%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GEO112-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 : Mon Jun 24 06:03:51 EDT 2024
% Result : Unsatisfiable 2.81s 2.88s
% Output : CNFRefutation 2.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO112-1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 08:32:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.54/0.59 start to proof:theBenchmark
% 2.81/2.88 %-------------------------------------------
% 2.81/2.88 % File :CSE---1.7
% 2.81/2.88 % Problem :theBenchmark
% 2.81/2.88 % Transform :cnf
% 2.81/2.88 % Format :tptp:raw
% 2.81/2.88 % Command :java -jar mcs_scs.jar %d %s
% 2.81/2.88
% 2.81/2.88 % Result :Theorem 2.250000s
% 2.81/2.88 % Output :CNFRefutation 2.250000s
% 2.81/2.88 %-------------------------------------------
% 2.81/2.88 %--------------------------------------------------------------------------
% 2.81/2.88 % File : GEO112-1 : TPTP v8.2.0. Released v2.4.0.
% 2.81/2.88 % Domain : Geometry (Oriented curves)
% 2.81/2.88 % Problem : Basic property of orderings on linear structures 2
% 2.81/2.88 % Version : [EHK99] axioms.
% 2.81/2.88 % English : If Q is between P and R wrt. c, then Q is between R and P wrt. c
% 2.81/2.88
% 2.81/2.88 % Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% 2.81/2.88 % : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% 2.81/2.88 % Source : [TPTP]
% 2.81/2.88 % Names :
% 2.81/2.88
% 2.81/2.88 % Status : Unsatisfiable
% 2.81/2.88 % Rating : 0.10 v8.2.0, 0.14 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.17 v5.2.0, 0.19 v5.1.0, 0.18 v5.0.0, 0.07 v4.1.0, 0.00 v4.0.1, 0.18 v4.0.0, 0.00 v3.3.0, 0.07 v3.2.0, 0.15 v3.1.0, 0.09 v2.7.0, 0.25 v2.6.0, 0.11 v2.5.0, 0.22 v2.4.0
% 2.81/2.88 % Syntax : Number of clauses : 56 ( 3 unt; 22 nHn; 51 RR)
% 2.81/2.88 % Number of literals : 172 ( 23 equ; 89 neg)
% 2.81/2.88 % Maximal clause size : 12 ( 3 avg)
% 2.81/2.88 % Maximal term depth : 3 ( 1 avg)
% 2.81/2.88 % Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty)
% 2.81/2.88 % Number of functors : 19 ( 19 usr; 4 con; 0-4 aty)
% 2.81/2.88 % Number of variables : 151 ( 12 sgn)
% 2.81/2.88 % SPC : CNF_UNS_RFO_SEQ_NHN
% 2.81/2.88
% 2.81/2.88 % Comments : Created by tptp2X -f tptp -t clausify:otter GEO112+1.p
% 2.81/2.88 %--------------------------------------------------------------------------
% 2.81/2.88 %----Include simple curve axioms
% 2.81/2.88 include('Axioms/GEO004-0.ax').
% 2.81/2.88 %----Include axioms of betweenness for simple curves
% 2.81/2.88 include('Axioms/GEO004-1.ax').
% 2.81/2.88 %--------------------------------------------------------------------------
% 2.81/2.88 cnf(theorem_3_8_2_77,negated_conjecture,
% 2.81/2.88 between_c(sk15,sk16,sk17,sk18) ).
% 2.81/2.88
% 2.81/2.88 cnf(theorem_3_8_2_78,negated_conjecture,
% 2.81/2.88 ~ between_c(sk15,sk18,sk17,sk16) ).
% 2.81/2.88
% 2.81/2.88 %--------------------------------------------------------------------------
% 2.81/2.88 %-------------------------------------------
% 2.81/2.88 % Proof found
% 2.81/2.88 % SZS status Theorem for theBenchmark
% 2.81/2.88 % SZS output start Proof
% 2.85/2.89 %ClaNum:102(EqnAxiom:51)
% 2.85/2.89 %VarNum:387(SingletonVarNum:138)
% 2.85/2.89 %MaxLitNum:12
% 2.85/2.89 %MaxfuncDepth:2
% 2.85/2.89 %SharedTerms:6
% 2.85/2.89 %goalClause: 53 54
% 2.85/2.89 %singleGoalClaCount:2
% 2.85/2.89 [53]P2(a13,a16,a17,a18)
% 2.85/2.89 [54]~P2(a13,a18,a17,a16)
% 2.85/2.89 [52]P1(f1(x521),x521)
% 2.85/2.89 [55]P3(x551)+P4(f2(x551),x551)
% 2.85/2.89 [57]~P6(x571)+P4(f12(x571),x571)
% 2.85/2.89 [56]P6(x561)+~P4(x562,x561)
% 2.85/2.89 [59]~P3(x591)+~P4(x592,x591)
% 2.85/2.89 [60]~P4(x601,x602)+P5(x601,x602)
% 2.85/2.89 [61]~P1(x611,x612)+P5(x611,x612)
% 2.85/2.89 [62]~P1(x621,x622)+~P4(x621,x622)
% 2.85/2.89 [63]~P4(x631,x632)+~E(f3(x631,x632),x631)
% 2.85/2.89 [65]P8(x651,x652)+P5(f4(x651,x652),x651)
% 2.85/2.89 [69]~P4(x691,x692)+P4(f3(x691,x692),x692)
% 2.85/2.89 [76]P8(x761,x762)+~P5(f4(x761,x762),x762)
% 2.85/2.89 [83]~P1(x831,x832)+P7(x831,f14(x831,x832),f5(x831,x832))
% 2.85/2.89 [78]~P1(x781,x782)+E(f19(f14(x781,x782),f5(x781,x782)),x782)
% 2.85/2.89 [79]P5(x791,x792)+~P7(x791,x793,x792)
% 2.85/2.89 [80]P5(x801,x802)+~P7(x801,x802,x803)
% 2.85/2.89 [81]~P7(x813,x812,x811)+E(f8(x811,x812),f19(x812,x811))
% 2.85/2.89 [95]~E(x951,x952)+~P2(x953,x951,x954,x952)
% 2.85/2.89 [99]~P2(x994,x993,x992,x991)+P4(x991,f15(x991,x992,x993,x994))
% 2.85/2.89 [100]~P2(x1004,x1001,x1003,x1002)+P4(x1001,f15(x1002,x1003,x1001,x1004))
% 2.85/2.89 [101]~P2(x1014,x1013,x1011,x1012)+P1(x1011,f15(x1012,x1011,x1013,x1014))
% 2.85/2.89 [102]~P2(x1024,x1023,x1022,x1021)+P8(f15(x1021,x1022,x1023,x1024),x1024)
% 2.85/2.89 [58]P6(x581)+~P8(x581,x582)+E(x581,x582)
% 2.85/2.89 [64]P1(x641,x642)+~P5(x641,x642)+P4(x641,x642)
% 2.85/2.89 [72]~P5(x721,x722)+P4(x721,x722)+P5(x721,f6(x722,x721))
% 2.85/2.89 [73]~P5(x731,x732)+P4(x731,x732)+P5(x731,f10(x732,x731))
% 2.85/2.89 [74]~P5(x741,x742)+P4(x741,x742)+P8(f6(x742,x741),x742)
% 2.85/2.89 [75]~P5(x751,x752)+P4(x751,x752)+P8(f10(x752,x751),x752)
% 2.85/2.89 [77]E(x771,x772)+P5(f7(x771,x772),x772)+P5(f7(x771,x772),x771)
% 2.85/2.89 [82]E(x821,x822)+~P5(f7(x821,x822),x822)+~P5(f7(x821,x822),x821)
% 2.85/2.89 [84]~P5(x841,x842)+P4(x841,x842)+~P8(f6(x842,x841),f10(x842,x841))
% 2.85/2.89 [85]~P5(x851,x852)+P4(x851,x852)+~P8(f10(x852,x851),f6(x852,x851))
% 2.85/2.89 [66]~P5(x661,x663)+P5(x661,x662)+~P8(x663,x662)
% 2.85/2.89 [96]~P5(f9(x963,x962,x961),x961)+~P5(f9(x963,x962,x961),x962)+E(x961,f19(x962,x963))
% 2.85/2.89 [97]~P5(f9(x973,x972,x971),x971)+~P5(f9(x973,x972,x971),x973)+E(x971,f19(x972,x973))
% 2.85/2.89 [67]~P5(x671,x674)+P5(x671,x672)+~E(x672,f19(x673,x674))
% 2.85/2.89 [68]~P5(x681,x683)+P5(x681,x682)+~E(x682,f19(x683,x684))
% 2.85/2.89 [90]~P5(x901,x903)+~P5(x901,x902)+P7(x901,x902,x903)+P5(f11(x903,x902,x901),x903)
% 2.85/2.89 [91]~P5(x911,x913)+~P5(x911,x912)+P7(x911,x912,x913)+P5(f11(x913,x912,x911),x912)
% 2.85/2.89 [94]P5(f9(x943,x942,x941),x941)+P5(f9(x943,x942,x941),x942)+P5(f9(x943,x942,x941),x943)+E(x941,f19(x942,x943))
% 2.85/2.89 [87]~P5(x871,x872)+P4(x871,x872)+~P7(x874,x873,x872)+~P5(x871,x873)
% 2.85/2.89 [88]~P5(x881,x882)+P4(x881,x882)+~P7(x884,x882,x883)+~P5(x881,x883)
% 2.85/2.89 [71]~P5(x711,x714)+P5(x711,x712)+P5(x711,x713)+~E(x714,f19(x713,x712))
% 2.85/2.89 [98]~P5(x981,x983)+~P5(x981,x982)+P7(x981,x982,x983)+~P4(f11(x983,x982,x981),x983)+~P4(f11(x983,x982,x981),x982)
% 2.85/2.89 [89]~P3(x894)+~P4(x891,x892)+P7(x891,x892,x893)+~P7(x895,x892,x893)+~E(x894,f19(x892,x893))
% 2.85/2.89 [70]E(x703,x701)+~P4(x701,x704)+~P4(x703,x704)+E(x701,x702)+E(x703,x702)+~P4(x702,x704)
% 2.85/2.89 [93]~P4(x932,x935)+~P4(x931,x935)+~P1(x934,x935)+E(x931,x932)+P2(x933,x931,x934,x932)+~P8(x935,x933)
% 2.85/2.89 [86]P8(x862,x861)+~P8(x862,x863)+~P5(x864,x862)+~P4(x864,x863)+P8(x861,x862)+~P8(x861,x863)+~P5(x864,x861)
% 2.85/2.89 [92]P8(x922,x921)+P8(x922,x923)+P8(x923,x921)+P8(x923,x922)+~P8(x922,x924)+~P8(x923,x924)+~P4(x925,x922)+~P4(x925,x923)+P8(x921,x922)+P8(x921,x923)+~P8(x921,x924)+~P4(x925,x921)
% 2.85/2.89 %EqnAxiom
% 2.85/2.89 [1]E(x11,x11)
% 2.85/2.89 [2]E(x22,x21)+~E(x21,x22)
% 2.85/2.89 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.85/2.89 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 2.85/2.89 [5]~E(x51,x52)+E(f2(x51),f2(x52))
% 2.85/2.89 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 2.85/2.89 [7]~E(x71,x72)+E(f3(x71,x73),f3(x72,x73))
% 2.85/2.89 [8]~E(x81,x82)+E(f3(x83,x81),f3(x83,x82))
% 2.85/2.89 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 2.85/2.89 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 2.85/2.89 [11]~E(x111,x112)+E(f19(x111,x113),f19(x112,x113))
% 2.85/2.89 [12]~E(x121,x122)+E(f19(x123,x121),f19(x123,x122))
% 2.85/2.89 [13]~E(x131,x132)+E(f15(x131,x133,x134,x135),f15(x132,x133,x134,x135))
% 2.85/2.89 [14]~E(x141,x142)+E(f15(x143,x141,x144,x145),f15(x143,x142,x144,x145))
% 2.85/2.89 [15]~E(x151,x152)+E(f15(x153,x154,x151,x155),f15(x153,x154,x152,x155))
% 2.85/2.89 [16]~E(x161,x162)+E(f15(x163,x164,x165,x161),f15(x163,x164,x165,x162))
% 2.85/2.89 [17]~E(x171,x172)+E(f9(x171,x173,x174),f9(x172,x173,x174))
% 2.85/2.89 [18]~E(x181,x182)+E(f9(x183,x181,x184),f9(x183,x182,x184))
% 2.85/2.89 [19]~E(x191,x192)+E(f9(x193,x194,x191),f9(x193,x194,x192))
% 2.85/2.89 [20]~E(x201,x202)+E(f11(x201,x203,x204),f11(x202,x203,x204))
% 2.85/2.89 [21]~E(x211,x212)+E(f11(x213,x211,x214),f11(x213,x212,x214))
% 2.85/2.89 [22]~E(x221,x222)+E(f11(x223,x224,x221),f11(x223,x224,x222))
% 2.85/2.89 [23]~E(x231,x232)+E(f6(x231,x233),f6(x232,x233))
% 2.85/2.89 [24]~E(x241,x242)+E(f6(x243,x241),f6(x243,x242))
% 2.85/2.89 [25]~E(x251,x252)+E(f10(x251,x253),f10(x252,x253))
% 2.85/2.89 [26]~E(x261,x262)+E(f10(x263,x261),f10(x263,x262))
% 2.85/2.89 [27]~E(x271,x272)+E(f5(x271,x273),f5(x272,x273))
% 2.85/2.89 [28]~E(x281,x282)+E(f5(x283,x281),f5(x283,x282))
% 2.85/2.89 [29]~E(x291,x292)+E(f7(x291,x293),f7(x292,x293))
% 2.85/2.89 [30]~E(x301,x302)+E(f7(x303,x301),f7(x303,x302))
% 2.85/2.89 [31]~E(x311,x312)+E(f14(x311,x313),f14(x312,x313))
% 2.85/2.89 [32]~E(x321,x322)+E(f14(x323,x321),f14(x323,x322))
% 2.85/2.89 [33]~E(x331,x332)+E(f8(x331,x333),f8(x332,x333))
% 2.85/2.89 [34]~E(x341,x342)+E(f8(x343,x341),f8(x343,x342))
% 2.85/2.89 [35]P1(x352,x353)+~E(x351,x352)+~P1(x351,x353)
% 2.85/2.89 [36]P1(x363,x362)+~E(x361,x362)+~P1(x363,x361)
% 2.85/2.89 [37]P2(x372,x373,x374,x375)+~E(x371,x372)+~P2(x371,x373,x374,x375)
% 2.85/2.89 [38]P2(x383,x382,x384,x385)+~E(x381,x382)+~P2(x383,x381,x384,x385)
% 2.85/2.89 [39]P2(x393,x394,x392,x395)+~E(x391,x392)+~P2(x393,x394,x391,x395)
% 2.85/2.89 [40]P2(x403,x404,x405,x402)+~E(x401,x402)+~P2(x403,x404,x405,x401)
% 2.85/2.89 [41]P4(x412,x413)+~E(x411,x412)+~P4(x411,x413)
% 2.85/2.89 [42]P4(x423,x422)+~E(x421,x422)+~P4(x423,x421)
% 2.85/2.89 [43]~P3(x431)+P3(x432)+~E(x431,x432)
% 2.85/2.89 [44]P5(x442,x443)+~E(x441,x442)+~P5(x441,x443)
% 2.85/2.89 [45]P5(x453,x452)+~E(x451,x452)+~P5(x453,x451)
% 2.85/2.89 [46]~P6(x461)+P6(x462)+~E(x461,x462)
% 2.85/2.89 [47]P7(x472,x473,x474)+~E(x471,x472)+~P7(x471,x473,x474)
% 2.85/2.89 [48]P7(x483,x482,x484)+~E(x481,x482)+~P7(x483,x481,x484)
% 2.85/2.89 [49]P7(x493,x494,x492)+~E(x491,x492)+~P7(x493,x494,x491)
% 2.85/2.89 [50]P8(x502,x503)+~E(x501,x502)+~P8(x501,x503)
% 2.85/2.89 [51]P8(x513,x512)+~E(x511,x512)+~P8(x513,x511)
% 2.85/2.89
% 2.85/2.89 %-------------------------------------------
% 2.85/2.89 cnf(103,plain,
% 2.85/2.89 (~P5(x1031,x1032)+P5(x1031,f19(x1033,x1032))),
% 2.85/2.89 inference(equality_inference,[],[67])).
% 2.85/2.89 cnf(107,plain,
% 2.85/2.89 (~P2(x1072,x1071,x1073,x1071)),
% 2.85/2.89 inference(equality_inference,[],[95])).
% 2.85/2.89 cnf(109,plain,
% 2.85/2.89 (~P2(x1091,x1092,x1093,x1092)),
% 2.85/2.89 inference(rename_variables,[],[107])).
% 2.85/2.89 cnf(110,plain,
% 2.85/2.89 (~E(a18,a16)),
% 2.85/2.89 inference(scs_inference,[],[53,107,109,38,40])).
% 2.85/2.89 cnf(112,plain,
% 2.85/2.89 (P2(x1121,a16,a17,a18)+~E(a13,x1121)),
% 2.85/2.89 inference(scs_inference,[],[53,107,109,38,40,37])).
% 2.85/2.89 cnf(113,plain,
% 2.85/2.89 (P2(a13,a16,x1131,a18)+~E(a17,x1131)),
% 2.85/2.89 inference(scs_inference,[],[53,107,109,38,40,37,39])).
% 2.85/2.89 cnf(219,plain,
% 2.85/2.89 (~P4(x2191,x2192)+P5(x2191,f19(x2193,x2192))),
% 2.85/2.89 inference(scs_inference,[],[60,103])).
% 2.85/2.89 cnf(454,plain,
% 2.85/2.89 (P4(f3(a18,f15(a18,a17,a16,a13)),f15(a18,a17,a16,a13))),
% 2.85/2.89 inference(scs_inference,[],[53,69,99])).
% 2.85/2.89 cnf(457,plain,
% 2.85/2.89 (~P1(f3(a18,f15(a18,a17,a16,a13)),f15(a18,a17,a16,a13))),
% 2.85/2.89 inference(scs_inference,[],[454,219,62])).
% 2.85/2.89 cnf(813,plain,
% 2.85/2.89 (~P8(x8131,a13)+~P4(a16,x8131)+~P4(a18,x8131)+~P1(a17,x8131)),
% 2.85/2.89 inference(scs_inference,[],[110,54,454,93])).
% 2.85/2.89 cnf(1016,plain,
% 2.85/2.89 (P4(a16,f15(a18,a17,a16,x10161))+~E(a13,x10161)),
% 2.85/2.89 inference(scs_inference,[],[100,112])).
% 2.85/2.89 cnf(1017,plain,
% 2.85/2.89 (P4(a16,f15(a18,a17,a16,a13))),
% 2.85/2.89 inference(equality_inference,[],[1016])).
% 2.85/2.89 cnf(1064,plain,
% 2.85/2.89 (P1(x10641,f15(a18,x10641,a16,a13))+~E(a17,x10641)),
% 2.85/2.89 inference(scs_inference,[],[101,113])).
% 2.85/2.89 cnf(1065,plain,
% 2.85/2.89 (P1(a17,f15(a18,a17,a16,a13))),
% 2.85/2.89 inference(equality_inference,[],[1064])).
% 2.85/2.89 cnf(1070,plain,
% 2.85/2.89 (~P4(a18,f15(a18,a17,a16,a13))+~P8(f15(a18,a17,a16,a13),a13)),
% 2.85/2.89 inference(scs_inference,[],[1017,1065,457,35,58,36,813])).
% 2.85/2.89 cnf(1171,plain,
% 2.85/2.89 (P8(f15(a18,a17,a16,x11711),x11711)+~E(a13,x11711)),
% 2.85/2.89 inference(scs_inference,[],[102,112])).
% 2.85/2.89 cnf(1172,plain,
% 2.85/2.89 (P8(f15(a18,a17,a16,a13),a13)),
% 2.85/2.89 inference(equality_inference,[],[1171])).
% 2.85/2.89 cnf(1173,plain,
% 2.85/2.89 (~P4(a18,f15(a18,a17,a16,a13))),
% 2.85/2.89 inference(scs_inference,[],[1172,1070])).
% 2.85/2.89 cnf(1185,plain,
% 2.85/2.89 ($false),
% 2.85/2.89 inference(scs_inference,[],[53,1173,99]),
% 2.85/2.89 ['proof']).
% 2.85/2.89 % SZS output end Proof
% 2.85/2.89 % Total time :2.250000s
%------------------------------------------------------------------------------