 68.51/68.75 cnf(c17264,plain,cong(X7191,X7191,X7192,X7192),inference(resolution,status(thm),[c16457, c16673])).
% 68.51/68.75 fof(ruleD57,axiom,(![A]:(![B]:(![P]:(![Q]:(((cong(A,P,B,P)&cong(A,Q,B,Q))&cyclic(A,B,P,Q))=>perp(P,A,A,Q)))))),input).
% 68.51/68.75 fof(c222,axiom,(![A]:(![B]:(![P]:(![Q]:(((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q))|perp(P,A,A,Q)))))),inference(fof_nnf,status(thm),[ruleD57])).
% 68.51/68.75 fof(c223,axiom,(![X216]:(![X217]:(![X218]:(![X219]:(((~cong(X216,X218,X217,X218)|~cong(X216,X219,X217,X219))|~cyclic(X216,X217,X218,X219))|perp(X218,X216,X216,X219)))))),inference(variable_rename,status(thm),[c222])).
% 68.51/68.75 cnf(c224,axiom,~cong(X1004,X1001,X1003,X1001)|~cong(X1004,X1002,X1003,X1002)|~cyclic(X1004,X1003,X1001,X1002)|perp(X1001,X1004,X1004,X1002),inference(split_conjunct,status(thm),[c223])).
% 68.51/68.75 cnf(c16647,plain,~cong(X7318,X7316,X7317,X7316)|perp(X7316,X7318,X7318,X7316),inference(resolution,status(thm),[c16645, c224])).
% 68.51/68.75 cnf(c17592,plain,perp(X7319,X7319,X7319,X7319),inference(resolution,status(thm),[c16647, c17264])).
% 68.51/68.75 cnf(c17597,plain,perp(X7327,X7326,X7326,X7327),inference(resolution,status(thm),[c17592, c16535])).
% 68.51/68.75 cnf(c17753,plain,~midp(X7384,X7385,X7385)|cong(X7385,X7384,X7386,X7384),inference(resolution,status(thm),[c17597, c241])).
% 68.51/68.75 cnf(c17760,plain,cong(X7387,X7387,X7388,X7387),inference(resolution,status(thm),[c17753, c17363])).
% 68.51/68.75 cnf(c17793,plain,cong(X7389,X7389,X7389,X7390),inference(resolution,status(thm),[c17760, c341])).
% 68.51/68.75 cnf(c17822,plain,~coll(X7415,X7415,X7414)|midp(X7415,X7415,X7414),inference(resolution,status(thm),[c17793, c189])).
% 68.51/68.75 cnf(c17950,plain,midp(X7417,X7417,X7416),inference(resolution,status(thm),[c17822, c16117])).
% 68.51/68.75 cnf(c18253,plain,midp(X7419,X7418,X7419),inference(resolution,status(thm),[c17950, c379])).
% 68.51/68.75 fof(ruleD44,axiom,(![A]:(![B]:(![C]:(![E]:(![F]:((midp(E,A,B)&midp(F,A,C))=>para(E,F,B,C))))))),input).
% 68.51/68.75 fof(c264,axiom,(![A]:(![B]:(![C]:(![E]:(![F]:((~midp(E,A,B)|~midp(F,A,C))|para(E,F,B,C))))))),inference(fof_nnf,status(thm),[ruleD44])).
% 68.51/68.75 fof(c265,axiom,(![X271]:(![X272]:(![X273]:(![X274]:(![X275]:((~midp(X274,X271,X272)|~midp(X275,X271,X273))|para(X274,X275,X272,X273))))))),inference(variable_rename,status(thm),[c264])).
% 68.51/68.75 cnf(c266,axiom,~midp(X1059,X1056,X1058)|~midp(X1060,X1056,X1057)|para(X1059,X1060,X1058,X1057),inference(split_conjunct,status(thm),[c265])).
% 68.51/68.75 cnf(c17999,plain,~midp(X8343,X8344,X8346)|para(X8343,X8344,X8346,X8345),inference(resolution,status(thm),[c17950, c266])).
% 68.51/68.75 cnf(c20255,plain,para(X8351,X8350,X8351,X8352),inference(resolution,status(thm),[c17999, c18253])).
% 68.51/68.75 cnf(c20338,plain,perp(skolem0001,X8564,skolem0001,skolem0004),inference(resolution,status(thm),[c20255, c2790])).
% 68.51/68.75 cnf(c20889,plain,perp(skolem0001,skolem0004,skolem0001,X8651),inference(resolution,status(thm),[c20338, c388])).
% 68.51/68.75 cnf(c16662,plain,cyclic(X6235,X6234,X6234,X6236),inference(resolution,status(thm),[c16649, c368])).
% 68.51/68.75 cnf(c16678,plain,eqangle(X6299,X6298,X6299,X6299,X6300,X6298,X6300,X6299),inference(resolution,status(thm),[c16662, c281])).
% 68.51/68.75 cnf(c16737,plain,~perp(X10884,X10883,X10884,X10882)|perp(X10882,X10883,X10882,X10882),inference(resolution,status(thm),[c16678, c164])).
% 68.51/68.75 cnf(c23464,plain,perp(X10892,skolem0004,X10892,X10892),inference(resolution,status(thm),[c16737, c20889])).
% 68.51/68.75 cnf(c23530,plain,perp(X10914,X10914,X10914,skolem0004),inference(resolution,status(thm),[c23464, c388])).
% 68.51/68.75 cnf(c23803,plain,perp(X10998,X10997,X10998,skolem0004),inference(resolution,status(thm),[c23530, c16723])).
% 68.51/68.75 cnf(c24472,plain,perp(X11141,X11140,X11140,skolem0004),inference(resolution,status(thm),[c23803, c16303])).
% 68.51/68.75 cnf(c24921,plain,$false,inference(resolution,status(thm),[c24472, c24])).
% 68.51/68.75 # SZS output end CNFRefutation
% 68.51/68.75
% 68.51/68.75 # Initial clauses : 136
% 68.51/68.75 # Processed clauses : 3449
% 68.51/68.75 # Factors computed : 0
% 68.51/68.75 # Resolvents computed: 24535
% 68.51/68.75 # Tautologies deleted: 8
% 68.51/68.75 # Forward subsumed : 7617
% 68.51/68.75 # Backward subsumed : 1841
% 68.51/68.75 # -------- CPU Time ---------
% 68.51/68.75 # User time : 68.328 s
% 68.51/68.75 # System time : 0.050 s
% 68.51/68.75 # Total time : 68.378 s
%------------------------------------------------------------------------------