%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 06:04:23 AM UTC 2026
% Result : Theorem 0.24s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 14:16:37 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 0.24/0.51 %-------------------------------------------
% 0.24/0.51 % File :CSE---1.7
% 0.24/0.51 % Problem :theBenchmark
% 0.24/0.51 % Transform :cnf
% 0.24/0.51 % Format :tptp:raw
% 0.24/0.51 % Command :java -jar mcs_scs.jar %d %s
% 0.24/0.51
% 0.24/0.51 % Result :Theorem 0.012457s
% 0.24/0.51 % Output :CNFRefutation 0.012457s
% 0.24/0.51 %-------------------------------------------
% 0.24/0.51 %--------------------------------------------------------------------------
% 0.24/0.51 % File : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.24/0.52 % Domain : Management
% 0.24/0.52 % Problem : width < 600 vs width >= 600: open/closed boundary
% 0.24/0.52 % Version : Especial.
% 0.24/0.52 % English : width lt 600 => (0, 600) width gteq 600 => [600, infinity)
% 0.24/0.52 % (0, 600) intersection [600, infinity) = null
% 0.24/0.52 % Conflict Criterion: u1=600 open, l2=600 closed => u1 =< l2.
% 0.24/0.52 % Proof is order contradiction (X<600 & X>=600); density not
% 0.24/0.52 % needed.
% 0.24/0.52
% 0.24/0.52 % Refs : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% 0.24/0.52 % Source : [MC+26]
% 0.24/0.52 % Names : ODRL302-1.p [MC+26]
% 0.24/0.52
% 0.24/0.52 % Status : Theorem
% 0.24/0.52 % Rating : ? v9.3.1
% 0.24/0.52 % Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% 0.24/0.52 % Number of atoms : 83 ( 24 equ)
% 0.24/0.52 % Maximal formula atoms : 7 ( 2 avg)
% 0.24/0.52 % Number of connectives : 60 ( 9 ~; 9 |; 22 &)
% 0.24/0.52 % ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% 0.24/0.52 % Maximal formula depth : 9 ( 5 avg)
% 0.24/0.52 % Maximal term depth : 2 ( 1 avg)
% 0.24/0.52 % Number of predicates : 12 ( 11 usr; 0 prp; 1-4 aty)
% 0.24/0.52 % Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% 0.24/0.52 % Number of variables : 58 ( 55 !; 3 ?)
% 0.24/0.52 % SPC : FOF_THM_RFO_SEQ
% 0.24/0.52
% 0.24/0.52 % Comments : Requires MGT002+0.ax + MGT002+2.ax.
% 0.24/0.52 % Bugfixes : v9.3.1 - $distinct expanded to inequalities.
% 0.24/0.52 %--------------------------------------------------------------------------
% 0.24/0.52 include('Axioms/MGT002+0.ax').
% 0.24/0.52 include('Axioms/MGT002+2.ax').
% 0.24/0.52 %--------------------------------------------------------------------------
% 0.24/0.52 %----Named constants and ordering
% 0.24/0.52 %----v0 = domain lower bound (excluded); v600 = constraint value
% 0.24/0.52 %----in_open(X,v0,v600) encodes (0,600) = sem(lt 600) over D_k=(0,inf)
% 0.24/0.52 fof(val_v0,axiom,
% 0.24/0.52 val(v0) ).
% 0.24/0.52
% 0.24/0.52 fof(val_v600,axiom,
% 0.24/0.52 val(v600) ).
% 0.24/0.52
% 0.24/0.52 fof(ord_v0_v600,axiom,
% 0.24/0.52 less(v0,v600) ).
% 0.24/0.52
% 0.24/0.52 fof(distinct,axiom,
% 0.24/0.52 v0 != v600 ).
% 0.24/0.52
% 0.24/0.52 fof(odrl302,conjecture,
% 0.24/0.52 ~ ? [X] :
% 0.24/0.52 ( in_open(X,v0,v600)
% 0.24/0.52 & leq(v600,X) ) ).
% 0.24/0.52
% 0.24/0.52 %--------------------------------------------------------------------------
% 0.24/0.52 %-------------------------------------------
% 0.24/0.52 % Proof found
% 0.24/0.52 % SZS status Theorem for theBenchmark
% 0.24/0.52 % SZS output start Proof
% 0.24/0.52 %ClaNum:98(EqnAxiom:47)
% 0.24/0.52 %VarNum:252(SingletonVarNum:111)
% 0.24/0.52 %MaxLitNum:6
% 0.24/0.52 %MaxfuncDepth:1
% 0.24/0.52 %SharedTerms:18
% 0.24/0.52 %goalClause: 54 55
% 0.24/0.52 %singleGoalClaCount:2
% 0.24/0.52 [48]P1(a1)
% 0.24/0.52 [49]P1(a2)
% 0.24/0.52 [50]P1(a4)
% 0.24/0.52 [51]P9(a9)
% 0.24/0.52 [52]P9(a10)
% 0.24/0.52 [53]P10(a9,a10)
% 0.24/0.52 [54]P11(a10,a5)
% 0.24/0.52 [55]P2(a5,a9,a10)
% 0.24/0.52 [56]~E(a1,a2)
% 0.24/0.52 [57]~E(a1,a4)
% 0.24/0.52 [58]~E(a4,a2)
% 0.24/0.52 [59]~E(a10,a9)
% 0.24/0.52 [60]~P10(x601,x601)
% 0.24/0.52 [62]~E(x621,x622)+P11(x621,x622)
% 0.24/0.52 [70]~P10(x701,x702)+P11(x701,x702)
% 0.24/0.52 [82]P10(x821,x822)+~P7(x822,x821,x823)
% 0.24/0.52 [83]P10(x831,x832)+~P8(x831,x833,x832)
% 0.24/0.52 [84]P10(x841,x842)+~P2(x842,x841,x843)
% 0.24/0.52 [85]P10(x851,x852)+~P2(x851,x853,x852)
% 0.24/0.52 [86]P11(x861,x862)+~P3(x862,x861,x863)
% 0.24/0.52 [87]P11(x871,x872)+~P3(x871,x873,x872)
% 0.24/0.52 [88]P11(x881,x882)+~P7(x881,x883,x882)
% 0.24/0.52 [89]P11(x891,x892)+~P8(x892,x891,x893)
% 0.24/0.52 [93]P6(x931,x932,x933,x934)+P3(f6(x931,x932,x933,x934),x933,x934)
% 0.24/0.52 [94]P6(x941,x942,x943,x944)+P3(f6(x941,x942,x943,x944),x941,x942)
% 0.24/0.52 [95]P5(x951,x952,x953,x954)+P3(f7(x951,x952,x953,x954),x951,x952)
% 0.24/0.52 [96]~P4(x961,x962,x963,x964)+P3(f8(x961,x962,x963,x964),x963,x964)
% 0.24/0.52 [97]~P4(x971,x972,x973,x974)+P3(f8(x971,x972,x973,x974),x971,x972)
% 0.24/0.52 [98]P5(x981,x982,x983,x984)+~P3(f7(x981,x982,x983,x984),x983,x984)
% 0.24/0.52 [63]P10(x632,x631)+P10(x631,x632)+E(x631,x632)
% 0.24/0.52 [71]P10(x711,x712)+~P11(x711,x712)+E(x711,x712)
% 0.24/0.52 [72]~P11(x722,x721)+~P11(x721,x722)+E(x721,x722)
% 0.24/0.52 [74]~P10(x741,x743)+P10(x741,x742)+~P10(x743,x742)
% 0.24/0.52 [75]~P11(x751,x753)+P10(x751,x752)+~P10(x753,x752)
% 0.24/0.52 [76]~P11(x763,x762)+P10(x761,x762)+~P10(x761,x763)
% 0.24/0.52 [77]~P11(x771,x773)+P11(x771,x772)+~P11(x773,x772)
% 0.24/0.52 [78]~P11(x781,x783)+~P11(x782,x781)+P3(x781,x782,x783)
% 0.24/0.52 [79]~P10(x792,x791)+~P11(x791,x793)+P7(x791,x792,x793)
% 0.24/0.52 [80]~P10(x801,x803)+~P11(x802,x801)+P8(x801,x802,x803)
% 0.24/0.52 [81]~P10(x811,x813)+~P10(x812,x811)+P2(x811,x812,x813)
% 0.24/0.52 [90]~P3(x905,x901,x902)+P4(x901,x902,x903,x904)+~P3(x905,x903,x904)
% 0.24/0.52 [91]~P5(x914,x915,x912,x913)+P3(x911,x912,x913)+~P3(x911,x914,x915)
% 0.24/0.52 [92]~P6(x924,x925,x922,x923)+~P3(x921,x922,x923)+~P3(x921,x924,x925)
% 0.24/0.52 [61]~P1(x611)+E(x611,a2)+E(x611,a4)+E(x611,a1)
% 0.24/0.52 [64]~P1(x641)+~P1(x642)+~E(x642,a1)+E(f3(x641,x642),a1)
% 0.24/0.52 [65]~P1(x652)+~P1(x651)+~E(x651,a1)+E(f3(x651,x652),a1)
% 0.24/0.52 [66]~P1(x662)+~P1(x661)+~E(x662,a2)+~E(x661,a2)+E(f3(x661,x662),a2)
% 0.24/0.52 [73]~P1(x732)+~P1(x731)+E(f3(x731,x732),a1)+E(f3(x731,x732),a2)+E(f3(x731,x732),a4)
% 0.24/0.52 [67]~P1(x671)+~P1(x672)+~E(x672,a4)+E(x671,a1)+E(x672,a1)+E(f3(x671,x672),a4)
% 0.24/0.52 [68]~P1(x681)+~P1(x682)+~E(x682,a4)+E(x681,a1)+E(x682,a1)+E(f3(x682,x681),a4)
% 0.24/0.52 %EqnAxiom
% 0.24/0.52 [1]E(x11,x11)
% 0.24/0.52 [2]E(x22,x21)+~E(x21,x22)
% 0.24/0.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.24/0.52 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.24/0.52 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.24/0.52 [6]~E(x61,x62)+E(f7(x61,x63,x64,x65),f7(x62,x63,x64,x65))
% 0.24/0.52 [7]~E(x71,x72)+E(f7(x73,x71,x74,x75),f7(x73,x72,x74,x75))
% 0.24/0.52 [8]~E(x81,x82)+E(f7(x83,x84,x81,x85),f7(x83,x84,x82,x85))
% 0.24/0.52 [9]~E(x91,x92)+E(f7(x93,x94,x95,x91),f7(x93,x94,x95,x92))
% 0.24/0.52 [10]~E(x101,x102)+E(f8(x101,x103,x104,x105),f8(x102,x103,x104,x105))
% 0.24/0.52 [11]~E(x111,x112)+E(f8(x113,x111,x114,x115),f8(x113,x112,x114,x115))
% 0.24/0.52 [12]~E(x121,x122)+E(f8(x123,x124,x121,x125),f8(x123,x124,x122,x125))
% 0.24/0.52 [13]~E(x131,x132)+E(f8(x133,x134,x135,x131),f8(x133,x134,x135,x132))
% 0.24/0.52 [14]~E(x141,x142)+E(f6(x141,x143,x144,x145),f6(x142,x143,x144,x145))
% 0.24/0.52 [15]~E(x151,x152)+E(f6(x153,x151,x154,x155),f6(x153,x152,x154,x155))
% 0.24/0.52 [16]~E(x161,x162)+E(f6(x163,x164,x161,x165),f6(x163,x164,x162,x165))
% 0.24/0.52 [17]~E(x171,x172)+E(f6(x173,x174,x175,x171),f6(x173,x174,x175,x172))
% 0.24/0.52 [18]~P1(x181)+P1(x182)+~E(x181,x182)
% 0.24/0.52 [19]P3(x192,x193,x194)+~E(x191,x192)+~P3(x191,x193,x194)
% 0.24/0.52 [20]P3(x203,x202,x204)+~E(x201,x202)+~P3(x203,x201,x204)
% 0.24/0.52 [21]P3(x213,x214,x212)+~E(x211,x212)+~P3(x213,x214,x211)
% 0.24/0.52 [22]P5(x222,x223,x224,x225)+~E(x221,x222)+~P5(x221,x223,x224,x225)
% 0.24/0.52 [23]P5(x233,x232,x234,x235)+~E(x231,x232)+~P5(x233,x231,x234,x235)
% 0.24/0.52 [24]P5(x243,x244,x242,x245)+~E(x241,x242)+~P5(x243,x244,x241,x245)
% 0.24/0.52 [25]P5(x253,x254,x255,x252)+~E(x251,x252)+~P5(x253,x254,x255,x251)
% 0.24/0.52 [26]~P9(x261)+P9(x262)+~E(x261,x262)
% 0.24/0.52 [27]P2(x272,x273,x274)+~E(x271,x272)+~P2(x271,x273,x274)
% 0.24/0.52 [28]P2(x283,x282,x284)+~E(x281,x282)+~P2(x283,x281,x284)
% 0.24/0.52 [29]P2(x293,x294,x292)+~E(x291,x292)+~P2(x293,x294,x291)
% 0.24/0.52 [30]P10(x302,x303)+~E(x301,x302)+~P10(x301,x303)
% 0.24/0.52 [31]P10(x313,x312)+~E(x311,x312)+~P10(x313,x311)
% 0.24/0.52 [32]P11(x322,x323)+~E(x321,x322)+~P11(x321,x323)
% 0.24/0.52 [33]P11(x333,x332)+~E(x331,x332)+~P11(x333,x331)
% 0.24/0.52 [34]P7(x342,x343,x344)+~E(x341,x342)+~P7(x341,x343,x344)
% 0.24/0.52 [35]P7(x353,x352,x354)+~E(x351,x352)+~P7(x353,x351,x354)
% 0.24/0.52 [36]P7(x363,x364,x362)+~E(x361,x362)+~P7(x363,x364,x361)
% 0.24/0.53 [37]P6(x372,x373,x374,x375)+~E(x371,x372)+~P6(x371,x373,x374,x375)
% 0.24/0.53 [38]P6(x383,x382,x384,x385)+~E(x381,x382)+~P6(x383,x381,x384,x385)
% 0.24/0.53 [39]P6(x393,x394,x392,x395)+~E(x391,x392)+~P6(x393,x394,x391,x395)
% 0.24/0.53 [40]P6(x403,x404,x405,x402)+~E(x401,x402)+~P6(x403,x404,x405,x401)
% 0.24/0.53 [41]P4(x412,x413,x414,x415)+~E(x411,x412)+~P4(x411,x413,x414,x415)
% 0.24/0.53 [42]P4(x423,x422,x424,x425)+~E(x421,x422)+~P4(x423,x421,x424,x425)
% 0.24/0.53 [43]P4(x433,x434,x432,x435)+~E(x431,x432)+~P4(x433,x434,x431,x435)
% 0.24/0.53 [44]P4(x443,x444,x445,x442)+~E(x441,x442)+~P4(x443,x444,x445,x441)
% 0.24/0.53 [45]P8(x452,x453,x454)+~E(x451,x452)+~P8(x451,x453,x454)
% 0.24/0.53 [46]P8(x463,x462,x464)+~E(x461,x462)+~P8(x463,x461,x464)
% 0.24/0.53 [47]P8(x473,x474,x472)+~E(x471,x472)+~P8(x473,x474,x471)
% 0.24/0.53
% 0.24/0.53 %-------------------------------------------
% 0.24/0.53 cnf(108,plain,
% 0.24/0.53 (~P2(x1081,x1081,x1082)),
% 0.24/0.53 inference(scs_inference,[],[60,84])).
% 0.24/0.53 cnf(110,plain,
% 0.24/0.53 (~P2(x1101,x1102,x1101)),
% 0.24/0.53 inference(scs_inference,[],[60,84,85])).
% 0.24/0.53 cnf(116,plain,
% 0.24/0.53 (P10(a9,a5)),
% 0.24/0.53 inference(scs_inference,[],[54,60,53,84,85,82,83,76])).
% 0.24/0.53 cnf(121,plain,
% 0.24/0.53 (P2(a5,a9,a5)+P10(a10,a5)),
% 0.24/0.53 inference(scs_inference,[],[54,55,60,53,84,85,82,83,76,27,71,29])).
% 0.24/0.53 cnf(130,plain,
% 0.24/0.53 (~P2(x1301,x1302,x1301)),
% 0.24/0.53 inference(rename_variables,[],[110])).
% 0.24/0.53 cnf(134,plain,
% 0.24/0.53 (~P10(x1341,x1341)),
% 0.24/0.53 inference(rename_variables,[],[60])).
% 0.24/0.53 cnf(139,plain,
% 0.24/0.53 (~P10(x1391,x1391)),
% 0.24/0.53 inference(rename_variables,[],[60])).
% 0.24/0.53 cnf(153,plain,
% 0.24/0.53 (~P10(a5,a10)),
% 0.24/0.53 inference(scs_inference,[],[54,55,108,110,130,116,60,134,139,53,121,29,74,28,31,30,83,84,82,85,72,33,70])).
% 0.24/0.53 cnf(168,plain,
% 0.24/0.53 ($false),
% 0.24/0.53 inference(scs_inference,[],[55,153,84,85]),
% 0.24/0.53 ['proof']).
% 0.24/0.53 % SZS output end Proof
% 0.24/0.53 % Total time :0.012457s
%------------------------------------------------------------------------------