%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN070+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 : n025.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 13:29:38 EDT 2024
% Result : Theorem 0.55s 0.71s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.15 % Problem : NUN070+2 : TPTP v8.2.0. Released v7.3.0.
% 0.16/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n025.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Jun 18 21:21:09 EDT 2024
% 0.16/0.35 % CPUTime :
% 0.48/0.59 start to proof:theBenchmark
% 0.55/0.71 %-------------------------------------------
% 0.55/0.71 % File :CSE---1.7
% 0.55/0.71 % Problem :theBenchmark
% 0.55/0.71 % Transform :cnf
% 0.55/0.71 % Format :tptp:raw
% 0.55/0.71 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.71
% 0.55/0.71 % Result :Theorem 0.080000s
% 0.55/0.71 % Output :CNFRefutation 0.080000s
% 0.55/0.71 %-------------------------------------------
% 0.55/0.71 %------------------------------------------------------------------------------
% 0.55/0.71 % File : NUN070+2 : TPTP v8.2.0. Released v7.3.0.
% 0.55/0.71 % Domain : Number Theory
% 0.55/0.71 % Problem : Robinson arithmetic: 1 + 0 = 1
% 0.55/0.71 % Version : Especial.
% 0.55/0.71 % English :
% 0.55/0.71
% 0.55/0.71 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.55/0.71 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.55/0.71 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.55/0.71 % Source : [Lam18]
% 0.55/0.71 % Names : onepluszeroeqone [Lam18]
% 0.55/0.71
% 0.55/0.71 % Status : Theorem
% 0.55/0.71 % Rating : 0.17 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.17 v7.3.0
% 0.55/0.71 % Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% 0.55/0.71 % Number of atoms : 51 ( 18 equ)
% 0.55/0.71 % Maximal formula atoms : 7 ( 4 avg)
% 0.55/0.71 % Number of connectives : 53 ( 14 ~; 10 |; 29 &)
% 0.55/0.71 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.55/0.71 % Maximal formula depth : 9 ( 7 avg)
% 0.55/0.71 % Maximal term depth : 1 ( 1 avg)
% 0.55/0.71 % Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% 0.55/0.71 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.55/0.71 % Number of variables : 49 ( 23 !; 26 ?)
% 0.55/0.71 % SPC : FOF_THM_RFO_SEQ
% 0.55/0.71
% 0.55/0.71 % Comments : Translated to FOL with equality.
% 0.55/0.71 %------------------------------------------------------------------------------
% 0.55/0.71 include('Axioms/NUM008+0.ax').
% 0.55/0.71 %------------------------------------------------------------------------------
% 0.55/0.71 fof(onepluszeroeqone,conjecture,
% 0.55/0.71 ? [Y1] :
% 0.55/0.71 ( ? [Y2] :
% 0.55/0.71 ( ? [Y4] :
% 0.55/0.71 ( r1(Y4)
% 0.55/0.71 & r3(Y2,Y4,Y1) )
% 0.55/0.71 & ? [Y5] :
% 0.55/0.71 ( r1(Y5)
% 0.55/0.71 & r2(Y5,Y2) ) )
% 0.55/0.71 & ? [Y3] :
% 0.55/0.71 ( Y1 = Y3
% 0.55/0.71 & ? [Y6] :
% 0.55/0.71 ( r1(Y6)
% 0.55/0.71 & r2(Y6,Y3) ) ) ) ).
% 0.55/0.71
% 0.55/0.71 %------------------------------------------------------------------------------
% 0.55/0.71 %-------------------------------------------
% 0.55/0.71 % Proof found
% 0.55/0.71 % SZS status Theorem for theBenchmark
% 0.55/0.71 % SZS output start Proof
% 0.55/0.71 %ClaNum:63(EqnAxiom:35)
% 0.55/0.71 %VarNum:117(SingletonVarNum:56)
% 0.55/0.71 %MaxLitNum:7
% 0.55/0.71 %MaxfuncDepth:1
% 0.55/0.71 %SharedTerms:1
% 0.55/0.71 %goalClause: 63
% 0.55/0.71 [36]P1(f1(x361))
% 0.55/0.71 [37]P1(f4(x371))
% 0.55/0.71 [38]P1(f5(x381))
% 0.55/0.71 [41]P3(x411,f1(x411),x411)
% 0.55/0.71 [43]P4(x431,f5(x431),f4(x431))
% 0.55/0.71 [39]P2(x391,f6(x392,x391))
% 0.55/0.71 [40]P2(x401,f2(x402,x401))
% 0.55/0.71 [42]P2(f15(x421,x422),f7(x421,x422))
% 0.55/0.71 [44]P3(x441,x442,f15(x441,x442))
% 0.55/0.71 [45]P4(x451,x452,f3(x451,x452))
% 0.55/0.71 [46]P3(x461,f6(x461,x462),f7(x461,x462))
% 0.55/0.71 [47]P4(x471,f2(x471,x472),f16(x471,x472))
% 0.55/0.71 [48]P3(f3(x481,x482),x481,f16(x481,x482))
% 0.55/0.71 [49]P1(x491)+~E(x491,a8)
% 0.55/0.71 [50]~P1(x501)+E(x501,a8)
% 0.55/0.71 [51]E(f11(x511),x511)+E(f9(x511),x511)
% 0.55/0.71 [52]E(f11(x521),x521)+P1(f9(x521))
% 0.55/0.71 [55]P2(f10(x551),f11(x551))+E(f9(x551),x551)
% 0.55/0.71 [57]P2(f10(x571),f11(x571))+P1(f9(x571))
% 0.55/0.71 [53]P2(x531,x532)+~E(x532,f12(x531))
% 0.55/0.71 [54]~P2(x542,x541)+E(x541,f12(x542))
% 0.55/0.71 [59]P3(x591,x592,x593)+~E(x593,f13(x591,x592))
% 0.55/0.71 [60]P4(x601,x602,x603)+~E(x603,f14(x601,x602))
% 0.55/0.71 [61]~P3(x612,x613,x611)+E(x611,f13(x612,x613))
% 0.55/0.71 [62]~P4(x622,x623,x621)+E(x621,f14(x622,x623))
% 0.55/0.71 [56]~P1(x561)+~E(x561,x562)+~P2(x563,x562)
% 0.55/0.71 [58]~P2(x582,x584)+~P2(x581,x583)+E(x581,x582)+~E(x583,x584)
% 0.55/0.71 [63]~P2(x633,x632)+~P3(x636,x635,x631)+~E(x631,x632)+~P1(x633)+~P2(x634,x636)+~P1(x634)+~P1(x635)
% 0.55/0.71 %EqnAxiom
% 0.55/0.71 [1]E(x11,x11)
% 0.55/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.71 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 0.55/0.71 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 0.55/0.71 [6]~E(x61,x62)+E(f5(x61),f5(x62))
% 0.55/0.71 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.55/0.71 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.55/0.71 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93))
% 0.55/0.71 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102))
% 0.55/0.71 [11]~E(x111,x112)+E(f14(x111,x113),f14(x112,x113))
% 0.55/0.71 [12]~E(x121,x122)+E(f14(x123,x121),f14(x123,x122))
% 0.55/0.71 [13]~E(x131,x132)+E(f15(x131,x133),f15(x132,x133))
% 0.55/0.71 [14]~E(x141,x142)+E(f15(x143,x141),f15(x143,x142))
% 0.55/0.71 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.55/0.71 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.55/0.71 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.55/0.71 [18]~E(x181,x182)+E(f13(x181,x183),f13(x182,x183))
% 0.55/0.71 [19]~E(x191,x192)+E(f13(x193,x191),f13(x193,x192))
% 0.55/0.71 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.55/0.71 [21]~E(x211,x212)+E(f3(x211,x213),f3(x212,x213))
% 0.55/0.71 [22]~E(x221,x222)+E(f3(x223,x221),f3(x223,x222))
% 0.55/0.71 [23]~E(x231,x232)+E(f12(x231),f12(x232))
% 0.55/0.71 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 0.55/0.71 [25]~E(x251,x252)+E(f16(x251,x253),f16(x252,x253))
% 0.55/0.71 [26]~E(x261,x262)+E(f16(x263,x261),f16(x263,x262))
% 0.55/0.71 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 0.55/0.71 [28]P3(x282,x283,x284)+~E(x281,x282)+~P3(x281,x283,x284)
% 0.55/0.71 [29]P3(x293,x292,x294)+~E(x291,x292)+~P3(x293,x291,x294)
% 0.55/0.71 [30]P3(x303,x304,x302)+~E(x301,x302)+~P3(x303,x304,x301)
% 0.55/0.71 [31]P2(x312,x313)+~E(x311,x312)+~P2(x311,x313)
% 0.55/0.71 [32]P2(x323,x322)+~E(x321,x322)+~P2(x323,x321)
% 0.55/0.71 [33]P4(x332,x333,x334)+~E(x331,x332)+~P4(x331,x333,x334)
% 0.55/0.71 [34]P4(x343,x342,x344)+~E(x341,x342)+~P4(x343,x341,x344)
% 0.55/0.71 [35]P4(x353,x354,x352)+~E(x351,x352)+~P4(x353,x354,x351)
% 0.55/0.71
% 0.55/0.71 %-------------------------------------------
% 0.55/0.71 cnf(70,plain,
% 0.55/0.71 (~P1(x702)+~P1(x703)+~P1(x704)+~P2(x702,x701)+~P3(x705,x704,x701)+~P2(x703,x705)),
% 0.55/0.71 inference(equality_inference,[],[63])).
% 0.55/0.71 cnf(207,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(scs_inference,[],[37,39,41,36,70]),
% 0.55/0.71 ['proof']).
% 0.55/0.71 % SZS output end Proof
% 0.55/0.71 % Total time :0.080000s
%------------------------------------------------------------------------------