%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN067+1 : 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 : n017.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 13:29:37 EDT 2024
% Result : Theorem 0.43s 0.62s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUN067+1 : TPTP v8.2.0. Released v7.3.0.
% 0.06/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32 % Computer : n017.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Jun 18 21:10:24 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.43/0.56 start to proof:theBenchmark
% 0.43/0.62 %-------------------------------------------
% 0.43/0.62 % File :CSE---1.7
% 0.43/0.62 % Problem :theBenchmark
% 0.43/0.62 % Transform :cnf
% 0.43/0.62 % Format :tptp:raw
% 0.43/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.43/0.62
% 0.43/0.62 % Result :Theorem 0.010000s
% 0.43/0.62 % Output :CNFRefutation 0.010000s
% 0.43/0.62 %-------------------------------------------
% 0.43/0.62 %------------------------------------------------------------------------------
% 0.43/0.62 % File : NUN067+1 : TPTP v8.2.0. Released v7.3.0.
% 0.43/0.62 % Domain : Number Theory
% 0.43/0.62 % Problem : Robinson arithmetic: There exists X != 0
% 0.43/0.62 % Version : Especial.
% 0.43/0.62 % English :
% 0.43/0.62
% 0.43/0.62 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.43/0.62 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.43/0.62 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.43/0.62 % Source : [Lam18]
% 0.43/0.62 % Names : nonzerosexistid [Lam18]
% 0.43/0.62
% 0.43/0.62 % Status : Theorem
% 0.43/0.62 % Rating : 0.06 v8.2.0, 0.07 v7.5.0, 0.10 v7.4.0, 0.06 v7.3.0
% 0.43/0.62 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 0.43/0.62 % Number of atoms : 77 ( 0 equ)
% 0.43/0.62 % Maximal formula atoms : 7 ( 4 avg)
% 0.43/0.62 % Number of connectives : 94 ( 36 ~; 27 |; 31 &)
% 0.43/0.62 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.43/0.62 % Maximal formula depth : 13 ( 8 avg)
% 0.43/0.62 % Maximal term depth : 1 ( 1 avg)
% 0.43/0.62 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.43/0.62 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.43/0.62 % Number of variables : 69 ( 48 !; 21 ?)
% 0.43/0.62 % SPC : FOF_THM_RFO_NEQ
% 0.43/0.62
% 0.43/0.62 % Comments : Translated to FOL without equality.
% 0.43/0.62 %------------------------------------------------------------------------------
% 0.43/0.62 include('Axioms/NUM009+0.ax').
% 0.43/0.62 %------------------------------------------------------------------------------
% 0.43/0.62 fof(nonzerosexistid,conjecture,
% 0.43/0.62 ? [Y1] :
% 0.43/0.62 ! [Y2] :
% 0.43/0.62 ( ~ id(Y1,Y2)
% 0.43/0.62 | ~ r1(Y2) ) ).
% 0.43/0.62
% 0.43/0.62 %------------------------------------------------------------------------------
% 0.43/0.62 %-------------------------------------------
% 0.43/0.62 % Proof found
% 0.43/0.62 % SZS status Theorem for theBenchmark
% 0.43/0.62 % SZS output start Proof
% 0.43/0.63 %ClaNum:44(EqnAxiom:0)
% 0.43/0.63 %VarNum:204(SingletonVarNum:100)
% 0.43/0.63 %MaxLitNum:5
% 0.43/0.63 %MaxfuncDepth:1
% 0.43/0.63 %SharedTerms:1
% 0.43/0.63 %goalClause: 4 6
% 0.43/0.63 %singleGoalClaCount:2
% 0.43/0.63 [5]P2(x51,x51)
% 0.43/0.63 [1]P1(f1(x11))
% 0.43/0.63 [2]P1(f6(x21))
% 0.43/0.63 [3]P1(f8(x31))
% 0.43/0.63 [4]P1(f9(x41))
% 0.43/0.63 [6]P2(x61,f9(x61))
% 0.43/0.63 [7]P2(f2(x71),x71)
% 0.43/0.63 [8]P2(f7(x81),f8(x81))
% 0.43/0.63 [14]P4(x141,f1(x141),f2(x141))
% 0.43/0.63 [15]P5(x151,f6(x151),f7(x151))
% 0.43/0.63 [9]P3(x91,f14(x92,x91))
% 0.43/0.63 [10]P3(x101,f3(x102,x101))
% 0.43/0.63 [11]P2(f15(x111,x112),f16(x111,x112))
% 0.43/0.63 [12]P2(f4(x121,x122),f20(x121,x122))
% 0.43/0.63 [13]P3(f21(x131,x132),f16(x131,x132))
% 0.43/0.63 [16]P4(x161,x162,f21(x161,x162))
% 0.43/0.63 [17]P5(x171,x172,f5(x171,x172))
% 0.43/0.63 [18]P4(x181,f14(x181,x182),f15(x181,x182))
% 0.43/0.63 [19]P5(x191,f3(x191,x192),f4(x191,x192))
% 0.43/0.63 [20]P4(f5(x201,x202),x201,f20(x201,x202))
% 0.43/0.63 [21]~P1(x211)+P2(x211,a10)
% 0.43/0.63 [22]P1(x221)+~P2(x221,a10)
% 0.43/0.63 [23]P2(x231,f13(x231))+P1(f11(x231))
% 0.43/0.63 [27]P3(f12(x271),f13(x271))+P1(f11(x271))
% 0.43/0.63 [28]P2(x281,f13(x281))+P2(x281,f11(x281))
% 0.43/0.63 [31]P3(f12(x311),f13(x311))+P2(x311,f11(x311))
% 0.43/0.63 [26]~P2(x262,x261)+P2(x261,x262)
% 0.43/0.63 [29]~P3(x292,x291)+P2(x291,f17(x292))
% 0.43/0.63 [30]P3(x301,x302)+~P2(x302,f17(x301))
% 0.43/0.63 [37]P4(x371,x372,x373)+~P2(x373,f18(x371,x372))
% 0.43/0.63 [38]P5(x381,x382,x383)+~P2(x383,f19(x381,x382))
% 0.43/0.63 [39]~P4(x392,x393,x391)+P2(x391,f18(x392,x393))
% 0.43/0.63 [40]~P5(x402,x403,x401)+P2(x401,f19(x402,x403))
% 0.43/0.63 [24]~P2(x242,x241)+P1(x241)+~P1(x242)
% 0.43/0.63 [25]~P2(x251,x252)+P1(x251)+~P1(x252)
% 0.43/0.63 [32]~P1(x321)+~P2(x321,x322)+~P3(x323,x322)
% 0.43/0.63 [33]~P2(x331,x333)+P2(x331,x332)+~P2(x333,x332)
% 0.43/0.63 [34]~P3(x342,x344)+~P3(x341,x343)+P2(x341,x342)+~P2(x343,x344)
% 0.43/0.63 [35]~P3(x354,x353)+P3(x351,x352)+~P2(x353,x352)+~P2(x354,x351)
% 0.43/0.63 [36]~P3(x364,x363)+P3(x361,x362)+~P2(x362,x363)+~P2(x361,x364)
% 0.43/0.63 [41]~P4(x416,x415,x414)+P4(x411,x412,x413)+~P2(x414,x413)+~P2(x415,x412)+~P2(x416,x411)
% 0.43/0.63 [42]~P4(x426,x425,x424)+P4(x421,x422,x423)+~P2(x423,x424)+~P2(x422,x425)+~P2(x421,x426)
% 0.43/0.63 [43]~P5(x436,x435,x434)+P5(x431,x432,x433)+~P2(x434,x433)+~P2(x435,x432)+~P2(x436,x431)
% 0.43/0.63 [44]~P5(x446,x445,x444)+P5(x441,x442,x443)+~P2(x443,x444)+~P2(x442,x445)+~P2(x441,x446)
% 0.43/0.63 %EqnAxiom
% 0.43/0.63
% 0.43/0.63 %-------------------------------------------
% 0.53/0.63 cnf(46,plain,
% 0.53/0.63 (P2(x461,x461)),
% 0.53/0.63 inference(rename_variables,[],[5])).
% 0.53/0.63 cnf(49,plain,
% 0.53/0.63 (P2(x491,x491)),
% 0.53/0.63 inference(rename_variables,[],[5])).
% 0.53/0.63 cnf(52,plain,
% 0.53/0.63 (P2(x521,x521)),
% 0.53/0.63 inference(rename_variables,[],[5])).
% 0.53/0.63 cnf(55,plain,
% 0.53/0.63 (P2(x551,x551)),
% 0.53/0.63 inference(rename_variables,[],[5])).
% 0.53/0.63 cnf(57,plain,
% 0.53/0.63 (~P3(x571,f9(f9(x572)))),
% 0.53/0.63 inference(scs_inference,[],[4,6,5,46,49,52,22,30,37,38,32])).
% 0.53/0.63 cnf(58,plain,
% 0.53/0.63 (P2(x581,f9(x581))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(61,plain,
% 0.53/0.63 (P2(x611,f9(x611))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(62,plain,
% 0.53/0.63 (P2(x621,f9(x621))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(64,plain,
% 0.53/0.63 (P3(x641,f14(x642,f9(x641)))),
% 0.53/0.63 inference(scs_inference,[],[4,6,58,62,5,46,49,52,55,9,22,30,37,38,32,35,36])).
% 0.53/0.63 cnf(65,plain,
% 0.53/0.63 (P2(x651,x651)),
% 0.53/0.63 inference(rename_variables,[],[5])).
% 0.53/0.63 cnf(70,plain,
% 0.53/0.63 (P2(x701,f9(x701))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(71,plain,
% 0.53/0.63 (P2(x711,f9(x711))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(72,plain,
% 0.53/0.63 (P4(x721,x722,f21(x721,x722))),
% 0.53/0.63 inference(rename_variables,[],[16])).
% 0.53/0.63 cnf(75,plain,
% 0.53/0.63 (P2(x751,x751)),
% 0.53/0.63 inference(rename_variables,[],[5])).
% 0.53/0.63 cnf(80,plain,
% 0.53/0.63 (P2(x801,f9(x801))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(81,plain,
% 0.53/0.63 (P2(x811,f9(x811))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(82,plain,
% 0.53/0.63 (P5(x821,x822,f5(x821,x822))),
% 0.53/0.63 inference(rename_variables,[],[17])).
% 0.53/0.63 cnf(88,plain,
% 0.53/0.63 (P2(x881,f9(f9(x881)))),
% 0.53/0.63 inference(scs_inference,[],[4,6,58,62,71,81,80,70,61,5,46,49,52,55,65,75,16,72,17,82,9,22,30,37,38,32,35,36,41,42,43,44,33])).
% 0.53/0.63 cnf(92,plain,
% 0.53/0.63 (P2(f2(x921),x921)),
% 0.53/0.63 inference(rename_variables,[],[7])).
% 0.53/0.63 cnf(95,plain,
% 0.53/0.63 (P2(f2(x951),x951)),
% 0.53/0.63 inference(rename_variables,[],[7])).
% 0.53/0.63 cnf(98,plain,
% 0.53/0.63 (P2(f2(x981),x981)),
% 0.53/0.63 inference(rename_variables,[],[7])).
% 0.53/0.63 cnf(100,plain,
% 0.53/0.63 (P1(f2(a10))),
% 0.53/0.63 inference(scs_inference,[],[7,92,95,98,37,30,38,22])).
% 0.53/0.63 cnf(137,plain,
% 0.53/0.63 (P2(x1371,f9(x1371))),
% 0.53/0.63 inference(rename_variables,[],[6])).
% 0.53/0.63 cnf(139,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(scs_inference,[],[6,137,88,64,57,11,100,7,33,32,35]),
% 0.53/0.63 ['proof']).
% 0.53/0.63 % SZS output end Proof
% 0.53/0.63 % Total time :0.010000s
%------------------------------------------------------------------------------