TSTP Solution File: GEO011-4 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GEO011-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %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 : 300s
% DateTime : Wed Aug 30 22:42:24 EDT 2023
% Result : Unsatisfiable 0.21s 0.63s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO011-4 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %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 : 300
% 0.14/0.34 % DateTime : Tue Aug 29 18:47:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % File :CSE---1.6
% 0.21/0.62 % Problem :theBenchmark
% 0.21/0.62 % Transform :cnf
% 0.21/0.62 % Format :tptp:raw
% 0.21/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.62
% 0.21/0.62 % Result :Theorem 0.000000s
% 0.21/0.62 % Output :CNFRefutation 0.000000s
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 % File : GEO011-4 : TPTP v8.1.2. Released v1.0.0.
% 0.21/0.62 % Domain : Geometry
% 0.21/0.62 % Problem : The axiom set points are not collinear
% 0.21/0.62 % Version : [Qua89] axioms : Reduced & Augmented > Complete.
% 0.21/0.62 % English :
% 0.21/0.62
% 0.21/0.62 % Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 0.21/0.62 % : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% 0.21/0.62 % : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% 0.21/0.62 % Source : [TPTP]
% 0.21/0.62 % Names :
% 0.21/0.62
% 0.21/0.62 % Status : Unsatisfiable
% 0.21/0.62 % Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.12 v5.1.0, 0.06 v5.0.0, 0.00 v3.3.0, 0.07 v3.2.0, 0.00 v2.7.0, 0.08 v2.6.0, 0.00 v2.0.0
% 0.21/0.62 % Syntax : Number of clauses : 23 ( 7 unt; 6 nHn; 20 RR)
% 0.21/0.62 % Number of literals : 67 ( 7 equ; 38 neg)
% 0.21/0.62 % Maximal clause size : 8 ( 2 avg)
% 0.21/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.62 % Number of predicates : 4 ( 3 usr; 0 prp; 2-3 aty)
% 0.21/0.62 % Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% 0.21/0.62 % Number of variables : 83 ( 3 sgn)
% 0.21/0.62 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.21/0.62
% 0.21/0.62 % Comments : Equidistant reformulated to same_distance
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 %----Include Tarski geometry axioms for colinearity
% 0.21/0.62 include('Axioms/GEO002-1.ax').
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 %----A1 - Reflexivity axiom for equidistance
% 0.21/0.62 cnf(reflexivity_for_equidistance,axiom,
% 0.21/0.62 equal_distance(distance(X,Y),distance(Y,X)) ).
% 0.21/0.62
% 0.21/0.62 %----A2 - Transitivity axiom for equidistance
% 0.21/0.62 cnf(transitivity_for_equidistance,axiom,
% 0.21/0.62 ( ~ equal_distance(distance(X,Y),distance(Z,V))
% 0.21/0.62 | ~ equal_distance(distance(X,Y),distance(V2,W))
% 0.21/0.62 | equal_distance(distance(Z,V),distance(V2,W)) ) ).
% 0.21/0.62
% 0.21/0.62 %----A3 Indentity axiom for equidistance
% 0.21/0.62 cnf(identity_for_equidistance,axiom,
% 0.21/0.62 ( ~ equal_distance(distance(X,Y),distance(Z,Z))
% 0.21/0.62 | X = Y ) ).
% 0.21/0.62
% 0.21/0.62 %----A4 - Segment construction axiom, two clauses.
% 0.21/0.62 %----A4.1
% 0.21/0.62 cnf(segment_construction1,axiom,
% 0.21/0.62 between(X,Y,extension(X,Y,W,V)) ).
% 0.21/0.62
% 0.21/0.62 %----A4.2
% 0.21/0.62 cnf(segment_construction2,axiom,
% 0.21/0.62 equal_distance(distance(Y,extension(X,Y,W,V)),distance(W,V)) ).
% 0.21/0.62
% 0.21/0.62 %----A5 - Outer five-segment axiom
% 0.21/0.62 cnf(outer_five_segment,axiom,
% 0.21/0.62 ( ~ equal_distance(distance(X,Y),distance(X1,Y1))
% 0.21/0.62 | ~ equal_distance(distance(Y,Z),distance(Y1,Z1))
% 0.21/0.62 | ~ equal_distance(distance(X,V),distance(X1,V1))
% 0.21/0.62 | ~ equal_distance(distance(Y,V),distance(Y1,V1))
% 0.21/0.62 | ~ between(X,Y,Z)
% 0.21/0.62 | ~ between(X1,Y1,Z1)
% 0.21/0.62 | X = Y
% 0.21/0.62 | equal_distance(distance(Z,V),distance(Z1,V1)) ) ).
% 0.21/0.62
% 0.21/0.62 %----A6 - Identity axiom for betweenness
% 0.21/0.62 cnf(identity_for_betweeness,axiom,
% 0.21/0.62 ( ~ between(X,Y,X)
% 0.21/0.62 | X = Y ) ).
% 0.21/0.62
% 0.21/0.62 %----A7 - Inner Pasch axiom, two clauses.
% 0.21/0.62 %----A7.1
% 0.21/0.63 cnf(inner_pasch1,axiom,
% 0.21/0.63 ( ~ between(U,V,W)
% 0.21/0.63 | ~ between(Y,X,W)
% 0.21/0.63 | between(V,inner_pasch(U,V,W,X,Y),Y) ) ).
% 0.21/0.63
% 0.21/0.63 %----A7.2
% 0.21/0.63 cnf(inner_pasch2,axiom,
% 0.21/0.63 ( ~ between(U,V,W)
% 0.21/0.63 | ~ between(Y,X,W)
% 0.21/0.63 | between(X,inner_pasch(U,V,W,X,Y),U) ) ).
% 0.21/0.63
% 0.21/0.63 %----A8 - Lower dimension axiom, three clauses. A8.1
% 0.21/0.63 cnf(lower_dimension1,axiom,
% 0.21/0.63 ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ).
% 0.21/0.63
% 0.21/0.63 %----A8.2
% 0.21/0.63 cnf(lower_dimension2,axiom,
% 0.21/0.63 ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ).
% 0.21/0.63
% 0.21/0.63 %----A8.3
% 0.21/0.63 cnf(lower_dimension3,axiom,
% 0.21/0.63 ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ).
% 0.21/0.63
% 0.21/0.63 %----A9 - Upper dimension axiom
% 0.21/0.63 cnf(upper_dimension,axiom,
% 0.21/0.63 ( ~ equal_distance(distance(X,W),distance(X,V))
% 0.21/0.63 | ~ equal_distance(distance(Y,W),distance(Y,V))
% 0.21/0.63 | ~ equal_distance(distance(Z,W),distance(Z,V))
% 0.21/0.63 | between(X,Y,Z)
% 0.21/0.63 | between(Y,Z,X)
% 0.21/0.63 | between(Z,X,Y)
% 0.21/0.63 | W = V ) ).
% 0.21/0.63
% 0.21/0.63 %----A10 - Euclid's axiom, three clauses.
% 0.21/0.63 %----A10.1
% 0.21/0.63 cnf(euclid1,axiom,
% 0.21/0.63 ( ~ between(U,W,Y)
% 0.21/0.63 | ~ between(V,W,X)
% 0.21/0.63 | U = W
% 0.21/0.63 | between(U,V,euclid1(U,V,W,X,Y)) ) ).
% 0.21/0.63
% 0.21/0.63 %----A10.2
% 0.21/0.63 cnf(euclid2,axiom,
% 0.21/0.63 ( ~ between(U,W,Y)
% 0.21/0.63 | ~ between(V,W,X)
% 0.21/0.63 | U = W
% 0.21/0.63 | between(U,X,euclid2(U,V,W,X,Y)) ) ).
% 0.21/0.63
% 0.21/0.63 %----A10.3
% 0.21/0.63 cnf(euclid3,axiom,
% 0.21/0.63 ( ~ between(U,W,Y)
% 0.21/0.63 | ~ between(V,W,X)
% 0.21/0.63 | U = W
% 0.21/0.63 | between(euclid1(U,V,W,X,Y),Y,euclid2(U,V,W,X,Y)) ) ).
% 0.21/0.63
% 0.21/0.63 %----A11 - Weakened continuity axiom, two clauses.
% 0.21/0.63 %----A11.1
% 0.21/0.63 cnf(continuity1,axiom,
% 0.21/0.63 ( ~ equal_distance(distance(U,V),distance(U,V1))
% 0.21/0.63 | ~ equal_distance(distance(U,X),distance(U,X1))
% 0.21/0.63 | ~ between(U,V,X)
% 0.21/0.63 | ~ between(V,W,X)
% 0.21/0.63 | between(V1,continuous(U,V,V1,W,X,X1),X1) ) ).
% 0.21/0.63
% 0.21/0.63 %----A11.2
% 0.21/0.63 cnf(continuity2,axiom,
% 0.21/0.63 ( ~ equal_distance(distance(U,V),distance(U,V1))
% 0.21/0.63 | ~ equal_distance(distance(U,X),distance(U,X1))
% 0.21/0.63 | ~ between(U,V,X)
% 0.21/0.63 | ~ between(V,W,X)
% 0.21/0.63 | equal_distance(distance(U,W),distance(U,continuous(U,V,V1,W,X,X1))) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(prove_lower_dimension_points_not_colinear,negated_conjecture,
% 0.21/0.63 colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ).
% 0.21/0.63
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 % Proof found
% 0.21/0.63 % SZS status Theorem for theBenchmark
% 0.21/0.63 % SZS output start Proof
% 0.21/0.63 %ClaNum:61(EqnAxiom:38)
% 0.21/0.63 %VarNum:241(SingletonVarNum:83)
% 0.21/0.63 %MaxLitNum:8
% 0.21/0.63 %MaxfuncDepth:2
% 0.21/0.63 %SharedTerms:7
% 0.21/0.63 %goalClause: 39
% 0.21/0.63 %singleGoalClaCount:1
% 0.21/0.63 [39]P1(a1,a8,a9)
% 0.21/0.63 [43]~P2(a1,a8,a9)
% 0.21/0.63 [44]~P2(a8,a9,a1)
% 0.21/0.63 [45]~P2(a9,a1,a8)
% 0.21/0.63 [40]P3(f2(x401,x402),f2(x402,x401))
% 0.21/0.63 [41]P2(x411,x412,f4(x411,x412,x413,x414))
% 0.21/0.63 [42]P3(f2(x421,f4(x422,x421,x423,x424)),f2(x423,x424))
% 0.21/0.63 [46]~P2(x461,x462,x461)+E(x461,x462)
% 0.21/0.63 [48]~P2(x482,x483,x481)+P1(x481,x482,x483)
% 0.21/0.63 [49]~P2(x493,x491,x492)+P1(x491,x492,x493)
% 0.21/0.63 [50]~P2(x501,x502,x503)+P1(x501,x502,x503)
% 0.21/0.63 [47]E(x471,x472)+~P3(f2(x471,x472),f2(x473,x473))
% 0.21/0.63 [55]~P2(x555,x551,x554)+~P2(x552,x553,x554)+P2(x551,f7(x552,x553,x554,x551,x555),x552)
% 0.21/0.63 [56]~P2(x565,x564,x563)+~P2(x562,x561,x563)+P2(x561,f7(x562,x561,x563,x564,x565),x565)
% 0.21/0.63 [52]P3(f2(x521,x522),f2(x523,x524))+~P3(f2(x525,x526),f2(x523,x524))+~P3(f2(x525,x526),f2(x521,x522))
% 0.21/0.63 [51]P2(x513,x511,x512)+P2(x512,x513,x511)+~P1(x512,x513,x511)+P2(x511,x512,x513)
% 0.21/0.63 [57]~P2(x574,x572,x573)+~P2(x571,x572,x575)+E(x571,x572)+P2(x571,x573,f5(x571,x574,x572,x573,x575))
% 0.21/0.63 [58]~P2(x583,x582,x584)+~P2(x581,x582,x585)+E(x581,x582)+P2(x581,x583,f6(x581,x583,x582,x584,x585))
% 0.21/0.63 [59]~P2(x593,x592,x594)+~P2(x591,x592,x595)+E(x591,x592)+P2(f6(x591,x593,x592,x594,x595),x595,f5(x591,x593,x592,x594,x595))
% 0.21/0.63 [60]~P2(x603,x604,x605)+~P2(x602,x603,x605)+P2(x601,f3(x602,x603,x601,x604,x605,x606),x606)+~P3(f2(x602,x605),f2(x602,x606))+~P3(f2(x602,x603),f2(x602,x601))
% 0.21/0.63 [61]~P2(x613,x612,x615)+~P2(x611,x613,x615)+~P3(f2(x611,x615),f2(x611,x616))+~P3(f2(x611,x613),f2(x611,x614))+P3(f2(x611,x612),f2(x611,f3(x611,x613,x614,x612,x615,x616)))
% 0.21/0.63 [53]P2(x535,x533,x534)+P2(x534,x535,x533)+E(x531,x532)+P2(x533,x534,x535)+~P3(f2(x533,x531),f2(x533,x532))+~P3(f2(x535,x531),f2(x535,x532))+~P3(f2(x534,x531),f2(x534,x532))
% 0.21/0.63 [54]~P2(x541,x542,x543)+E(x541,x542)+~P2(x547,x548,x545)+~P3(f2(x542,x544),f2(x548,x546))+~P3(f2(x542,x543),f2(x548,x545))+~P3(f2(x541,x544),f2(x547,x546))+~P3(f2(x541,x542),f2(x547,x548))+P3(f2(x543,x544),f2(x545,x546))
% 0.21/0.63 %EqnAxiom
% 0.21/0.63 [1]E(x11,x11)
% 0.21/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.63 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.21/0.63 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.21/0.63 [6]~E(x61,x62)+E(f3(x61,x63,x64,x65,x66,x67),f3(x62,x63,x64,x65,x66,x67))
% 0.21/0.63 [7]~E(x71,x72)+E(f3(x73,x71,x74,x75,x76,x77),f3(x73,x72,x74,x75,x76,x77))
% 0.21/0.63 [8]~E(x81,x82)+E(f3(x83,x84,x81,x85,x86,x87),f3(x83,x84,x82,x85,x86,x87))
% 0.21/0.63 [9]~E(x91,x92)+E(f3(x93,x94,x95,x91,x96,x97),f3(x93,x94,x95,x92,x96,x97))
% 0.21/0.63 [10]~E(x101,x102)+E(f3(x103,x104,x105,x106,x101,x107),f3(x103,x104,x105,x106,x102,x107))
% 0.21/0.63 [11]~E(x111,x112)+E(f3(x113,x114,x115,x116,x117,x111),f3(x113,x114,x115,x116,x117,x112))
% 0.21/0.63 [12]~E(x121,x122)+E(f4(x121,x123,x124,x125),f4(x122,x123,x124,x125))
% 0.21/0.63 [13]~E(x131,x132)+E(f4(x133,x131,x134,x135),f4(x133,x132,x134,x135))
% 0.21/0.63 [14]~E(x141,x142)+E(f4(x143,x144,x141,x145),f4(x143,x144,x142,x145))
% 0.21/0.63 [15]~E(x151,x152)+E(f4(x153,x154,x155,x151),f4(x153,x154,x155,x152))
% 0.21/0.63 [16]~E(x161,x162)+E(f7(x161,x163,x164,x165,x166),f7(x162,x163,x164,x165,x166))
% 0.21/0.63 [17]~E(x171,x172)+E(f7(x173,x171,x174,x175,x176),f7(x173,x172,x174,x175,x176))
% 0.21/0.63 [18]~E(x181,x182)+E(f7(x183,x184,x181,x185,x186),f7(x183,x184,x182,x185,x186))
% 0.21/0.63 [19]~E(x191,x192)+E(f7(x193,x194,x195,x191,x196),f7(x193,x194,x195,x192,x196))
% 0.21/0.63 [20]~E(x201,x202)+E(f7(x203,x204,x205,x206,x201),f7(x203,x204,x205,x206,x202))
% 0.21/0.63 [21]~E(x211,x212)+E(f5(x211,x213,x214,x215,x216),f5(x212,x213,x214,x215,x216))
% 0.21/0.63 [22]~E(x221,x222)+E(f5(x223,x221,x224,x225,x226),f5(x223,x222,x224,x225,x226))
% 0.21/0.63 [23]~E(x231,x232)+E(f5(x233,x234,x231,x235,x236),f5(x233,x234,x232,x235,x236))
% 0.21/0.63 [24]~E(x241,x242)+E(f5(x243,x244,x245,x241,x246),f5(x243,x244,x245,x242,x246))
% 0.21/0.63 [25]~E(x251,x252)+E(f5(x253,x254,x255,x256,x251),f5(x253,x254,x255,x256,x252))
% 0.21/0.63 [26]~E(x261,x262)+E(f6(x261,x263,x264,x265,x266),f6(x262,x263,x264,x265,x266))
% 0.21/0.63 [27]~E(x271,x272)+E(f6(x273,x271,x274,x275,x276),f6(x273,x272,x274,x275,x276))
% 0.21/0.63 [28]~E(x281,x282)+E(f6(x283,x284,x281,x285,x286),f6(x283,x284,x282,x285,x286))
% 0.21/0.63 [29]~E(x291,x292)+E(f6(x293,x294,x295,x291,x296),f6(x293,x294,x295,x292,x296))
% 0.21/0.63 [30]~E(x301,x302)+E(f6(x303,x304,x305,x306,x301),f6(x303,x304,x305,x306,x302))
% 0.21/0.63 [31]P1(x312,x313,x314)+~E(x311,x312)+~P1(x311,x313,x314)
% 0.21/0.63 [32]P1(x323,x322,x324)+~E(x321,x322)+~P1(x323,x321,x324)
% 0.21/0.63 [33]P1(x333,x334,x332)+~E(x331,x332)+~P1(x333,x334,x331)
% 0.21/0.63 [34]P3(x342,x343)+~E(x341,x342)+~P3(x341,x343)
% 0.21/0.63 [35]P3(x353,x352)+~E(x351,x352)+~P3(x353,x351)
% 0.21/0.63 [36]P2(x362,x363,x364)+~E(x361,x362)+~P2(x361,x363,x364)
% 0.21/0.63 [37]P2(x373,x372,x374)+~E(x371,x372)+~P2(x373,x371,x374)
% 0.21/0.63 [38]P2(x383,x384,x382)+~E(x381,x382)+~P2(x383,x384,x381)
% 0.21/0.63
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 cnf(65,plain,
% 0.21/0.63 (P2(x651,x652,f4(x651,x652,x653,x654))),
% 0.21/0.63 inference(rename_variables,[],[41])).
% 0.21/0.63 cnf(67,plain,
% 0.21/0.63 (P2(x671,x672,f4(x671,x672,x673,x674))),
% 0.21/0.63 inference(rename_variables,[],[41])).
% 0.21/0.63 cnf(73,plain,
% 0.21/0.63 ($false),
% 0.21/0.63 inference(scs_inference,[],[39,43,44,45,41,65,67,40,42,47,38,37,36,35,34,51]),
% 0.21/0.63 ['proof']).
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------