TSTP Solution File: NUN088+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN088+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 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 : Thu Aug 31 12:45:29 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN088+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 09:34:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % File :CSE---1.6
% 0.20/0.61 % Problem :theBenchmark
% 0.20/0.61 % Transform :cnf
% 0.20/0.61 % Format :tptp:raw
% 0.20/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.61
% 0.20/0.61 % Result :Theorem 0.000000s
% 0.20/0.61 % Output :CNFRefutation 0.000000s
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 % File : NUN088+2 : TPTP v8.1.2. Released v7.3.0.
% 0.20/0.61 % Domain : Number Theory
% 0.20/0.61 % Problem : Robinson arithmetic: 0 != 1
% 0.20/0.61 % Version : Especial.
% 0.20/0.61 % English :
% 0.20/0.61
% 0.20/0.61 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.20/0.61 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.20/0.61 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.20/0.61 % Source : [Lam18]
% 0.20/0.61 % Names : zerouneqone [Lam18]
% 0.20/0.61
% 0.20/0.61 % Status : Theorem
% 0.20/0.61 % Rating : 0.03 v7.3.0
% 0.20/0.61 % Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% 0.20/0.61 % Number of atoms : 48 ( 18 equ)
% 0.20/0.61 % Maximal formula atoms : 5 ( 4 avg)
% 0.20/0.61 % Number of connectives : 54 ( 18 ~; 13 |; 23 &)
% 0.20/0.61 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.61 % Maximal formula depth : 9 ( 7 avg)
% 0.20/0.61 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.61 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 0.20/0.61 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.61 % Number of variables : 46 ( 26 !; 20 ?)
% 0.20/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.61
% 0.20/0.61 % Comments : Translated to FOL with equality.
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 include('Axioms/NUM008+0.ax').
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 fof(zerouneqone,conjecture,
% 0.20/0.61 ! [Y1] :
% 0.20/0.61 ( ! [Y2] :
% 0.20/0.61 ( ~ r1(Y2)
% 0.20/0.61 | Y2 != Y1 )
% 0.20/0.61 | ! [Y3] :
% 0.20/0.61 ( ~ r1(Y3)
% 0.20/0.61 | ~ r2(Y3,Y1) ) ) ).
% 0.20/0.61
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark
% 0.20/0.61 % SZS output start Proof
% 0.20/0.62 %ClaNum:66(EqnAxiom:35)
% 0.20/0.62 %VarNum:105(SingletonVarNum:50)
% 0.20/0.62 %MaxLitNum:4
% 0.20/0.62 %MaxfuncDepth:1
% 0.20/0.62 %SharedTerms:8
% 0.20/0.62 %goalClause: 36 37 38 42
% 0.20/0.62 %singleGoalClaCount:4
% 0.20/0.62 [36]E(a1,a2)
% 0.20/0.62 [37]P1(a1)
% 0.20/0.62 [38]P1(a12)
% 0.20/0.62 [42]P2(a12,a2)
% 0.20/0.62 [39]P1(f3(x391))
% 0.20/0.62 [40]P1(f6(x401))
% 0.20/0.62 [41]P1(f7(x411))
% 0.20/0.62 [45]P3(x451,f3(x451),x451)
% 0.20/0.62 [47]P4(x471,f7(x471),f6(x471))
% 0.20/0.62 [43]P2(x431,f13(x432,x431))
% 0.20/0.62 [44]P2(x441,f4(x442,x441))
% 0.20/0.62 [46]P2(f18(x461,x462),f14(x461,x462))
% 0.20/0.62 [48]P3(x481,x482,f18(x481,x482))
% 0.20/0.62 [49]P4(x491,x492,f5(x491,x492))
% 0.20/0.62 [50]P3(x501,f13(x501,x502),f14(x501,x502))
% 0.20/0.62 [51]P4(x511,f4(x511,x512),f19(x511,x512))
% 0.20/0.62 [52]P3(f5(x521,x522),x521,f19(x521,x522))
% 0.20/0.62 [53]P1(x531)+~E(x531,a8)
% 0.20/0.62 [54]~P1(x541)+E(x541,a8)
% 0.20/0.62 [55]E(f11(x551),x551)+E(f9(x551),x551)
% 0.20/0.62 [56]E(f11(x561),x561)+P1(f9(x561))
% 0.20/0.62 [59]P2(f10(x591),f11(x591))+E(f9(x591),x591)
% 0.20/0.62 [61]P2(f10(x611),f11(x611))+P1(f9(x611))
% 0.20/0.62 [57]P2(x571,x572)+~E(x572,f15(x571))
% 0.20/0.62 [58]~P2(x582,x581)+E(x581,f15(x582))
% 0.20/0.62 [63]P3(x631,x632,x633)+~E(x633,f16(x631,x632))
% 0.20/0.62 [64]P4(x641,x642,x643)+~E(x643,f17(x641,x642))
% 0.20/0.62 [65]~P3(x652,x653,x651)+E(x651,f16(x652,x653))
% 0.20/0.62 [66]~P4(x662,x663,x661)+E(x661,f17(x662,x663))
% 0.20/0.62 [60]~P1(x601)+~E(x601,x602)+~P2(x603,x602)
% 0.20/0.62 [62]~P2(x622,x624)+~P2(x621,x623)+E(x621,x622)+~E(x623,x624)
% 0.20/0.62 %EqnAxiom
% 0.20/0.62 [1]E(x11,x11)
% 0.20/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.62 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.20/0.62 [5]~E(x51,x52)+E(f6(x51),f6(x52))
% 0.20/0.62 [6]~E(x61,x62)+E(f7(x61),f7(x62))
% 0.20/0.62 [7]~E(x71,x72)+E(f13(x71,x73),f13(x72,x73))
% 0.20/0.62 [8]~E(x81,x82)+E(f13(x83,x81),f13(x83,x82))
% 0.20/0.62 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.20/0.62 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.20/0.62 [11]~E(x111,x112)+E(f17(x111,x113),f17(x112,x113))
% 0.20/0.62 [12]~E(x121,x122)+E(f17(x123,x121),f17(x123,x122))
% 0.20/0.62 [13]~E(x131,x132)+E(f18(x131,x133),f18(x132,x133))
% 0.20/0.62 [14]~E(x141,x142)+E(f18(x143,x141),f18(x143,x142))
% 0.20/0.62 [15]~E(x151,x152)+E(f14(x151,x153),f14(x152,x153))
% 0.20/0.62 [16]~E(x161,x162)+E(f14(x163,x161),f14(x163,x162))
% 0.20/0.62 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.20/0.62 [18]~E(x181,x182)+E(f16(x181,x183),f16(x182,x183))
% 0.20/0.62 [19]~E(x191,x192)+E(f16(x193,x191),f16(x193,x192))
% 0.20/0.62 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.20/0.62 [21]~E(x211,x212)+E(f5(x211,x213),f5(x212,x213))
% 0.20/0.62 [22]~E(x221,x222)+E(f5(x223,x221),f5(x223,x222))
% 0.20/0.62 [23]~E(x231,x232)+E(f15(x231),f15(x232))
% 0.20/0.62 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 0.20/0.62 [25]~E(x251,x252)+E(f19(x251,x253),f19(x252,x253))
% 0.20/0.62 [26]~E(x261,x262)+E(f19(x263,x261),f19(x263,x262))
% 0.20/0.62 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 0.20/0.62 [28]P4(x282,x283,x284)+~E(x281,x282)+~P4(x281,x283,x284)
% 0.20/0.62 [29]P4(x293,x292,x294)+~E(x291,x292)+~P4(x293,x291,x294)
% 0.20/0.62 [30]P4(x303,x304,x302)+~E(x301,x302)+~P4(x303,x304,x301)
% 0.20/0.62 [31]P3(x312,x313,x314)+~E(x311,x312)+~P3(x311,x313,x314)
% 0.20/0.62 [32]P3(x323,x322,x324)+~E(x321,x322)+~P3(x323,x321,x324)
% 0.20/0.62 [33]P3(x333,x334,x332)+~E(x331,x332)+~P3(x333,x334,x331)
% 0.20/0.62 [34]P2(x342,x343)+~E(x341,x342)+~P2(x341,x343)
% 0.20/0.62 [35]P2(x353,x352)+~E(x351,x352)+~P2(x353,x351)
% 0.20/0.62
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 cnf(67,plain,
% 0.20/0.62 ($false),
% 0.20/0.62 inference(scs_inference,[],[37,36,42,60]),
% 0.20/0.62 ['proof']).
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------