%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN076+2 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 13:29:40 EDT 2024
% Result : Theorem 1.61s 1.70s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.15 % Problem : NUN076+2 : TPTP v8.2.0. Released v7.3.0.
% 0.05/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37 % Computer : n014.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Jun 18 21:27:24 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.23/0.61 start to proof:theBenchmark
% 1.61/1.70 %-------------------------------------------
% 1.61/1.70 % File :CSE---1.7
% 1.61/1.70 % Problem :theBenchmark
% 1.61/1.70 % Transform :cnf
% 1.61/1.70 % Format :tptp:raw
% 1.61/1.70 % Command :java -jar mcs_scs.jar %d %s
% 1.61/1.70
% 1.61/1.70 % Result :Theorem 1.040000s
% 1.61/1.70 % Output :CNFRefutation 1.040000s
% 1.61/1.70 %-------------------------------------------
% 1.61/1.70 %------------------------------------------------------------------------------
% 1.61/1.70 % File : NUN076+2 : TPTP v8.2.0. Released v7.3.0.
% 1.61/1.70 % Domain : Number Theory
% 1.61/1.70 % Problem : Robinson arithmetic: There exists even X
% 1.61/1.70 % Version : Especial.
% 1.61/1.70 % English :
% 1.61/1.70
% 1.61/1.70 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 1.61/1.70 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 1.61/1.70 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 1.61/1.70 % Source : [Lam18]
% 1.61/1.70 % Names : thereexistsanevennumber [Lam18]
% 1.61/1.70
% 1.61/1.70 % Status : Theorem
% 1.61/1.70 % Rating : 0.25 v8.2.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.20 v7.3.0
% 1.61/1.70 % Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% 1.61/1.70 % Number of atoms : 51 ( 19 equ)
% 1.61/1.70 % Maximal formula atoms : 7 ( 4 avg)
% 1.61/1.70 % Number of connectives : 53 ( 14 ~; 10 |; 29 &)
% 1.61/1.70 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 1.61/1.70 % Maximal formula depth : 13 ( 8 avg)
% 1.61/1.70 % Maximal term depth : 1 ( 1 avg)
% 1.61/1.70 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 1.61/1.70 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 1.61/1.70 % Number of variables : 51 ( 23 !; 28 ?)
% 1.61/1.70 % SPC : FOF_THM_RFO_SEQ
% 1.61/1.70
% 1.61/1.70 % Comments : Translated to FOL with equality.
% 1.61/1.70 %------------------------------------------------------------------------------
% 1.61/1.70 include('Axioms/NUM008+0.ax').
% 1.61/1.70 %------------------------------------------------------------------------------
% 1.61/1.70 fof(thereexistsanevennumber,conjecture,
% 1.61/1.70 ? [Y1,Y2,Y3] :
% 1.61/1.70 ( ? [Y4] :
% 1.61/1.70 ( Y4 = Y1
% 1.61/1.70 & ? [Y6] :
% 1.61/1.70 ( r4(Y6,Y2,Y4)
% 1.61/1.70 & ? [Y7] :
% 1.61/1.70 ( r2(Y7,Y6)
% 1.61/1.70 & ? [Y8] :
% 1.61/1.70 ( r1(Y8)
% 1.61/1.70 & r2(Y8,Y7) ) ) ) )
% 1.61/1.70 & ? [Y5] :
% 1.61/1.70 ( r3(Y2,Y3,Y5)
% 1.61/1.70 & Y5 = Y1 ) ) ).
% 1.61/1.70
% 1.61/1.70 %------------------------------------------------------------------------------
% 1.61/1.70 %-------------------------------------------
% 1.61/1.70 % Proof found
% 1.61/1.70 % SZS status Theorem for theBenchmark
% 1.61/1.70 % SZS output start Proof
% 1.61/1.70 %ClaNum:63(EqnAxiom:35)
% 1.61/1.70 %VarNum:120(SingletonVarNum:58)
% 1.61/1.70 %MaxLitNum:7
% 1.61/1.70 %MaxfuncDepth:1
% 1.61/1.70 %SharedTerms:1
% 1.61/1.70 %goalClause: 63
% 1.61/1.70 [36]P1(f1(x361))
% 1.61/1.70 [37]P1(f4(x371))
% 1.61/1.70 [38]P1(f5(x381))
% 1.61/1.70 [41]P3(x411,f1(x411),x411)
% 1.61/1.70 [43]P4(x431,f5(x431),f4(x431))
% 1.61/1.70 [39]P2(x391,f6(x392,x391))
% 1.61/1.70 [40]P2(x401,f2(x402,x401))
% 1.61/1.70 [42]P2(f15(x421,x422),f7(x421,x422))
% 1.61/1.70 [44]P3(x441,x442,f15(x441,x442))
% 1.61/1.70 [45]P4(x451,x452,f3(x451,x452))
% 1.61/1.70 [46]P3(x461,f6(x461,x462),f7(x461,x462))
% 1.61/1.70 [47]P4(x471,f2(x471,x472),f16(x471,x472))
% 1.61/1.70 [48]P3(f3(x481,x482),x481,f16(x481,x482))
% 1.61/1.70 [49]P1(x491)+~E(x491,a8)
% 1.61/1.70 [50]~P1(x501)+E(x501,a8)
% 1.61/1.70 [51]E(f11(x511),x511)+E(f9(x511),x511)
% 1.61/1.70 [52]E(f11(x521),x521)+P1(f9(x521))
% 1.61/1.70 [55]P2(f10(x551),f11(x551))+E(f9(x551),x551)
% 1.61/1.70 [57]P2(f10(x571),f11(x571))+P1(f9(x571))
% 1.61/1.70 [53]P2(x531,x532)+~E(x532,f12(x531))
% 1.61/1.70 [54]~P2(x542,x541)+E(x541,f12(x542))
% 1.61/1.70 [59]P3(x591,x592,x593)+~E(x593,f13(x591,x592))
% 1.61/1.70 [60]P4(x601,x602,x603)+~E(x603,f14(x601,x602))
% 1.61/1.70 [61]~P3(x612,x613,x611)+E(x611,f13(x612,x613))
% 1.61/1.70 [62]~P4(x622,x623,x621)+E(x621,f14(x622,x623))
% 1.61/1.70 [56]~P1(x561)+~E(x561,x562)+~P2(x563,x562)
% 1.61/1.70 [58]~P2(x582,x584)+~P2(x581,x583)+E(x581,x582)+~E(x583,x584)
% 1.61/1.70 [63]~P4(x636,x637,x633)+~E(x631,x632)+~E(x633,x631)+~P2(x634,x635)+~P3(x637,x638,x632)+~P2(x635,x636)+~P1(x634)
% 1.61/1.70 %EqnAxiom
% 1.61/1.70 [1]E(x11,x11)
% 1.61/1.70 [2]E(x22,x21)+~E(x21,x22)
% 1.61/1.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.61/1.70 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 1.61/1.70 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 1.61/1.70 [6]~E(x61,x62)+E(f5(x61),f5(x62))
% 1.61/1.70 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 1.61/1.70 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 1.61/1.70 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93))
% 1.61/1.70 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102))
% 1.61/1.71 [11]~E(x111,x112)+E(f14(x111,x113),f14(x112,x113))
% 1.61/1.71 [12]~E(x121,x122)+E(f14(x123,x121),f14(x123,x122))
% 1.61/1.71 [13]~E(x131,x132)+E(f15(x131,x133),f15(x132,x133))
% 1.61/1.71 [14]~E(x141,x142)+E(f15(x143,x141),f15(x143,x142))
% 1.61/1.71 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 1.61/1.71 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 1.61/1.71 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 1.61/1.71 [18]~E(x181,x182)+E(f13(x181,x183),f13(x182,x183))
% 1.61/1.71 [19]~E(x191,x192)+E(f13(x193,x191),f13(x193,x192))
% 1.61/1.71 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 1.61/1.71 [21]~E(x211,x212)+E(f3(x211,x213),f3(x212,x213))
% 1.61/1.71 [22]~E(x221,x222)+E(f3(x223,x221),f3(x223,x222))
% 1.61/1.71 [23]~E(x231,x232)+E(f12(x231),f12(x232))
% 1.61/1.71 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 1.61/1.71 [25]~E(x251,x252)+E(f16(x251,x253),f16(x252,x253))
% 1.61/1.71 [26]~E(x261,x262)+E(f16(x263,x261),f16(x263,x262))
% 1.61/1.71 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 1.61/1.71 [28]P4(x282,x283,x284)+~E(x281,x282)+~P4(x281,x283,x284)
% 1.61/1.71 [29]P4(x293,x292,x294)+~E(x291,x292)+~P4(x293,x291,x294)
% 1.61/1.71 [30]P4(x303,x304,x302)+~E(x301,x302)+~P4(x303,x304,x301)
% 1.61/1.71 [31]P3(x312,x313,x314)+~E(x311,x312)+~P3(x311,x313,x314)
% 1.61/1.71 [32]P3(x323,x322,x324)+~E(x321,x322)+~P3(x323,x321,x324)
% 1.61/1.71 [33]P3(x333,x334,x332)+~E(x331,x332)+~P3(x333,x334,x331)
% 1.61/1.71 [34]P2(x342,x343)+~E(x341,x342)+~P2(x341,x343)
% 1.61/1.71 [35]P2(x353,x352)+~E(x351,x352)+~P2(x353,x351)
% 1.61/1.71
% 1.61/1.71 %-------------------------------------------
% 1.61/1.71 cnf(64,plain,
% 1.61/1.71 (P1(a8)),
% 1.61/1.71 inference(equality_inference,[],[49])).
% 1.61/1.71 cnf(65,plain,
% 1.61/1.71 (P2(x651,f12(x651))),
% 1.61/1.71 inference(equality_inference,[],[53])).
% 1.61/1.71 cnf(66,plain,
% 1.61/1.71 (~P1(x661)+~P2(x662,x661)),
% 1.61/1.71 inference(equality_inference,[],[56])).
% 1.61/1.71 cnf(78,plain,
% 1.61/1.71 (P4(x781,f5(x781),x782)+~E(f4(x781),x782)),
% 1.61/1.71 inference(scs_inference,[],[36,43,65,66,56,35,28,29,30])).
% 1.61/1.71 cnf(228,plain,
% 1.61/1.71 (E(f4(f5(x2281)),f4(a8))),
% 1.61/1.71 inference(scs_inference,[],[38,5,50])).
% 1.61/1.71 cnf(230,plain,
% 1.61/1.71 (E(f4(a8),f4(f5(x2301)))),
% 1.61/1.71 inference(scs_inference,[],[228,78,2])).
% 1.61/1.71 cnf(245,plain,
% 1.61/1.71 (~P4(f6(x2451,f12(a8)),f4(a8),f4(a8))),
% 1.61/1.71 inference(scs_inference,[],[39,65,64,228,230,41,56,63])).
% 1.61/1.71 cnf(360,plain,
% 1.61/1.71 (P4(x3601,f5(x3601),a8)),
% 1.61/1.71 inference(scs_inference,[],[37,50,78])).
% 1.61/1.71 cnf(361,plain,
% 1.61/1.71 (P4(x3611,x3612,a8)+~E(f5(x3611),x3612)),
% 1.61/1.71 inference(scs_inference,[],[360,29])).
% 1.61/1.71 cnf(406,plain,
% 1.61/1.71 (P4(x4061,a8,a8)),
% 1.61/1.71 inference(scs_inference,[],[38,50,361])).
% 1.61/1.71 cnf(408,plain,
% 1.61/1.71 (~E(a8,f4(a8))),
% 1.61/1.71 inference(scs_inference,[],[245,406,30,29])).
% 1.61/1.71 cnf(519,plain,
% 1.61/1.71 (E(f14(x5191,f5(x5191)),f4(x5191))),
% 1.61/1.71 inference(scs_inference,[],[43,2,62])).
% 1.61/1.71 cnf(540,plain,
% 1.61/1.71 ($false),
% 1.61/1.71 inference(scs_inference,[],[360,519,408,3,62]),
% 1.61/1.71 ['proof']).
% 1.61/1.71 % SZS output end Proof
% 1.61/1.71 % Total time :1.040000s
%------------------------------------------------------------------------------