%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN089+2 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 13:29:45 EDT 2024
% Result : Theorem 0.55s 0.68s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUN089+2 : TPTP v8.2.0. Released v7.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Jun 18 20:43:38 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.52/0.58 start to proof:theBenchmark
% 0.55/0.67 %-------------------------------------------
% 0.55/0.67 % File :CSE---1.7
% 0.55/0.67 % Problem :theBenchmark
% 0.55/0.67 % Transform :cnf
% 0.55/0.67 % Format :tptp:raw
% 0.55/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.67
% 0.55/0.67 % Result :Theorem 0.000000s
% 0.55/0.67 % Output :CNFRefutation 0.000000s
% 0.55/0.67 %-------------------------------------------
% 0.55/0.68 %------------------------------------------------------------------------------
% 0.55/0.68 % File : NUN089+2 : TPTP v8.2.0. Released v7.3.0.
% 0.55/0.68 % Domain : Number Theory
% 0.55/0.68 % Problem : Robinson arithmetic: 0 != 2
% 0.55/0.68 % Version : Especial.
% 0.55/0.68 % English :
% 0.55/0.68
% 0.55/0.68 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.55/0.68 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.55/0.68 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.55/0.68 % Source : [Lam18]
% 0.55/0.68 % Names : zerouneqtwo [Lam18]
% 0.55/0.68
% 0.55/0.68 % Status : Theorem
% 0.55/0.68 % Rating : 0.06 v7.4.0, 0.07 v7.3.0
% 0.55/0.68 % Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% 0.55/0.68 % Number of atoms : 49 ( 18 equ)
% 0.55/0.68 % Maximal formula atoms : 5 ( 4 avg)
% 0.55/0.68 % Number of connectives : 56 ( 19 ~; 14 |; 23 &)
% 0.55/0.68 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.55/0.68 % Maximal formula depth : 9 ( 7 avg)
% 0.55/0.68 % Maximal term depth : 1 ( 1 avg)
% 0.55/0.68 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 0.55/0.68 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.55/0.68 % Number of variables : 47 ( 27 !; 20 ?)
% 0.55/0.68 % SPC : FOF_THM_RFO_SEQ
% 0.55/0.68
% 0.55/0.68 % Comments : Translated to FOL with equality.
% 0.55/0.68 %------------------------------------------------------------------------------
% 0.55/0.68 include('Axioms/NUM008+0.ax').
% 0.55/0.68 %------------------------------------------------------------------------------
% 0.55/0.68 fof(zerouneqtwo,conjecture,
% 0.55/0.68 ! [Y1] :
% 0.55/0.68 ( ! [Y2] :
% 0.55/0.68 ( ! [Y3] :
% 0.55/0.68 ( ~ r1(Y3)
% 0.55/0.68 | ~ r2(Y3,Y2) )
% 0.55/0.68 | ~ r2(Y2,Y1) )
% 0.55/0.68 | ! [Y4] :
% 0.55/0.68 ( Y4 != Y1
% 0.55/0.68 | ~ r1(Y4) ) ) ).
% 0.55/0.68
% 0.55/0.68 %------------------------------------------------------------------------------
% 0.55/0.68 %-------------------------------------------
% 0.55/0.68 % Proof found
% 0.55/0.68 % SZS status Theorem for theBenchmark
% 0.55/0.68 % SZS output start Proof
% 0.55/0.68 %ClaNum:67(EqnAxiom:35)
% 0.55/0.68 %VarNum:105(SingletonVarNum:50)
% 0.55/0.68 %MaxLitNum:4
% 0.55/0.68 %MaxfuncDepth:1
% 0.55/0.68 %SharedTerms:10
% 0.55/0.68 %goalClause: 36 37 38 42 43
% 0.55/0.68 %singleGoalClaCount:5
% 0.55/0.68 [36]E(a1,a2)
% 0.55/0.68 [37]P1(a12)
% 0.55/0.68 [38]P1(a1)
% 0.55/0.68 [42]P2(a13,a2)
% 0.55/0.68 [43]P2(a12,a13)
% 0.55/0.68 [39]P1(f3(x391))
% 0.55/0.68 [40]P1(f6(x401))
% 0.55/0.68 [41]P1(f7(x411))
% 0.55/0.68 [46]P3(x461,f3(x461),x461)
% 0.55/0.68 [48]P4(x481,f7(x481),f6(x481))
% 0.55/0.68 [44]P2(x441,f14(x442,x441))
% 0.55/0.68 [45]P2(x451,f4(x452,x451))
% 0.55/0.68 [47]P2(f19(x471,x472),f15(x471,x472))
% 0.55/0.68 [49]P3(x491,x492,f19(x491,x492))
% 0.55/0.68 [50]P4(x501,x502,f5(x501,x502))
% 0.55/0.68 [51]P3(x511,f14(x511,x512),f15(x511,x512))
% 0.55/0.68 [52]P4(x521,f4(x521,x522),f20(x521,x522))
% 0.55/0.68 [53]P3(f5(x531,x532),x531,f20(x531,x532))
% 0.55/0.68 [54]P1(x541)+~E(x541,a8)
% 0.55/0.68 [55]~P1(x551)+E(x551,a8)
% 0.55/0.68 [56]E(f11(x561),x561)+E(f9(x561),x561)
% 0.55/0.68 [57]E(f11(x571),x571)+P1(f9(x571))
% 0.55/0.68 [60]P2(f10(x601),f11(x601))+E(f9(x601),x601)
% 0.55/0.68 [62]P2(f10(x621),f11(x621))+P1(f9(x621))
% 0.55/0.68 [58]P2(x581,x582)+~E(x582,f16(x581))
% 0.55/0.68 [59]~P2(x592,x591)+E(x591,f16(x592))
% 0.55/0.68 [64]P3(x641,x642,x643)+~E(x643,f17(x641,x642))
% 0.55/0.68 [65]P4(x651,x652,x653)+~E(x653,f18(x651,x652))
% 0.55/0.68 [66]~P3(x662,x663,x661)+E(x661,f17(x662,x663))
% 0.55/0.68 [67]~P4(x672,x673,x671)+E(x671,f18(x672,x673))
% 0.55/0.68 [61]~P1(x611)+~E(x611,x612)+~P2(x613,x612)
% 0.55/0.68 [63]~P2(x632,x634)+~P2(x631,x633)+E(x631,x632)+~E(x633,x634)
% 0.55/0.68 %EqnAxiom
% 0.55/0.68 [1]E(x11,x11)
% 0.55/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.68 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.55/0.68 [5]~E(x51,x52)+E(f6(x51),f6(x52))
% 0.55/0.68 [6]~E(x61,x62)+E(f7(x61),f7(x62))
% 0.55/0.68 [7]~E(x71,x72)+E(f14(x71,x73),f14(x72,x73))
% 0.55/0.68 [8]~E(x81,x82)+E(f14(x83,x81),f14(x83,x82))
% 0.55/0.68 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.55/0.68 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.55/0.68 [11]~E(x111,x112)+E(f18(x111,x113),f18(x112,x113))
% 0.55/0.68 [12]~E(x121,x122)+E(f18(x123,x121),f18(x123,x122))
% 0.55/0.68 [13]~E(x131,x132)+E(f19(x131,x133),f19(x132,x133))
% 0.55/0.68 [14]~E(x141,x142)+E(f19(x143,x141),f19(x143,x142))
% 0.55/0.68 [15]~E(x151,x152)+E(f15(x151,x153),f15(x152,x153))
% 0.55/0.68 [16]~E(x161,x162)+E(f15(x163,x161),f15(x163,x162))
% 0.55/0.68 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.55/0.68 [18]~E(x181,x182)+E(f17(x181,x183),f17(x182,x183))
% 0.55/0.68 [19]~E(x191,x192)+E(f17(x193,x191),f17(x193,x192))
% 0.55/0.68 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.55/0.68 [21]~E(x211,x212)+E(f5(x211,x213),f5(x212,x213))
% 0.55/0.68 [22]~E(x221,x222)+E(f5(x223,x221),f5(x223,x222))
% 0.55/0.68 [23]~E(x231,x232)+E(f16(x231),f16(x232))
% 0.55/0.68 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 0.55/0.68 [25]~E(x251,x252)+E(f20(x251,x253),f20(x252,x253))
% 0.55/0.68 [26]~E(x261,x262)+E(f20(x263,x261),f20(x263,x262))
% 0.55/0.68 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 0.55/0.68 [28]P4(x282,x283,x284)+~E(x281,x282)+~P4(x281,x283,x284)
% 0.55/0.68 [29]P4(x293,x292,x294)+~E(x291,x292)+~P4(x293,x291,x294)
% 0.55/0.68 [30]P4(x303,x304,x302)+~E(x301,x302)+~P4(x303,x304,x301)
% 0.55/0.68 [31]P3(x312,x313,x314)+~E(x311,x312)+~P3(x311,x313,x314)
% 0.55/0.68 [32]P3(x323,x322,x324)+~E(x321,x322)+~P3(x323,x321,x324)
% 0.55/0.68 [33]P3(x333,x334,x332)+~E(x331,x332)+~P3(x333,x334,x331)
% 0.55/0.68 [34]P2(x342,x343)+~E(x341,x342)+~P2(x341,x343)
% 0.55/0.68 [35]P2(x353,x352)+~E(x351,x352)+~P2(x353,x351)
% 0.55/0.68
% 0.55/0.68 %-------------------------------------------
% 0.55/0.68 cnf(70,plain,
% 0.55/0.68 (~P1(x701)+~P2(x702,x701)),
% 0.55/0.68 inference(equality_inference,[],[61])).
% 0.55/0.68 cnf(72,plain,
% 0.55/0.68 (P3(x721,x722,f17(x721,x722))),
% 0.55/0.68 inference(equality_inference,[],[64])).
% 0.55/0.68 cnf(73,plain,
% 0.55/0.68 (P4(x731,x732,f18(x731,x732))),
% 0.55/0.68 inference(equality_inference,[],[65])).
% 0.55/0.68 cnf(82,plain,
% 0.55/0.68 (P4(x821,x822,f18(x821,x822))),
% 0.55/0.68 inference(rename_variables,[],[73])).
% 0.55/0.68 cnf(86,plain,
% 0.55/0.68 (P3(x861,x862,f17(x861,x862))),
% 0.55/0.68 inference(rename_variables,[],[72])).
% 0.55/0.68 cnf(87,plain,
% 0.55/0.68 (P3(x871,a2,f17(x871,a1))),
% 0.55/0.68 inference(scs_inference,[],[36,37,38,42,72,86,73,82,70,2,61,3,27,28,29,31,32])).
% 0.55/0.68 cnf(104,plain,
% 0.55/0.68 ($false),
% 0.55/0.68 inference(scs_inference,[],[36,38,42,87,44,70,34,31,61]),
% 0.55/0.68 ['proof']).
% 0.55/0.68 % SZS output end Proof
% 0.55/0.68 % Total time :0.000000s
%------------------------------------------------------------------------------