TSTP Solution File: NUN073+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN073+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 : n015.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 12:45:24 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n015.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 09:45:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 % File :CSE---1.6
% 0.19/0.67 % Problem :theBenchmark
% 0.19/0.67 % Transform :cnf
% 0.19/0.67 % Format :tptp:raw
% 0.19/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.67
% 0.19/0.67 % Result :Theorem 0.040000s
% 0.19/0.67 % Output :CNFRefutation 0.040000s
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 % File : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.19/0.67 % Domain : Number Theory
% 0.19/0.67 % Problem : Robinson arithmetic: 1 != 2
% 0.19/0.67 % Version : Especial.
% 0.19/0.67 % English :
% 0.19/0.67
% 0.19/0.67 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.19/0.67 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.19/0.67 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.19/0.67 % Source : [Lam18]
% 0.19/0.67 % Names : oneuneqtwo [Lam18]
% 0.19/0.67
% 0.19/0.67 % Status : Theorem
% 0.19/0.67 % Rating : 0.06 v8.1.0, 0.03 v7.3.0
% 0.19/0.67 % Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% 0.19/0.67 % Number of atoms : 50 ( 18 equ)
% 0.19/0.67 % Maximal formula atoms : 6 ( 4 avg)
% 0.19/0.67 % Number of connectives : 58 ( 20 ~; 15 |; 23 &)
% 0.19/0.67 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.67 % Maximal formula depth : 9 ( 7 avg)
% 0.19/0.67 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.67 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 0.19/0.67 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.67 % Number of variables : 48 ( 28 !; 20 ?)
% 0.19/0.67 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.67
% 0.19/0.67 % Comments : Translated to FOL with equality.
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 include('Axioms/NUM008+0.ax').
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 fof(oneuneqtwo,conjecture,
% 0.19/0.67 ! [Y1] :
% 0.19/0.67 ( ! [Y2] :
% 0.19/0.67 ( ! [Y4] :
% 0.19/0.67 ( ~ r1(Y4)
% 0.19/0.67 | ~ r2(Y4,Y2) )
% 0.19/0.67 | Y2 != Y1 )
% 0.19/0.67 | ! [Y3] :
% 0.19/0.67 ( ! [Y5] :
% 0.19/0.67 ( ~ r1(Y5)
% 0.19/0.67 | ~ r2(Y5,Y3) )
% 0.19/0.67 | ~ r2(Y3,Y1) ) ) ).
% 0.19/0.67
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark
% 0.19/0.67 % SZS output start Proof
% 0.19/0.68 %ClaNum:68(EqnAxiom:35)
% 0.19/0.68 %VarNum:105(SingletonVarNum:50)
% 0.19/0.68 %MaxLitNum:4
% 0.19/0.68 %MaxfuncDepth:1
% 0.19/0.68 %SharedTerms:12
% 0.19/0.68 %goalClause: 36 37 38 42 43 44
% 0.19/0.68 %singleGoalClaCount:6
% 0.19/0.68 [36]E(a1,a2)
% 0.19/0.68 [37]P1(a12)
% 0.19/0.68 [38]P1(a13)
% 0.19/0.68 [42]P2(a12,a1)
% 0.19/0.68 [43]P2(a14,a2)
% 0.19/0.68 [44]P2(a13,a14)
% 0.19/0.68 [39]P1(f3(x391))
% 0.19/0.68 [40]P1(f6(x401))
% 0.19/0.68 [41]P1(f7(x411))
% 0.19/0.68 [47]P3(x471,f3(x471),x471)
% 0.19/0.68 [49]P4(x491,f7(x491),f6(x491))
% 0.19/0.68 [45]P2(x451,f15(x452,x451))
% 0.19/0.68 [46]P2(x461,f4(x462,x461))
% 0.19/0.68 [48]P2(f20(x481,x482),f16(x481,x482))
% 0.19/0.68 [50]P3(x501,x502,f20(x501,x502))
% 0.19/0.68 [51]P4(x511,x512,f5(x511,x512))
% 0.19/0.68 [52]P3(x521,f15(x521,x522),f16(x521,x522))
% 0.19/0.68 [53]P4(x531,f4(x531,x532),f21(x531,x532))
% 0.19/0.68 [54]P3(f5(x541,x542),x541,f21(x541,x542))
% 0.19/0.68 [55]P1(x551)+~E(x551,a8)
% 0.19/0.68 [56]~P1(x561)+E(x561,a8)
% 0.19/0.68 [57]E(f11(x571),x571)+E(f9(x571),x571)
% 0.19/0.68 [58]E(f11(x581),x581)+P1(f9(x581))
% 0.19/0.68 [61]P2(f10(x611),f11(x611))+E(f9(x611),x611)
% 0.19/0.68 [63]P2(f10(x631),f11(x631))+P1(f9(x631))
% 0.19/0.68 [59]P2(x591,x592)+~E(x592,f17(x591))
% 0.19/0.68 [60]~P2(x602,x601)+E(x601,f17(x602))
% 0.19/0.68 [65]P3(x651,x652,x653)+~E(x653,f18(x651,x652))
% 0.19/0.68 [66]P4(x661,x662,x663)+~E(x663,f19(x661,x662))
% 0.19/0.68 [67]~P3(x672,x673,x671)+E(x671,f18(x672,x673))
% 0.19/0.68 [68]~P4(x682,x683,x681)+E(x681,f19(x682,x683))
% 0.19/0.68 [62]~P1(x621)+~E(x621,x622)+~P2(x623,x622)
% 0.19/0.68 [64]~P2(x642,x644)+~P2(x641,x643)+E(x641,x642)+~E(x643,x644)
% 0.19/0.68 %EqnAxiom
% 0.19/0.68 [1]E(x11,x11)
% 0.19/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.68 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.19/0.68 [5]~E(x51,x52)+E(f6(x51),f6(x52))
% 0.19/0.68 [6]~E(x61,x62)+E(f7(x61),f7(x62))
% 0.19/0.68 [7]~E(x71,x72)+E(f15(x71,x73),f15(x72,x73))
% 0.19/0.68 [8]~E(x81,x82)+E(f15(x83,x81),f15(x83,x82))
% 0.19/0.68 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.19/0.68 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.19/0.68 [11]~E(x111,x112)+E(f19(x111,x113),f19(x112,x113))
% 0.19/0.68 [12]~E(x121,x122)+E(f19(x123,x121),f19(x123,x122))
% 0.19/0.68 [13]~E(x131,x132)+E(f20(x131,x133),f20(x132,x133))
% 0.19/0.68 [14]~E(x141,x142)+E(f20(x143,x141),f20(x143,x142))
% 0.19/0.68 [15]~E(x151,x152)+E(f16(x151,x153),f16(x152,x153))
% 0.19/0.68 [16]~E(x161,x162)+E(f16(x163,x161),f16(x163,x162))
% 0.19/0.68 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.19/0.68 [18]~E(x181,x182)+E(f18(x181,x183),f18(x182,x183))
% 0.19/0.68 [19]~E(x191,x192)+E(f18(x193,x191),f18(x193,x192))
% 0.19/0.68 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.19/0.68 [21]~E(x211,x212)+E(f5(x211,x213),f5(x212,x213))
% 0.19/0.68 [22]~E(x221,x222)+E(f5(x223,x221),f5(x223,x222))
% 0.19/0.68 [23]~E(x231,x232)+E(f17(x231),f17(x232))
% 0.19/0.68 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 0.19/0.68 [25]~E(x251,x252)+E(f21(x251,x253),f21(x252,x253))
% 0.19/0.68 [26]~E(x261,x262)+E(f21(x263,x261),f21(x263,x262))
% 0.19/0.68 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 0.19/0.68 [28]P4(x282,x283,x284)+~E(x281,x282)+~P4(x281,x283,x284)
% 0.19/0.68 [29]P4(x293,x292,x294)+~E(x291,x292)+~P4(x293,x291,x294)
% 0.19/0.68 [30]P4(x303,x304,x302)+~E(x301,x302)+~P4(x303,x304,x301)
% 0.19/0.68 [31]P3(x312,x313,x314)+~E(x311,x312)+~P3(x311,x313,x314)
% 0.19/0.68 [32]P3(x323,x322,x324)+~E(x321,x322)+~P3(x323,x321,x324)
% 0.19/0.68 [33]P3(x333,x334,x332)+~E(x331,x332)+~P3(x333,x334,x331)
% 0.19/0.68 [34]P2(x342,x343)+~E(x341,x342)+~P2(x341,x343)
% 0.19/0.68 [35]P2(x353,x352)+~E(x351,x352)+~P2(x353,x351)
% 0.19/0.68
% 0.19/0.68 %-------------------------------------------
% 0.19/0.68 cnf(69,plain,
% 0.19/0.68 (E(a2,a1)),
% 0.19/0.68 inference(scs_inference,[],[36,2])).
% 0.19/0.68 cnf(74,plain,
% 0.19/0.68 (P3(x741,f3(x741),x741)),
% 0.19/0.68 inference(rename_variables,[],[47])).
% 0.19/0.68 cnf(82,plain,
% 0.19/0.68 (~P2(a1,a2)),
% 0.19/0.68 inference(scs_inference,[],[36,37,42,47,74,50,51,45,2,35,34,33,32,31,29,28,62,64])).
% 0.19/0.68 cnf(88,plain,
% 0.19/0.68 (~E(a2,f17(a1))),
% 0.19/0.68 inference(scs_inference,[],[36,37,42,47,74,50,51,45,2,35,34,33,32,31,29,28,62,64,56,60,59])).
% 0.19/0.68 cnf(93,plain,
% 0.19/0.68 (E(f17(a1),f17(a2))),
% 0.19/0.68 inference(scs_inference,[],[36,37,42,47,74,50,51,45,2,35,34,33,32,31,29,28,62,64,56,60,59,26,25,24,23])).
% 0.19/0.68 cnf(94,plain,
% 0.19/0.68 (E(f5(x941,a1),f5(x941,a2))),
% 0.19/0.68 inference(scs_inference,[],[36,37,42,47,74,50,51,45,2,35,34,33,32,31,29,28,62,64,56,60,59,26,25,24,23,22])).
% 0.19/0.68 cnf(126,plain,
% 0.19/0.68 (E(a12,a14)),
% 0.19/0.68 inference(scs_inference,[],[36,43,42,93,59,64])).
% 0.19/0.68 cnf(129,plain,
% 0.19/0.68 (~P2(a1,a1)),
% 0.19/0.68 inference(scs_inference,[],[36,43,42,93,88,82,59,64,2,35])).
% 0.19/0.68 cnf(158,plain,
% 0.19/0.68 ($false),
% 0.19/0.68 inference(scs_inference,[],[37,44,46,43,69,94,126,129,59,2,35,34,62]),
% 0.19/0.68 ['proof']).
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time :0.040000s
%------------------------------------------------------------------------------