TSTP Solution File: NUN060+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN060+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n003.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 : Thu Aug 31 12:45:19 EDT 2023
% Result : Theorem 0.17s 0.82s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN060+2 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 09:58:09 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.56 start to proof:theBenchmark
% 0.17/0.81 %-------------------------------------------
% 0.17/0.81 % File :CSE---1.6
% 0.17/0.81 % Problem :theBenchmark
% 0.17/0.81 % Transform :cnf
% 0.17/0.81 % Format :tptp:raw
% 0.17/0.81 % Command :java -jar mcs_scs.jar %d %s
% 0.17/0.81
% 0.17/0.81 % Result :Theorem 0.190000s
% 0.17/0.81 % Output :CNFRefutation 0.190000s
% 0.17/0.81 %-------------------------------------------
% 0.17/0.82 %------------------------------------------------------------------------------
% 0.17/0.82 % File : NUN060+2 : TPTP v8.1.2. Released v7.3.0.
% 0.17/0.82 % Domain : Number Theory
% 0.17/0.82 % Problem : Robinson arithmetic: There exists X > 4
% 0.17/0.82 % Version : Especial.
% 0.17/0.82 % English :
% 0.17/0.82
% 0.17/0.82 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.17/0.82 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.17/0.82 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.17/0.82 % Source : [Lam18]
% 0.17/0.82 % Names : greq4 [Lam18]
% 0.17/0.82
% 0.17/0.82 % Status : Theorem
% 0.17/0.82 % Rating : 0.25 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.20 v7.3.0
% 0.17/0.82 % Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% 0.17/0.82 % Number of atoms : 51 ( 18 equ)
% 0.17/0.82 % Maximal formula atoms : 7 ( 4 avg)
% 0.17/0.82 % Number of connectives : 53 ( 14 ~; 10 |; 29 &)
% 0.17/0.82 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.82 % Maximal formula depth : 15 ( 8 avg)
% 0.17/0.82 % Maximal term depth : 1 ( 1 avg)
% 0.17/0.82 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 0.17/0.82 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.82 % Number of variables : 51 ( 23 !; 28 ?)
% 0.17/0.82 % SPC : FOF_THM_RFO_SEQ
% 0.17/0.82
% 0.17/0.82 % Comments : Translated to FOL with equality.
% 0.17/0.82 %------------------------------------------------------------------------------
% 0.17/0.82 include('Axioms/NUM008+0.ax').
% 0.17/0.82 %------------------------------------------------------------------------------
% 0.17/0.82 fof(greq4,conjecture,
% 0.17/0.82 ? [Y1,Y2,Y3] :
% 0.17/0.82 ( Y3 = Y1
% 0.17/0.82 & ? [Y4] :
% 0.17/0.82 ( r3(Y2,Y4,Y3)
% 0.17/0.82 & ? [Y5] :
% 0.17/0.82 ( r2(Y5,Y4)
% 0.17/0.82 & ? [Y6] :
% 0.17/0.82 ( r2(Y6,Y5)
% 0.17/0.82 & ? [Y7] :
% 0.17/0.82 ( r2(Y7,Y6)
% 0.17/0.82 & ? [Y8] :
% 0.17/0.82 ( r1(Y8)
% 0.17/0.82 & r2(Y8,Y7) ) ) ) ) ) ) ).
% 0.17/0.82
% 0.17/0.82 %------------------------------------------------------------------------------
% 0.17/0.82 %-------------------------------------------
% 0.17/0.82 % Proof found
% 0.17/0.82 % SZS status Theorem for theBenchmark
% 0.17/0.82 % SZS output start Proof
% 0.17/0.82 %ClaNum:63(EqnAxiom:35)
% 0.17/0.82 %VarNum:119(SingletonVarNum:58)
% 0.17/0.82 %MaxLitNum:7
% 0.17/0.82 %MaxfuncDepth:1
% 0.17/0.82 %SharedTerms:1
% 0.17/0.82 %goalClause: 63
% 0.17/0.82 [36]P1(f1(x361))
% 0.17/0.82 [37]P1(f4(x371))
% 0.17/0.82 [38]P1(f5(x381))
% 0.17/0.82 [41]P3(x411,f1(x411),x411)
% 0.17/0.82 [43]P4(x431,f5(x431),f4(x431))
% 0.17/0.82 [39]P2(x391,f6(x392,x391))
% 0.17/0.82 [40]P2(x401,f2(x402,x401))
% 0.17/0.82 [42]P2(f15(x421,x422),f7(x421,x422))
% 0.17/0.82 [44]P3(x441,x442,f15(x441,x442))
% 0.17/0.82 [45]P4(x451,x452,f3(x451,x452))
% 0.17/0.82 [46]P3(x461,f6(x461,x462),f7(x461,x462))
% 0.17/0.82 [47]P4(x471,f2(x471,x472),f16(x471,x472))
% 0.17/0.82 [48]P3(f3(x481,x482),x481,f16(x481,x482))
% 0.17/0.82 [49]P1(x491)+~E(x491,a8)
% 0.17/0.82 [50]~P1(x501)+E(x501,a8)
% 0.17/0.82 [51]E(f11(x511),x511)+E(f9(x511),x511)
% 0.17/0.82 [52]E(f11(x521),x521)+P1(f9(x521))
% 0.17/0.82 [55]P2(f10(x551),f11(x551))+E(f9(x551),x551)
% 0.17/0.82 [57]P2(f10(x571),f11(x571))+P1(f9(x571))
% 0.17/0.82 [53]P2(x531,x532)+~E(x532,f12(x531))
% 0.17/0.82 [54]~P2(x542,x541)+E(x541,f12(x542))
% 0.17/0.82 [59]P3(x591,x592,x593)+~E(x593,f13(x591,x592))
% 0.17/0.82 [60]P4(x601,x602,x603)+~E(x603,f14(x601,x602))
% 0.17/0.82 [61]~P3(x612,x613,x611)+E(x611,f13(x612,x613))
% 0.17/0.82 [62]~P4(x622,x623,x621)+E(x621,f14(x622,x623))
% 0.17/0.82 [56]~P1(x561)+~E(x561,x562)+~P2(x563,x562)
% 0.17/0.82 [58]~P2(x582,x584)+~P2(x581,x583)+E(x581,x582)+~E(x583,x584)
% 0.17/0.82 [63]~E(x631,x632)+~P2(x633,x634)+~P2(x634,x635)+~P3(x638,x637,x631)+~P1(x633)+~P2(x635,x636)+~P2(x636,x637)
% 0.17/0.82 %EqnAxiom
% 0.17/0.82 [1]E(x11,x11)
% 0.17/0.82 [2]E(x22,x21)+~E(x21,x22)
% 0.17/0.82 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.17/0.82 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 0.17/0.82 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 0.17/0.82 [6]~E(x61,x62)+E(f5(x61),f5(x62))
% 0.17/0.82 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.17/0.82 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.17/0.82 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93))
% 0.17/0.82 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102))
% 0.17/0.82 [11]~E(x111,x112)+E(f14(x111,x113),f14(x112,x113))
% 0.17/0.82 [12]~E(x121,x122)+E(f14(x123,x121),f14(x123,x122))
% 0.17/0.82 [13]~E(x131,x132)+E(f15(x131,x133),f15(x132,x133))
% 0.17/0.82 [14]~E(x141,x142)+E(f15(x143,x141),f15(x143,x142))
% 0.17/0.82 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.17/0.82 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.17/0.82 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.17/0.82 [18]~E(x181,x182)+E(f13(x181,x183),f13(x182,x183))
% 0.17/0.82 [19]~E(x191,x192)+E(f13(x193,x191),f13(x193,x192))
% 0.17/0.82 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.17/0.82 [21]~E(x211,x212)+E(f3(x211,x213),f3(x212,x213))
% 0.17/0.82 [22]~E(x221,x222)+E(f3(x223,x221),f3(x223,x222))
% 0.17/0.82 [23]~E(x231,x232)+E(f12(x231),f12(x232))
% 0.17/0.82 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 0.17/0.82 [25]~E(x251,x252)+E(f16(x251,x253),f16(x252,x253))
% 0.17/0.82 [26]~E(x261,x262)+E(f16(x263,x261),f16(x263,x262))
% 0.17/0.82 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 0.17/0.82 [28]P3(x282,x283,x284)+~E(x281,x282)+~P3(x281,x283,x284)
% 0.17/0.82 [29]P3(x293,x292,x294)+~E(x291,x292)+~P3(x293,x291,x294)
% 0.17/0.82 [30]P3(x303,x304,x302)+~E(x301,x302)+~P3(x303,x304,x301)
% 0.17/0.82 [31]P2(x312,x313)+~E(x311,x312)+~P2(x311,x313)
% 0.17/0.82 [32]P2(x323,x322)+~E(x321,x322)+~P2(x323,x321)
% 0.17/0.82 [33]P4(x332,x333,x334)+~E(x331,x332)+~P4(x331,x333,x334)
% 0.17/0.82 [34]P4(x343,x342,x344)+~E(x341,x342)+~P4(x343,x341,x344)
% 0.17/0.82 [35]P4(x353,x354,x352)+~E(x351,x352)+~P4(x353,x354,x351)
% 0.17/0.82
% 0.17/0.82 %-------------------------------------------
% 0.17/0.83 cnf(64,plain,
% 0.17/0.83 (~E(f1(x641),f6(x642,x643))),
% 0.17/0.83 inference(scs_inference,[],[36,39,56])).
% 0.17/0.83 cnf(68,plain,
% 0.17/0.83 (E(f6(x681,x682),f12(x682))),
% 0.17/0.83 inference(scs_inference,[],[36,39,56,2,50,54])).
% 0.17/0.83 cnf(70,plain,
% 0.17/0.83 (E(f16(x701,f1(x702)),f16(x701,a8))),
% 0.17/0.83 inference(scs_inference,[],[36,39,56,2,50,54,26])).
% 0.17/0.83 cnf(77,plain,
% 0.17/0.83 (E(f13(x771,f1(x772)),f13(x771,a8))),
% 0.17/0.83 inference(scs_inference,[],[36,39,56,2,50,54,26,25,24,23,22,21,20,19])).
% 0.17/0.83 cnf(83,plain,
% 0.17/0.83 (E(f15(f1(x831),x832),f15(a8,x832))),
% 0.17/0.83 inference(scs_inference,[],[36,39,56,2,50,54,26,25,24,23,22,21,20,19,18,17,16,15,14,13])).
% 0.17/0.83 cnf(86,plain,
% 0.17/0.83 (E(f2(x861,f1(x862)),f2(x861,a8))),
% 0.17/0.83 inference(scs_inference,[],[36,39,56,2,50,54,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10])).
% 0.17/0.83 cnf(95,plain,
% 0.17/0.83 (E(x951,f13(x951,f1(x951)))),
% 0.17/0.83 inference(scs_inference,[],[36,41,45,39,56,2,50,54,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,62,61])).
% 0.17/0.83 cnf(98,plain,
% 0.17/0.83 (~E(a8,f6(x981,x982))),
% 0.17/0.83 inference(scs_inference,[],[36,41,45,39,56,2,50,54,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,62,61,27,3])).
% 0.17/0.83 cnf(101,plain,
% 0.17/0.83 (P2(a8,f12(f1(x1011)))),
% 0.17/0.83 inference(scs_inference,[],[36,41,45,39,56,2,50,54,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,62,61,27,3,58,53])).
% 0.17/0.83 cnf(126,plain,
% 0.17/0.83 (E(x1261,f13(x1261,a8))),
% 0.17/0.83 inference(scs_inference,[],[43,46,45,95,77,34,33,28,3])).
% 0.17/0.83 cnf(127,plain,
% 0.17/0.83 (E(x1271,f13(x1271,f1(x1271)))),
% 0.17/0.83 inference(rename_variables,[],[95])).
% 0.17/0.83 cnf(128,plain,
% 0.17/0.83 (E(f13(x1281,f1(x1282)),f13(x1281,a8))),
% 0.17/0.83 inference(rename_variables,[],[77])).
% 0.17/0.83 cnf(133,plain,
% 0.17/0.83 (P2(f13(x1331,f1(x1331)),f2(x1332,x1331))),
% 0.17/0.83 inference(scs_inference,[],[40,43,46,45,95,127,68,77,101,34,33,28,3,56,2,31])).
% 0.17/0.83 cnf(134,plain,
% 0.17/0.83 (P2(x1341,f2(x1342,x1341))),
% 0.17/0.83 inference(rename_variables,[],[40])).
% 0.17/0.83 cnf(137,plain,
% 0.17/0.83 (P1(f13(a8,f1(a8)))),
% 0.17/0.83 inference(scs_inference,[],[40,43,46,48,41,45,95,127,68,77,101,34,33,28,3,56,2,31,30,29,49])).
% 0.17/0.83 cnf(142,plain,
% 0.17/0.83 (P2(x1421,f2(x1422,x1421))),
% 0.17/0.83 inference(rename_variables,[],[40])).
% 0.17/0.83 cnf(145,plain,
% 0.17/0.83 (~E(f2(x1451,a8),f12(f6(x1452,x1453)))),
% 0.17/0.83 inference(scs_inference,[],[36,40,134,43,46,48,41,45,39,95,127,68,64,70,77,86,101,34,33,28,3,56,2,31,30,29,49,63,58,53])).
% 0.17/0.83 cnf(148,plain,
% 0.17/0.83 (P1(f13(a8,a8))),
% 0.17/0.83 inference(scs_inference,[],[36,40,134,142,43,46,48,41,45,39,95,127,68,64,70,77,128,86,101,34,33,28,3,56,2,31,30,29,49,63,58,53,32,27])).
% 0.17/0.83 cnf(150,plain,
% 0.17/0.83 (~E(f6(x1501,x1502),a8)),
% 0.17/0.83 inference(scs_inference,[],[36,40,134,142,43,46,48,41,45,39,95,127,68,64,70,77,128,86,101,34,33,28,3,56,2,31,30,29,49,63,58,53,32,27,10])).
% 0.17/0.83 cnf(155,plain,
% 0.17/0.83 (E(f2(x1551,x1552),f2(x1551,f13(x1552,a8)))),
% 0.17/0.83 inference(scs_inference,[],[126,145,150,50,2,10])).
% 0.17/0.83 cnf(164,plain,
% 0.17/0.83 (E(x1641,f13(x1641,a8))),
% 0.17/0.83 inference(rename_variables,[],[126])).
% 0.17/0.83 cnf(167,plain,
% 0.17/0.83 (P2(x1671,f2(x1672,f13(x1671,a8)))),
% 0.17/0.83 inference(scs_inference,[],[37,40,155,98,148,126,164,50,27,3,32])).
% 0.17/0.83 cnf(274,plain,
% 0.17/0.83 ($false),
% 0.17/0.83 inference(scs_inference,[],[39,44,40,133,83,137,167,56,63]),
% 0.17/0.83 ['proof']).
% 0.17/0.83 % SZS output end Proof
% 0.17/0.83 % Total time :0.190000s
%------------------------------------------------------------------------------