%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:04:24 AM UTC 2026
% Result : Theorem 0.26s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.07/0.34 % Computer : n029.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 14:23:26 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.26/0.51 start to proof:theBenchmark
% 0.26/0.51 %-------------------------------------------
% 0.26/0.51 % File :CSE---1.7
% 0.26/0.51 % Problem :theBenchmark
% 0.26/0.51 % Transform :cnf
% 0.26/0.51 % Format :tptp:raw
% 0.26/0.51 % Command :java -jar mcs_scs.jar %d %s
% 0.26/0.51
% 0.26/0.51 % Result :Theorem 0.010204s
% 0.26/0.51 % Output :CNFRefutation 0.010204s
% 0.26/0.51 %-------------------------------------------
% 0.26/0.51 %--------------------------------------------------------------------------
% 0.26/0.51 % File : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.26/0.51 % Domain : Management
% 0.26/0.51 % Problem : totality - lteq denotation is non-empty
% 0.26/0.51 % Version : Especial.
% 0.26/0.51 % English :
% 0.26/0.51
% 0.26/0.51 % Refs [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% 0.26/0.51 % Source [MC+26]
% 0.26/0.51 % Names ODRL500-1.p [MC+26]
% 0.26/0.51
% 0.26/0.51 % Status : Theorem
% 0.26/0.51 % Rating : ? v9.3.1
% 0.26/0.51 % Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% 0.26/0.51 % Number of atoms : 87 ( 26 equ)
% 0.26/0.51 % Maximal formula atoms : 7 ( 2 avg)
% 0.26/0.51 % Number of connectives : 62 ( 10 ~; 9 |; 23 &)
% 0.26/0.51 % ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% 0.26/0.51 % Maximal formula depth : 9 ( 4 avg)
% 0.26/0.51 % Maximal term depth : 2 ( 1 avg)
% 0.26/0.51 % Number of predicates : 12 ( 11 usr; 0 prp; 1-4 aty)
% 0.26/0.51 % Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% 0.26/0.51 % Number of variables : 58 ( 55 !; 3 ?)
% 0.26/0.51 % SPC : FOF_THM_RFO_SEQ
% 0.26/0.51
% 0.26/0.51 % Comments : Requires MGT002+0.ax + MGT002+2.ax.
% 0.26/0.51 % Bugfixes : v9.3.1 - $distinct expanded to inequalities.
% 0.26/0.51 %--------------------------------------------------------------------------
% 0.26/0.51 include('Axioms/MGT002+0.ax').
% 0.26/0.51 include('Axioms/MGT002+2.ax').
% 0.26/0.51 %--------------------------------------------------------------------------
% 0.26/0.51 %----Named constants and ordering
% 0.26/0.51 fof(val_v0,axiom,
% 0.26/0.51 val(v0) ).
% 0.26/0.51
% 0.26/0.51 fof(val_v200,axiom,
% 0.26/0.51 val(v200) ).
% 0.26/0.51
% 0.26/0.51 fof(val_v600,axiom,
% 0.26/0.51 val(v600) ).
% 0.26/0.51
% 0.26/0.51 fof(ord_v0_v200,axiom,
% 0.26/0.51 less(v0,v200) ).
% 0.26/0.51
% 0.26/0.51 fof(ord_v0_v600,axiom,
% 0.26/0.51 less(v0,v600) ).
% 0.26/0.51
% 0.26/0.51 fof(ord_v200_v600,axiom,
% 0.26/0.51 less(v200,v600) ).
% 0.26/0.51
% 0.26/0.51 fof(distinct,axiom,
% 0.26/0.51 ( v0 != v200
% 0.26/0.51 & v0 != v600
% 0.26/0.51 & v200 != v600 ) ).
% 0.26/0.51
% 0.26/0.51 fof(odrl500,conjecture,
% 0.26/0.51 ? [X] : in_lopen(X,v0,v600) ).
% 0.26/0.51
% 0.26/0.51 %--------------------------------------------------------------------------
% 0.26/0.51 %-------------------------------------------
% 0.26/0.51 % Proof found
% 0.26/0.51 % SZS status Theorem for theBenchmark
% 0.26/0.51 % SZS output start Proof
% 0.26/0.51 %ClaNum:102(EqnAxiom:47)
% 0.26/0.51 %VarNum:253(SingletonVarNum:112)
% 0.26/0.51 %MaxLitNum:6
% 0.26/0.51 %MaxfuncDepth:1
% 0.26/0.51 %SharedTerms:21
% 0.26/0.51 %goalClause: 64
% 0.26/0.51 %singleGoalClaCount:1
% 0.26/0.51 [48]P1(a1)
% 0.26/0.51 [49]P1(a2)
% 0.26/0.51 [50]P1(a4)
% 0.26/0.51 [51]P9(a8)
% 0.26/0.51 [52]P9(a9)
% 0.26/0.51 [53]P9(a10)
% 0.26/0.51 [54]P10(a8,a9)
% 0.26/0.51 [55]P10(a8,a10)
% 0.26/0.51 [56]P10(a9,a10)
% 0.26/0.51 [57]~E(a1,a2)
% 0.26/0.51 [58]~E(a1,a4)
% 0.26/0.51 [59]~E(a4,a2)
% 0.26/0.51 [60]~E(a9,a8)
% 0.26/0.51 [61]~E(a10,a8)
% 0.26/0.51 [62]~E(a10,a9)
% 0.26/0.51 [63]~P10(x631,x631)
% 0.26/0.51 [64]~P2(x641,a8,a10)
% 0.26/0.51 [66]~E(x661,x662)+P11(x661,x662)
% 0.26/0.51 [74]~P10(x741,x742)+P11(x741,x742)
% 0.26/0.51 [86]P10(x861,x862)+~P2(x862,x861,x863)
% 0.26/0.51 [87]P10(x871,x872)+~P7(x871,x873,x872)
% 0.26/0.51 [88]P10(x881,x882)+~P8(x882,x881,x883)
% 0.26/0.51 [89]P10(x891,x892)+~P8(x891,x893,x892)
% 0.26/0.51 [90]P11(x901,x902)+~P3(x902,x901,x903)
% 0.26/0.51 [91]P11(x911,x912)+~P3(x911,x913,x912)
% 0.26/0.51 [92]P11(x921,x922)+~P2(x921,x923,x922)
% 0.26/0.51 [93]P11(x931,x932)+~P7(x932,x931,x933)
% 0.26/0.51 [97]P6(x971,x972,x973,x974)+P3(f5(x971,x972,x973,x974),x973,x974)
% 0.26/0.51 [98]P6(x981,x982,x983,x984)+P3(f5(x981,x982,x983,x984),x981,x982)
% 0.26/0.51 [99]P5(x991,x992,x993,x994)+P3(f6(x991,x992,x993,x994),x991,x992)
% 0.26/0.51 [100]~P4(x1001,x1002,x1003,x1004)+P3(f7(x1001,x1002,x1003,x1004),x1003,x1004)
% 0.26/0.51 [101]~P4(x1011,x1012,x1013,x1014)+P3(f7(x1011,x1012,x1013,x1014),x1011,x1012)
% 0.26/0.51 [102]P5(x1021,x1022,x1023,x1024)+~P3(f6(x1021,x1022,x1023,x1024),x1023,x1024)
% 0.26/0.51 [67]P10(x672,x671)+P10(x671,x672)+E(x671,x672)
% 0.26/0.51 [75]P10(x751,x752)+~P11(x751,x752)+E(x751,x752)
% 0.26/0.51 [76]~P11(x762,x761)+~P11(x761,x762)+E(x761,x762)
% 0.26/0.51 [78]~P10(x781,x783)+P10(x781,x782)+~P10(x783,x782)
% 0.26/0.51 [79]~P11(x791,x793)+P10(x791,x792)+~P10(x793,x792)
% 0.26/0.51 [80]~P11(x803,x802)+P10(x801,x802)+~P10(x801,x803)
% 0.26/0.51 [81]~P11(x811,x813)+P11(x811,x812)+~P11(x813,x812)
% 0.26/0.51 [82]~P11(x821,x823)+~P11(x822,x821)+P3(x821,x822,x823)
% 0.26/0.51 [83]~P10(x832,x831)+~P11(x831,x833)+P2(x831,x832,x833)
% 0.26/0.51 [84]~P10(x841,x843)+~P11(x842,x841)+P7(x841,x842,x843)
% 0.26/0.51 [85]~P10(x851,x853)+~P10(x852,x851)+P8(x851,x852,x853)
% 0.26/0.51 [94]~P3(x945,x941,x942)+P4(x941,x942,x943,x944)+~P3(x945,x943,x944)
% 0.26/0.51 [95]~P5(x954,x955,x952,x953)+P3(x951,x952,x953)+~P3(x951,x954,x955)
% 0.26/0.51 [96]~P6(x964,x965,x962,x963)+~P3(x961,x962,x963)+~P3(x961,x964,x965)
% 0.26/0.51 [65]~P1(x651)+E(x651,a2)+E(x651,a4)+E(x651,a1)
% 0.26/0.51 [68]~P1(x681)+~P1(x682)+~E(x682,a1)+E(f3(x681,x682),a1)
% 0.26/0.51 [69]~P1(x692)+~P1(x691)+~E(x691,a1)+E(f3(x691,x692),a1)
% 0.26/0.51 [70]~P1(x702)+~P1(x701)+~E(x702,a2)+~E(x701,a2)+E(f3(x701,x702),a2)
% 0.26/0.52 [77]~P1(x772)+~P1(x771)+E(f3(x771,x772),a1)+E(f3(x771,x772),a2)+E(f3(x771,x772),a4)
% 0.26/0.52 [71]~P1(x711)+~P1(x712)+~E(x712,a4)+E(x711,a1)+E(x712,a1)+E(f3(x711,x712),a4)
% 0.26/0.52 [72]~P1(x721)+~P1(x722)+~E(x722,a4)+E(x721,a1)+E(x722,a1)+E(f3(x722,x721),a4)
% 0.26/0.52 %EqnAxiom
% 0.26/0.52 [1]E(x11,x11)
% 0.26/0.52 [2]E(x22,x21)+~E(x21,x22)
% 0.26/0.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.26/0.52 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.26/0.52 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.26/0.52 [6]~E(x61,x62)+E(f6(x61,x63,x64,x65),f6(x62,x63,x64,x65))
% 0.26/0.52 [7]~E(x71,x72)+E(f6(x73,x71,x74,x75),f6(x73,x72,x74,x75))
% 0.26/0.52 [8]~E(x81,x82)+E(f6(x83,x84,x81,x85),f6(x83,x84,x82,x85))
% 0.26/0.52 [9]~E(x91,x92)+E(f6(x93,x94,x95,x91),f6(x93,x94,x95,x92))
% 0.26/0.52 [10]~E(x101,x102)+E(f7(x101,x103,x104,x105),f7(x102,x103,x104,x105))
% 0.26/0.52 [11]~E(x111,x112)+E(f7(x113,x111,x114,x115),f7(x113,x112,x114,x115))
% 0.26/0.52 [12]~E(x121,x122)+E(f7(x123,x124,x121,x125),f7(x123,x124,x122,x125))
% 0.26/0.52 [13]~E(x131,x132)+E(f7(x133,x134,x135,x131),f7(x133,x134,x135,x132))
% 0.26/0.52 [14]~E(x141,x142)+E(f5(x141,x143,x144,x145),f5(x142,x143,x144,x145))
% 0.26/0.52 [15]~E(x151,x152)+E(f5(x153,x151,x154,x155),f5(x153,x152,x154,x155))
% 0.26/0.52 [16]~E(x161,x162)+E(f5(x163,x164,x161,x165),f5(x163,x164,x162,x165))
% 0.26/0.52 [17]~E(x171,x172)+E(f5(x173,x174,x175,x171),f5(x173,x174,x175,x172))
% 0.26/0.52 [18]~P1(x181)+P1(x182)+~E(x181,x182)
% 0.26/0.52 [19]P3(x192,x193,x194)+~E(x191,x192)+~P3(x191,x193,x194)
% 0.26/0.52 [20]P3(x203,x202,x204)+~E(x201,x202)+~P3(x203,x201,x204)
% 0.26/0.52 [21]P3(x213,x214,x212)+~E(x211,x212)+~P3(x213,x214,x211)
% 0.26/0.52 [22]P5(x222,x223,x224,x225)+~E(x221,x222)+~P5(x221,x223,x224,x225)
% 0.26/0.52 [23]P5(x233,x232,x234,x235)+~E(x231,x232)+~P5(x233,x231,x234,x235)
% 0.26/0.52 [24]P5(x243,x244,x242,x245)+~E(x241,x242)+~P5(x243,x244,x241,x245)
% 0.26/0.52 [25]P5(x253,x254,x255,x252)+~E(x251,x252)+~P5(x253,x254,x255,x251)
% 0.26/0.52 [26]~P9(x261)+P9(x262)+~E(x261,x262)
% 0.26/0.52 [27]P8(x272,x273,x274)+~E(x271,x272)+~P8(x271,x273,x274)
% 0.26/0.52 [28]P8(x283,x282,x284)+~E(x281,x282)+~P8(x283,x281,x284)
% 0.26/0.52 [29]P8(x293,x294,x292)+~E(x291,x292)+~P8(x293,x294,x291)
% 0.26/0.52 [30]P10(x302,x303)+~E(x301,x302)+~P10(x301,x303)
% 0.26/0.52 [31]P10(x313,x312)+~E(x311,x312)+~P10(x313,x311)
% 0.26/0.52 [32]P2(x322,x323,x324)+~E(x321,x322)+~P2(x321,x323,x324)
% 0.26/0.52 [33]P2(x333,x332,x334)+~E(x331,x332)+~P2(x333,x331,x334)
% 0.26/0.52 [34]P2(x343,x344,x342)+~E(x341,x342)+~P2(x343,x344,x341)
% 0.26/0.52 [35]P11(x352,x353)+~E(x351,x352)+~P11(x351,x353)
% 0.26/0.52 [36]P11(x363,x362)+~E(x361,x362)+~P11(x363,x361)
% 0.26/0.52 [37]P7(x372,x373,x374)+~E(x371,x372)+~P7(x371,x373,x374)
% 0.26/0.52 [38]P7(x383,x382,x384)+~E(x381,x382)+~P7(x383,x381,x384)
% 0.26/0.52 [39]P7(x393,x394,x392)+~E(x391,x392)+~P7(x393,x394,x391)
% 0.26/0.52 [40]P6(x402,x403,x404,x405)+~E(x401,x402)+~P6(x401,x403,x404,x405)
% 0.26/0.52 [41]P6(x413,x412,x414,x415)+~E(x411,x412)+~P6(x413,x411,x414,x415)
% 0.26/0.52 [42]P6(x423,x424,x422,x425)+~E(x421,x422)+~P6(x423,x424,x421,x425)
% 0.26/0.52 [43]P6(x433,x434,x435,x432)+~E(x431,x432)+~P6(x433,x434,x435,x431)
% 0.26/0.52 [44]P4(x442,x443,x444,x445)+~E(x441,x442)+~P4(x441,x443,x444,x445)
% 0.26/0.52 [45]P4(x453,x452,x454,x455)+~E(x451,x452)+~P4(x453,x451,x454,x455)
% 0.26/0.52 [46]P4(x463,x464,x462,x465)+~E(x461,x462)+~P4(x463,x464,x461,x465)
% 0.26/0.52 [47]P4(x473,x474,x475,x472)+~E(x471,x472)+~P4(x473,x474,x475,x471)
% 0.26/0.52
% 0.26/0.52 %-------------------------------------------
% 0.26/0.52 cnf(103,plain,
% 0.26/0.52 (P11(x1031,x1031)),
% 0.26/0.52 inference(equality_inference,[],[66])).
% 0.26/0.52 cnf(124,plain,
% 0.26/0.52 (~P10(x1241,x1241)),
% 0.26/0.52 inference(rename_variables,[],[63])).
% 0.26/0.52 cnf(130,plain,
% 0.26/0.52 ($false),
% 0.26/0.52 inference(scs_inference,[],[64,54,103,56,63,124,86,87,88,89,83,78,30,36,74]),
% 0.26/0.52 ['proof']).
% 0.26/0.52 % SZS output end Proof
% 0.26/0.52 % Total time :0.010204s
%------------------------------------------------------------------------------