TSTP Solution File: GEO058-3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GEO058-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n027.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 22:42:42 EDT 2023
% Result : Unsatisfiable 0.54s 0.72s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO058-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n027.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 : Tue Aug 29 21:04:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.56 start to proof:theBenchmark
% 0.54/0.71 %-------------------------------------------
% 0.54/0.71 % File :CSE---1.6
% 0.54/0.71 % Problem :theBenchmark
% 0.54/0.71 % Transform :cnf
% 0.54/0.71 % Format :tptp:raw
% 0.54/0.71 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.71
% 0.54/0.71 % Result :Theorem 0.080000s
% 0.54/0.71 % Output :CNFRefutation 0.080000s
% 0.54/0.71 %-------------------------------------------
% 0.54/0.71 %--------------------------------------------------------------------------
% 0.54/0.71 % File : GEO058-3 : TPTP v8.1.2. Released v1.0.0.
% 0.54/0.71 % Domain : Geometry
% 0.54/0.71 % Problem : U is the only fixed point of reflection(U,V)
% 0.54/0.71 % Version : [Qua89] axioms : Augmented.
% 0.54/0.71 % English :
% 0.54/0.71
% 0.54/0.71 % Refs : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% 0.54/0.71 % : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% 0.54/0.71 % Source : [Qua89]
% 0.54/0.71 % Names : R4 [Qua89]
% 0.54/0.71
% 0.54/0.72 % Status : Unsatisfiable
% 0.54/0.72 % Rating : 0.05 v8.1.0, 0.00 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.21 v6.0.0, 0.10 v5.5.0, 0.20 v5.4.0, 0.15 v5.3.0, 0.17 v5.2.0, 0.12 v5.0.0, 0.00 v4.0.1, 0.09 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0, 0.08 v3.1.0, 0.09 v2.7.0, 0.08 v2.6.0, 0.00 v2.5.0, 0.08 v2.4.0, 0.22 v2.2.1, 0.00 v2.1.0, 0.00 v2.0.0
% 0.54/0.72 % Syntax : Number of clauses : 36 ( 14 unt; 5 nHn; 27 RR)
% 0.54/0.72 % Number of literals : 85 ( 15 equ; 46 neg)
% 0.54/0.72 % Maximal clause size : 8 ( 2 avg)
% 0.54/0.72 % Maximal term depth : 2 ( 1 avg)
% 0.54/0.72 % Number of predicates : 3 ( 2 usr; 0 prp; 2-4 aty)
% 0.54/0.72 % Number of functors : 11 ( 11 usr; 5 con; 0-6 aty)
% 0.54/0.72 % Number of variables : 124 ( 6 sgn)
% 0.54/0.72 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.54/0.72
% 0.54/0.72 % Comments :
% 0.54/0.72 %--------------------------------------------------------------------------
% 0.54/0.72 %----Include Tarski geometry axioms
% 0.54/0.72 include('Axioms/GEO002-0.ax').
% 0.54/0.72 %----Include definition of reflection
% 0.54/0.72 include('Axioms/GEO002-2.ax').
% 0.54/0.72 %--------------------------------------------------------------------------
% 0.54/0.72 cnf(d1,axiom,
% 0.54/0.72 equidistant(U,V,U,V) ).
% 0.54/0.72
% 0.54/0.72 cnf(d2,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(W,X,U,V) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d3,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(V,U,W,X) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d4_1,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(U,V,X,W) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d4_2,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(V,U,X,W) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d4_3,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(W,X,V,U) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d4_4,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(X,W,U,V) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d4_5,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | equidistant(X,W,V,U) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(d5,axiom,
% 0.54/0.72 ( ~ equidistant(U,V,W,X)
% 0.54/0.72 | ~ equidistant(W,X,Y,Z)
% 0.54/0.72 | equidistant(U,V,Y,Z) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(e1,axiom,
% 0.54/0.72 V = extension(U,V,W,W) ).
% 0.54/0.72
% 0.54/0.72 cnf(b0,axiom,
% 0.54/0.72 ( Y != extension(U,V,W,X)
% 0.54/0.72 | between(U,V,Y) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(r2_1,axiom,
% 0.54/0.72 between(U,V,reflection(U,V)) ).
% 0.54/0.72
% 0.54/0.72 cnf(r2_2,axiom,
% 0.54/0.72 equidistant(V,reflection(U,V),U,V) ).
% 0.54/0.72
% 0.54/0.72 cnf(r3_1,axiom,
% 0.54/0.72 ( U != V
% 0.54/0.72 | V = reflection(U,V) ) ).
% 0.54/0.72
% 0.54/0.72 cnf(r3_2,axiom,
% 0.54/0.72 U = reflection(U,U) ).
% 0.54/0.72
% 0.54/0.72 cnf(v_equals_reflection,hypothesis,
% 0.54/0.72 v = reflection(u,v) ).
% 0.54/0.72
% 0.54/0.72 cnf(prove_u_equals_v,negated_conjecture,
% 0.54/0.72 u != v ).
% 0.54/0.72
% 0.54/0.72 %--------------------------------------------------------------------------
% 0.54/0.72 %-------------------------------------------
% 0.54/0.72 % Proof found
% 0.54/0.72 % SZS status Theorem for theBenchmark
% 0.54/0.72 % SZS output start Proof
% 0.54/0.72 %ClaNum:70(EqnAxiom:35)
% 0.54/0.72 %VarNum:303(SingletonVarNum:117)
% 0.54/0.72 %MaxLitNum:8
% 0.54/0.72 %MaxfuncDepth:1
% 0.54/0.72 %SharedTerms:11
% 0.54/0.72 %goalClause: 45
% 0.54/0.72 %singleGoalClaCount:1
% 0.54/0.72 [45]~E(a1,a10)
% 0.54/0.72 [46]~P2(a6,a8,a9)
% 0.54/0.72 [47]~P2(a8,a9,a6)
% 0.54/0.72 [48]~P2(a9,a6,a8)
% 0.54/0.72 [36]E(f2(a1,a10,a1,a10),a10)
% 0.54/0.72 [37]P1(x371,x372,x372,x371)
% 0.54/0.72 [38]P1(x381,x382,x381,x382)
% 0.54/0.72 [39]E(f2(x391,x392,x393,x393),x392)
% 0.54/0.72 [41]P2(x411,x412,f2(x411,x412,x413,x414))
% 0.54/0.72 [43]P1(x431,f2(x432,x431,x433,x434),x433,x434)
% 0.54/0.72 [49]~P2(x491,x492,x491)+E(x491,x492)
% 0.54/0.72 [50]~E(x501,x502)+E(f2(x501,x502,x501,x502),x502)
% 0.54/0.72 [51]~P1(x511,x512,x513,x513)+E(x511,x512)
% 0.54/0.72 [53]~P1(x534,x533,x532,x531)+P1(x531,x532,x533,x534)
% 0.54/0.72 [54]~P1(x543,x544,x542,x541)+P1(x541,x542,x543,x544)
% 0.54/0.72 [55]~P1(x554,x553,x551,x552)+P1(x551,x552,x553,x554)
% 0.54/0.72 [56]~P1(x563,x564,x561,x562)+P1(x561,x562,x563,x564)
% 0.54/0.72 [57]~P1(x572,x571,x574,x573)+P1(x571,x572,x573,x574)
% 0.54/0.72 [58]~P1(x582,x581,x583,x584)+P1(x581,x582,x583,x584)
% 0.54/0.72 [59]~P1(x591,x592,x594,x593)+P1(x591,x592,x593,x594)
% 0.54/0.72 [52]P2(x521,x522,x523)+~E(x523,f2(x521,x522,x524,x525))
% 0.54/0.72 [64]~P2(x645,x641,x644)+~P2(x642,x643,x644)+P2(x641,f7(x642,x643,x644,x641,x645),x642)
% 0.54/0.72 [65]~P2(x655,x654,x653)+~P2(x652,x651,x653)+P2(x651,f7(x652,x651,x653,x654,x655),x655)
% 0.54/0.72 [60]~P1(x605,x606,x601,x602)+P1(x601,x602,x603,x604)+~P1(x605,x606,x603,x604)
% 0.54/0.72 [61]~P1(x611,x612,x615,x616)+P1(x611,x612,x613,x614)+~P1(x615,x616,x613,x614)
% 0.54/0.72 [66]~P2(x664,x662,x663)+~P2(x661,x662,x665)+E(x661,x662)+P2(x661,x663,f3(x661,x664,x662,x663,x665))
% 0.54/0.72 [67]~P2(x673,x672,x674)+~P2(x671,x672,x675)+E(x671,x672)+P2(x671,x673,f4(x671,x673,x672,x674,x675))
% 0.54/0.72 [68]~P2(x683,x682,x684)+~P2(x681,x682,x685)+E(x681,x682)+P2(f4(x681,x683,x682,x684,x685),x685,f3(x681,x683,x682,x684,x685))
% 0.54/0.72 [69]~P2(x693,x694,x695)+~P2(x692,x693,x695)+~P1(x692,x695,x692,x696)+~P1(x692,x693,x692,x691)+P2(x691,f5(x692,x693,x691,x694,x695,x696),x696)
% 0.54/0.72 [70]~P2(x703,x702,x705)+~P2(x701,x703,x705)+~P1(x701,x705,x701,x706)+~P1(x701,x703,x701,x704)+P1(x701,x702,x701,f5(x701,x703,x704,x702,x705,x706))
% 0.54/0.72 [62]P2(x625,x623,x624)+P2(x624,x625,x623)+~P1(x623,x621,x623,x622)+~P1(x625,x621,x625,x622)+~P1(x624,x621,x624,x622)+E(x621,x622)+P2(x623,x624,x625)
% 0.54/0.72 [63]~P2(x631,x632,x633)+~P1(x632,x634,x638,x636)+~P1(x632,x633,x638,x635)+~P1(x631,x634,x637,x636)+~P1(x631,x632,x637,x638)+E(x631,x632)+P1(x633,x634,x635,x636)+~P2(x637,x638,x635)
% 0.54/0.72 %EqnAxiom
% 0.54/0.72 [1]E(x11,x11)
% 0.54/0.72 [2]E(x22,x21)+~E(x21,x22)
% 0.54/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.54/0.72 [4]~E(x41,x42)+E(f2(x41,x43,x44,x45),f2(x42,x43,x44,x45))
% 0.54/0.72 [5]~E(x51,x52)+E(f2(x53,x51,x54,x55),f2(x53,x52,x54,x55))
% 0.54/0.72 [6]~E(x61,x62)+E(f2(x63,x64,x61,x65),f2(x63,x64,x62,x65))
% 0.54/0.72 [7]~E(x71,x72)+E(f2(x73,x74,x75,x71),f2(x73,x74,x75,x72))
% 0.54/0.72 [8]~E(x81,x82)+E(f5(x81,x83,x84,x85,x86,x87),f5(x82,x83,x84,x85,x86,x87))
% 0.54/0.72 [9]~E(x91,x92)+E(f5(x93,x91,x94,x95,x96,x97),f5(x93,x92,x94,x95,x96,x97))
% 0.54/0.72 [10]~E(x101,x102)+E(f5(x103,x104,x101,x105,x106,x107),f5(x103,x104,x102,x105,x106,x107))
% 0.54/0.72 [11]~E(x111,x112)+E(f5(x113,x114,x115,x111,x116,x117),f5(x113,x114,x115,x112,x116,x117))
% 0.54/0.72 [12]~E(x121,x122)+E(f5(x123,x124,x125,x126,x121,x127),f5(x123,x124,x125,x126,x122,x127))
% 0.54/0.72 [13]~E(x131,x132)+E(f5(x133,x134,x135,x136,x137,x131),f5(x133,x134,x135,x136,x137,x132))
% 0.54/0.72 [14]~E(x141,x142)+E(f7(x141,x143,x144,x145,x146),f7(x142,x143,x144,x145,x146))
% 0.54/0.72 [15]~E(x151,x152)+E(f7(x153,x151,x154,x155,x156),f7(x153,x152,x154,x155,x156))
% 0.54/0.72 [16]~E(x161,x162)+E(f7(x163,x164,x161,x165,x166),f7(x163,x164,x162,x165,x166))
% 0.54/0.72 [17]~E(x171,x172)+E(f7(x173,x174,x175,x171,x176),f7(x173,x174,x175,x172,x176))
% 0.54/0.72 [18]~E(x181,x182)+E(f7(x183,x184,x185,x186,x181),f7(x183,x184,x185,x186,x182))
% 0.54/0.72 [19]~E(x191,x192)+E(f3(x191,x193,x194,x195,x196),f3(x192,x193,x194,x195,x196))
% 0.54/0.72 [20]~E(x201,x202)+E(f3(x203,x201,x204,x205,x206),f3(x203,x202,x204,x205,x206))
% 0.54/0.72 [21]~E(x211,x212)+E(f3(x213,x214,x211,x215,x216),f3(x213,x214,x212,x215,x216))
% 0.54/0.72 [22]~E(x221,x222)+E(f3(x223,x224,x225,x221,x226),f3(x223,x224,x225,x222,x226))
% 0.54/0.72 [23]~E(x231,x232)+E(f3(x233,x234,x235,x236,x231),f3(x233,x234,x235,x236,x232))
% 0.54/0.72 [24]~E(x241,x242)+E(f4(x241,x243,x244,x245,x246),f4(x242,x243,x244,x245,x246))
% 0.54/0.72 [25]~E(x251,x252)+E(f4(x253,x251,x254,x255,x256),f4(x253,x252,x254,x255,x256))
% 0.54/0.72 [26]~E(x261,x262)+E(f4(x263,x264,x261,x265,x266),f4(x263,x264,x262,x265,x266))
% 0.54/0.72 [27]~E(x271,x272)+E(f4(x273,x274,x275,x271,x276),f4(x273,x274,x275,x272,x276))
% 0.54/0.72 [28]~E(x281,x282)+E(f4(x283,x284,x285,x286,x281),f4(x283,x284,x285,x286,x282))
% 0.54/0.72 [29]P1(x292,x293,x294,x295)+~E(x291,x292)+~P1(x291,x293,x294,x295)
% 0.54/0.72 [30]P1(x303,x302,x304,x305)+~E(x301,x302)+~P1(x303,x301,x304,x305)
% 0.54/0.72 [31]P1(x313,x314,x312,x315)+~E(x311,x312)+~P1(x313,x314,x311,x315)
% 0.54/0.72 [32]P1(x323,x324,x325,x322)+~E(x321,x322)+~P1(x323,x324,x325,x321)
% 0.54/0.72 [33]P2(x332,x333,x334)+~E(x331,x332)+~P2(x331,x333,x334)
% 0.54/0.72 [34]P2(x343,x342,x344)+~E(x341,x342)+~P2(x343,x341,x344)
% 0.54/0.72 [35]P2(x353,x354,x352)+~E(x351,x352)+~P2(x353,x354,x351)
% 0.54/0.72
% 0.54/0.72 %-------------------------------------------
% 0.54/0.72 cnf(72,plain,
% 0.54/0.72 (~P1(a1,a10,x721,x721)),
% 0.54/0.72 inference(scs_inference,[],[45,36,2,51])).
% 0.54/0.72 cnf(80,plain,
% 0.54/0.72 (P2(x801,x802,f2(x801,x802,x803,x804))),
% 0.54/0.72 inference(rename_variables,[],[41])).
% 0.54/0.72 cnf(82,plain,
% 0.54/0.72 (P2(x821,x822,f2(x821,x822,x823,x824))),
% 0.54/0.72 inference(rename_variables,[],[41])).
% 0.54/0.72 cnf(84,plain,
% 0.54/0.72 (P2(x841,x842,f2(x841,x842,x843,x844))),
% 0.54/0.72 inference(rename_variables,[],[41])).
% 0.54/0.72 cnf(86,plain,
% 0.54/0.72 (P1(x861,x862,x861,x862)),
% 0.54/0.73 inference(rename_variables,[],[38])).
% 0.54/0.73 cnf(90,plain,
% 0.54/0.73 (P1(x901,f2(x902,x901,x903,x904),x903,x904)),
% 0.54/0.73 inference(rename_variables,[],[43])).
% 0.54/0.73 cnf(91,plain,
% 0.54/0.73 (P1(a10,x911,x911,f2(a1,a10,a1,a10))),
% 0.54/0.73 inference(scs_inference,[],[45,37,38,86,46,36,43,41,80,82,39,2,51,49,52,35,34,33,32,31,30,29])).
% 0.54/0.73 cnf(92,plain,
% 0.54/0.73 (P1(x921,x922,x922,x921)),
% 0.54/0.73 inference(rename_variables,[],[37])).
% 0.54/0.73 cnf(95,plain,
% 0.54/0.73 (P1(x951,f2(x952,x951,x953,x954),x953,x954)),
% 0.54/0.73 inference(rename_variables,[],[43])).
% 0.54/0.73 cnf(96,plain,
% 0.54/0.73 (P1(x961,x962,x962,x961)),
% 0.54/0.73 inference(rename_variables,[],[37])).
% 0.54/0.73 cnf(142,plain,
% 0.54/0.73 (P2(x1421,f7(x1422,x1421,f2(x1422,x1421,x1423,x1424),x1421,x1422),x1422)),
% 0.54/0.73 inference(scs_inference,[],[45,37,92,96,38,86,46,36,43,90,95,41,80,82,84,39,2,51,49,52,35,34,33,32,31,30,29,3,61,60,59,58,57,56,55,54,53,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,50,65])).
% 0.54/0.73 cnf(168,plain,
% 0.54/0.73 (P1(x1681,x1682,x1681,x1682)),
% 0.54/0.73 inference(rename_variables,[],[38])).
% 0.54/0.73 cnf(169,plain,
% 0.54/0.73 (P2(x1691,x1692,f2(x1691,x1692,x1693,x1694))),
% 0.54/0.73 inference(rename_variables,[],[41])).
% 0.54/0.73 cnf(170,plain,
% 0.54/0.73 (P1(x1701,x1702,x1702,x1701)),
% 0.54/0.73 inference(rename_variables,[],[37])).
% 0.54/0.73 cnf(171,plain,
% 0.54/0.73 (P2(x1711,x1712,f2(x1711,x1712,x1713,x1714))),
% 0.54/0.73 inference(rename_variables,[],[41])).
% 0.54/0.73 cnf(178,plain,
% 0.54/0.73 (P1(x1781,x1782,x1782,x1781)),
% 0.54/0.73 inference(rename_variables,[],[37])).
% 0.54/0.73 cnf(181,plain,
% 0.54/0.73 (P1(x1811,f2(x1812,x1811,x1813,x1814),x1813,x1814)),
% 0.54/0.73 inference(rename_variables,[],[43])).
% 0.54/0.73 cnf(186,plain,
% 0.54/0.73 (E(f2(x1861,x1862,x1863,x1863),x1862)),
% 0.54/0.73 inference(rename_variables,[],[39])).
% 0.54/0.73 cnf(191,plain,
% 0.54/0.73 (P2(x1911,x1912,f2(x1911,x1912,x1913,x1914))),
% 0.54/0.73 inference(rename_variables,[],[41])).
% 0.54/0.73 cnf(199,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(scs_inference,[],[45,37,170,178,38,168,47,43,181,41,171,191,169,39,186,142,91,72,49,70,56,53,61,51,52,34,29,67,69,60]),
% 0.54/0.73 ['proof']).
% 0.54/0.73 % SZS output end Proof
% 0.54/0.73 % Total time :0.080000s
%------------------------------------------------------------------------------