%------------------------------------------------------------------------------
% 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 : n028.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 06:03:52 EDT 2024
% Result : Theorem 3.06s 3.12s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO112+1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.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 : 300
% 0.12/0.33 % DateTime : Fri Jun 21 07:26:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 3.06/3.12 %-------------------------------------------
% 3.06/3.12 % File :CSE---1.7
% 3.06/3.12 % Problem :theBenchmark
% 3.06/3.12 % Transform :cnf
% 3.06/3.12 % Format :tptp:raw
% 3.06/3.12 % Command :java -jar mcs_scs.jar %d %s
% 3.06/3.12
% 3.06/3.12 % Result :Theorem 2.510000s
% 3.06/3.12 % Output :CNFRefutation 2.510000s
% 3.06/3.12 %-------------------------------------------
% 3.06/3.12 %--------------------------------------------------------------------------
% 3.06/3.12 % File : GEO112+1 : TPTP v8.2.0. Released v2.4.0.
% 3.06/3.12 % Domain : Geometry (Oriented curves)
% 3.06/3.12 % Problem : Basic property of orderings on linear structures 2
% 3.06/3.12 % Version : [EHK99] axioms.
% 3.06/3.12 % English : If Q is between P and R wrt. c, then Q is between R and P wrt. c
% 3.06/3.12
% 3.06/3.12 % Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% 3.06/3.12 % : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% 3.06/3.12 % Source : [KE99]
% 3.06/3.12 % Names : Theorem 3.8 (2) [KE99]
% 3.06/3.12 % : T5 [EHK99]
% 3.06/3.12
% 3.06/3.12 % Status : Theorem
% 3.06/3.12 % Rating : 0.28 v8.2.0, 0.31 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.23 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.26 v3.3.0, 0.14 v3.2.0, 0.27 v3.1.0, 0.33 v2.5.0, 0.50 v2.4.0
% 3.06/3.12 % Syntax : Number of formulae : 18 ( 1 unt; 0 def)
% 3.06/3.12 % Number of atoms : 75 ( 11 equ)
% 3.06/3.12 % Maximal formula atoms : 12 ( 4 avg)
% 3.06/3.12 % Number of connectives : 62 ( 5 ~; 9 |; 25 &)
% 3.06/3.12 % ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% 3.06/3.12 % Maximal formula depth : 12 ( 7 avg)
% 3.06/3.12 % Maximal term depth : 2 ( 1 avg)
% 3.06/3.12 % Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty)
% 3.06/3.12 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 3.06/3.12 % Number of variables : 62 ( 52 !; 10 ?)
% 3.06/3.12 % SPC : FOF_THM_RFO_SEQ
% 3.06/3.12
% 3.06/3.12 % Comments :
% 3.06/3.12 %--------------------------------------------------------------------------
% 3.06/3.12 %----Include simple curve axioms
% 3.06/3.12 include('Axioms/GEO004+0.ax').
% 3.06/3.12 %----Include axioms of betweenness for simple curves
% 3.06/3.12 include('Axioms/GEO004+1.ax').
% 3.06/3.12 %--------------------------------------------------------------------------
% 3.06/3.12 fof(theorem_3_8_2,conjecture,
% 3.06/3.12 ! [C,P,Q,R] :
% 3.06/3.12 ( between_c(C,P,Q,R)
% 3.06/3.12 => between_c(C,R,Q,P) ) ).
% 3.06/3.12
% 3.06/3.12 %--------------------------------------------------------------------------
% 3.06/3.12 %-------------------------------------------
% 3.06/3.12 % Proof found
% 3.06/3.12 % SZS status Theorem for theBenchmark
% 3.06/3.12 % SZS output start Proof
% 3.06/3.12 %ClaNum:102(EqnAxiom:51)
% 3.06/3.12 %VarNum:387(SingletonVarNum:138)
% 3.06/3.12 %MaxLitNum:12
% 3.06/3.12 %MaxfuncDepth:2
% 3.06/3.12 %SharedTerms:6
% 3.06/3.13 %goalClause: 53 54
% 3.06/3.13 %singleGoalClaCount:2
% 3.06/3.13 [53]P2(a2,a8,a9,a10)
% 3.06/3.13 [54]~P2(a2,a10,a9,a8)
% 3.06/3.13 [52]P1(f1(x521),x521)
% 3.06/3.13 [55]P3(x551)+P4(f11(x551),x551)
% 3.06/3.13 [57]~P6(x571)+P4(f17(x571),x571)
% 3.06/3.13 [56]P6(x561)+~P4(x562,x561)
% 3.06/3.13 [59]~P3(x591)+~P4(x592,x591)
% 3.06/3.13 [60]~P4(x601,x602)+P5(x601,x602)
% 3.06/3.13 [61]~P1(x611,x612)+P5(x611,x612)
% 3.06/3.13 [62]~P1(x621,x622)+~P4(x621,x622)
% 3.06/3.13 [63]~P4(x632,x631)+~E(f3(x631,x632),x632)
% 3.06/3.13 [65]P8(x651,x652)+P5(f12(x652,x651),x651)
% 3.06/3.13 [69]~P4(x692,x691)+P4(f3(x691,x692),x691)
% 3.06/3.13 [76]P8(x761,x762)+~P5(f12(x762,x761),x762)
% 3.06/3.13 [83]~P1(x831,x832)+P7(x831,f19(x832,x831),f4(x832,x831))
% 3.06/3.13 [78]~P1(x782,x781)+E(f18(f19(x781,x782),f4(x781,x782)),x781)
% 3.06/3.13 [79]P5(x791,x792)+~P7(x791,x793,x792)
% 3.06/3.13 [80]P5(x801,x802)+~P7(x801,x802,x803)
% 3.06/3.13 [81]~P7(x813,x811,x812)+E(f6(x811,x812),f18(x811,x812))
% 3.06/3.13 [95]~E(x951,x952)+~P2(x953,x951,x954,x952)
% 3.06/3.13 [99]~P2(x992,x993,x994,x991)+P4(x991,f7(x992,x993,x994,x991))
% 3.06/3.13 [100]~P2(x1002,x1001,x1003,x1004)+P4(x1001,f7(x1002,x1001,x1003,x1004))
% 3.06/3.13 [101]~P2(x1012,x1013,x1011,x1014)+P1(x1011,f7(x1012,x1013,x1011,x1014))
% 3.06/3.13 [102]~P2(x1021,x1022,x1023,x1024)+P8(f7(x1021,x1022,x1023,x1024),x1021)
% 3.06/3.13 [58]P6(x581)+~P8(x581,x582)+E(x581,x582)
% 3.06/3.13 [64]P1(x641,x642)+~P5(x641,x642)+P4(x641,x642)
% 3.06/3.13 [72]~P5(x721,x722)+P4(x721,x722)+P5(x721,f13(x721,x722))
% 3.06/3.13 [73]~P5(x731,x732)+P4(x731,x732)+P5(x731,f15(x731,x732))
% 3.06/3.13 [74]~P5(x741,x742)+P4(x741,x742)+P8(f13(x741,x742),x742)
% 3.06/3.13 [75]~P5(x751,x752)+P4(x751,x752)+P8(f15(x751,x752),x752)
% 3.06/3.13 [77]E(x771,x772)+P5(f5(x771,x772),x772)+P5(f5(x771,x772),x771)
% 3.06/3.13 [82]E(x821,x822)+~P5(f5(x821,x822),x822)+~P5(f5(x821,x822),x821)
% 3.06/3.13 [84]~P5(x841,x842)+P4(x841,x842)+~P8(f13(x841,x842),f15(x841,x842))
% 3.06/3.13 [85]~P5(x851,x852)+P4(x851,x852)+~P8(f15(x851,x852),f13(x851,x852))
% 3.06/3.13 [66]~P5(x661,x663)+P5(x661,x662)+~P8(x663,x662)
% 3.06/3.13 [96]~P5(f14(x961,x962,x963),x963)+~P5(f14(x961,x962,x963),x961)+E(x961,f18(x962,x963))
% 3.06/3.13 [97]~P5(f14(x971,x972,x973),x972)+~P5(f14(x971,x972,x973),x971)+E(x971,f18(x972,x973))
% 3.06/3.13 [67]~P5(x671,x674)+P5(x671,x672)+~E(x672,f18(x673,x674))
% 3.06/3.13 [68]~P5(x681,x683)+P5(x681,x682)+~E(x682,f18(x683,x684))
% 3.06/3.13 [90]~P5(x901,x903)+~P5(x901,x902)+P7(x901,x902,x903)+P5(f16(x901,x902,x903),x903)
% 3.06/3.13 [91]~P5(x911,x913)+~P5(x911,x912)+P7(x911,x912,x913)+P5(f16(x911,x912,x913),x912)
% 3.06/3.13 [94]P5(f14(x941,x942,x943),x943)+P5(f14(x941,x942,x943),x942)+P5(f14(x941,x942,x943),x941)+E(x941,f18(x942,x943))
% 3.06/3.13 [87]~P5(x871,x872)+P4(x871,x872)+~P7(x874,x873,x872)+~P5(x871,x873)
% 3.06/3.13 [88]~P5(x881,x882)+P4(x881,x882)+~P7(x884,x882,x883)+~P5(x881,x883)
% 3.06/3.13 [71]~P5(x711,x714)+P5(x711,x712)+P5(x711,x713)+~E(x714,f18(x713,x712))
% 3.06/3.13 [98]~P5(x981,x983)+~P5(x981,x982)+P7(x981,x982,x983)+~P4(f16(x981,x982,x983),x983)+~P4(f16(x981,x982,x983),x982)
% 3.06/3.13 [89]~P3(x894)+~P4(x891,x892)+P7(x891,x892,x893)+~P7(x895,x892,x893)+~E(x894,f18(x892,x893))
% 3.06/3.13 [70]E(x703,x701)+~P4(x701,x704)+~P4(x703,x704)+E(x701,x702)+E(x703,x702)+~P4(x702,x704)
% 3.06/3.13 [93]~P4(x932,x935)+~P4(x931,x935)+~P1(x934,x935)+E(x931,x932)+P2(x933,x931,x934,x932)+~P8(x935,x933)
% 3.06/3.13 [86]P8(x862,x861)+~P8(x862,x863)+~P5(x864,x862)+~P4(x864,x863)+P8(x861,x862)+~P8(x861,x863)+~P5(x864,x861)
% 3.06/3.13 [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)
% 3.06/3.13 %EqnAxiom
% 3.06/3.13 [1]E(x11,x11)
% 3.06/3.13 [2]E(x22,x21)+~E(x21,x22)
% 3.06/3.13 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 3.06/3.13 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 3.06/3.13 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 3.06/3.13 [6]~E(x61,x62)+E(f17(x61),f17(x62))
% 3.06/3.13 [7]~E(x71,x72)+E(f3(x71,x73),f3(x72,x73))
% 3.06/3.13 [8]~E(x81,x82)+E(f3(x83,x81),f3(x83,x82))
% 3.06/3.13 [9]~E(x91,x92)+E(f12(x91,x93),f12(x92,x93))
% 3.06/3.13 [10]~E(x101,x102)+E(f12(x103,x101),f12(x103,x102))
% 3.06/3.13 [11]~E(x111,x112)+E(f18(x111,x113),f18(x112,x113))
% 3.06/3.13 [12]~E(x121,x122)+E(f18(x123,x121),f18(x123,x122))
% 3.06/3.13 [13]~E(x131,x132)+E(f7(x131,x133,x134,x135),f7(x132,x133,x134,x135))
% 3.06/3.13 [14]~E(x141,x142)+E(f7(x143,x141,x144,x145),f7(x143,x142,x144,x145))
% 3.06/3.13 [15]~E(x151,x152)+E(f7(x153,x154,x151,x155),f7(x153,x154,x152,x155))
% 3.06/3.13 [16]~E(x161,x162)+E(f7(x163,x164,x165,x161),f7(x163,x164,x165,x162))
% 3.06/3.13 [17]~E(x171,x172)+E(f14(x171,x173,x174),f14(x172,x173,x174))
% 3.06/3.13 [18]~E(x181,x182)+E(f14(x183,x181,x184),f14(x183,x182,x184))
% 3.06/3.13 [19]~E(x191,x192)+E(f14(x193,x194,x191),f14(x193,x194,x192))
% 3.06/3.13 [20]~E(x201,x202)+E(f16(x201,x203,x204),f16(x202,x203,x204))
% 3.06/3.13 [21]~E(x211,x212)+E(f16(x213,x211,x214),f16(x213,x212,x214))
% 3.06/3.13 [22]~E(x221,x222)+E(f16(x223,x224,x221),f16(x223,x224,x222))
% 3.06/3.13 [23]~E(x231,x232)+E(f13(x231,x233),f13(x232,x233))
% 3.06/3.13 [24]~E(x241,x242)+E(f13(x243,x241),f13(x243,x242))
% 3.06/3.13 [25]~E(x251,x252)+E(f15(x251,x253),f15(x252,x253))
% 3.06/3.13 [26]~E(x261,x262)+E(f15(x263,x261),f15(x263,x262))
% 3.06/3.13 [27]~E(x271,x272)+E(f4(x271,x273),f4(x272,x273))
% 3.06/3.13 [28]~E(x281,x282)+E(f4(x283,x281),f4(x283,x282))
% 3.06/3.13 [29]~E(x291,x292)+E(f5(x291,x293),f5(x292,x293))
% 3.06/3.13 [30]~E(x301,x302)+E(f5(x303,x301),f5(x303,x302))
% 3.06/3.13 [31]~E(x311,x312)+E(f19(x311,x313),f19(x312,x313))
% 3.06/3.13 [32]~E(x321,x322)+E(f19(x323,x321),f19(x323,x322))
% 3.06/3.13 [33]~E(x331,x332)+E(f6(x331,x333),f6(x332,x333))
% 3.06/3.13 [34]~E(x341,x342)+E(f6(x343,x341),f6(x343,x342))
% 3.06/3.13 [35]P1(x352,x353)+~E(x351,x352)+~P1(x351,x353)
% 3.06/3.13 [36]P1(x363,x362)+~E(x361,x362)+~P1(x363,x361)
% 3.06/3.13 [37]P2(x372,x373,x374,x375)+~E(x371,x372)+~P2(x371,x373,x374,x375)
% 3.06/3.13 [38]P2(x383,x382,x384,x385)+~E(x381,x382)+~P2(x383,x381,x384,x385)
% 3.06/3.13 [39]P2(x393,x394,x392,x395)+~E(x391,x392)+~P2(x393,x394,x391,x395)
% 3.06/3.13 [40]P2(x403,x404,x405,x402)+~E(x401,x402)+~P2(x403,x404,x405,x401)
% 3.06/3.13 [41]P4(x412,x413)+~E(x411,x412)+~P4(x411,x413)
% 3.06/3.13 [42]P4(x423,x422)+~E(x421,x422)+~P4(x423,x421)
% 3.06/3.13 [43]~P3(x431)+P3(x432)+~E(x431,x432)
% 3.06/3.13 [44]P5(x442,x443)+~E(x441,x442)+~P5(x441,x443)
% 3.06/3.13 [45]P5(x453,x452)+~E(x451,x452)+~P5(x453,x451)
% 3.06/3.13 [46]~P6(x461)+P6(x462)+~E(x461,x462)
% 3.06/3.13 [47]P7(x472,x473,x474)+~E(x471,x472)+~P7(x471,x473,x474)
% 3.06/3.13 [48]P7(x483,x482,x484)+~E(x481,x482)+~P7(x483,x481,x484)
% 3.06/3.13 [49]P7(x493,x494,x492)+~E(x491,x492)+~P7(x493,x494,x491)
% 3.06/3.13 [50]P8(x502,x503)+~E(x501,x502)+~P8(x501,x503)
% 3.06/3.13 [51]P8(x513,x512)+~E(x511,x512)+~P8(x513,x511)
% 3.06/3.13
% 3.06/3.13 %-------------------------------------------
% 3.06/3.13 cnf(103,plain,
% 3.06/3.13 (~P5(x1031,x1032)+P5(x1031,f18(x1033,x1032))),
% 3.06/3.13 inference(equality_inference,[],[67])).
% 3.06/3.13 cnf(107,plain,
% 3.06/3.13 (~P2(x1072,x1071,x1073,x1071)),
% 3.06/3.13 inference(equality_inference,[],[95])).
% 3.06/3.13 cnf(109,plain,
% 3.06/3.13 (~P2(x1091,x1092,x1093,x1092)),
% 3.06/3.13 inference(rename_variables,[],[107])).
% 3.06/3.13 cnf(110,plain,
% 3.06/3.13 (~E(a10,a8)),
% 3.06/3.13 inference(scs_inference,[],[53,107,109,38,40])).
% 3.06/3.13 cnf(112,plain,
% 3.06/3.13 (P2(x1121,a8,a9,a10)+~E(a2,x1121)),
% 3.06/3.13 inference(scs_inference,[],[53,107,109,38,40,37])).
% 3.06/3.13 cnf(113,plain,
% 3.06/3.13 (P2(a2,a8,x1131,a10)+~E(a9,x1131)),
% 3.06/3.13 inference(scs_inference,[],[53,107,109,38,40,37,39])).
% 3.06/3.13 cnf(219,plain,
% 3.06/3.13 (~P4(x2191,x2192)+P5(x2191,f18(x2193,x2192))),
% 3.06/3.13 inference(scs_inference,[],[60,103])).
% 3.06/3.13 cnf(451,plain,
% 3.06/3.13 (P4(f3(f7(a2,a8,a9,a10),a10),f7(a2,a8,a9,a10))),
% 3.06/3.13 inference(scs_inference,[],[53,69,99])).
% 3.06/3.13 cnf(454,plain,
% 3.06/3.13 (~P1(f3(f7(a2,a8,a9,a10),a10),f7(a2,a8,a9,a10))),
% 3.06/3.13 inference(scs_inference,[],[451,219,62])).
% 3.06/3.13 cnf(797,plain,
% 3.06/3.13 (~P8(x7971,a2)+~P4(a8,x7971)+~P4(a10,x7971)+~P1(a9,x7971)),
% 3.06/3.13 inference(scs_inference,[],[110,54,451,93])).
% 3.06/3.13 cnf(1000,plain,
% 3.06/3.13 (P4(a8,f7(x10001,a8,a9,a10))+~E(a2,x10001)),
% 3.06/3.13 inference(scs_inference,[],[100,112])).
% 3.06/3.13 cnf(1001,plain,
% 3.06/3.13 (P4(a8,f7(a2,a8,a9,a10))),
% 3.06/3.13 inference(equality_inference,[],[1000])).
% 3.06/3.13 cnf(1032,plain,
% 3.06/3.13 (P1(x10321,f7(a2,a8,x10321,a10))+~E(a9,x10321)),
% 3.06/3.13 inference(scs_inference,[],[101,113])).
% 3.06/3.13 cnf(1033,plain,
% 3.06/3.13 (P1(a9,f7(a2,a8,a9,a10))),
% 3.06/3.13 inference(equality_inference,[],[1032])).
% 3.06/3.13 cnf(1040,plain,
% 3.06/3.13 (~P4(a10,f7(a2,a8,a9,a10))+~P8(f7(a2,a8,a9,a10),a2)),
% 3.06/3.13 inference(scs_inference,[],[1001,1033,454,35,36,58,797])).
% 3.06/3.13 cnf(1139,plain,
% 3.06/3.13 (P8(f7(x11391,a8,a9,a10),x11391)+~E(a2,x11391)),
% 3.06/3.13 inference(scs_inference,[],[102,112])).
% 3.06/3.13 cnf(1140,plain,
% 3.06/3.13 (P8(f7(a2,a8,a9,a10),a2)),
% 3.06/3.13 inference(equality_inference,[],[1139])).
% 3.06/3.13 cnf(1143,plain,
% 3.06/3.13 (~P4(a10,f7(a2,a8,a9,a10))),
% 3.06/3.13 inference(scs_inference,[],[1140,1040])).
% 3.06/3.13 cnf(1156,plain,
% 3.06/3.13 ($false),
% 3.06/3.13 inference(scs_inference,[],[53,1143,99]),
% 3.06/3.13 ['proof']).
% 3.06/3.13 % SZS output end Proof
% 3.06/3.13 % Total time :2.510000s
%------------------------------------------------------------------------------