%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN062+1 : TPTP v8.2.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n004.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 13:29:36 EDT 2024
% Result : Theorem 1.45s 1.51s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN062+1 : TPTP v8.2.0. Bugfixed v7.4.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Jun 18 20:46:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 1.45/1.50 %-------------------------------------------
% 1.45/1.50 % File :CSE---1.7
% 1.45/1.50 % Problem :theBenchmark
% 1.45/1.50 % Transform :cnf
% 1.45/1.50 % Format :tptp:raw
% 1.45/1.50 % Command :java -jar mcs_scs.jar %d %s
% 1.45/1.50
% 1.45/1.50 % Result :Theorem 0.900000s
% 1.45/1.50 % Output :CNFRefutation 0.900000s
% 1.45/1.50 %-------------------------------------------
% 1.45/1.51 %------------------------------------------------------------------------------
% 1.45/1.51 % File : NUN062+1 : TPTP v8.2.0. Bugfixed v7.4.0.
% 1.45/1.51 % Domain : Number Theory
% 1.45/1.51 % Problem : Robinson arithmetic: There exist infinite numbers
% 1.45/1.51 % Version : Especial.
% 1.45/1.51 % English :
% 1.45/1.51
% 1.45/1.51 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 1.45/1.51 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 1.45/1.51 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 1.45/1.51 % Source : [Lam18]
% 1.45/1.51 % Names : infiniteNumbersid [Lam18]
% 1.45/1.51
% 1.45/1.51 % Status : Theorem
% 1.45/1.51 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.57 v7.5.0, 0.81 v7.4.0
% 1.45/1.51 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 1.45/1.51 % Number of atoms : 79 ( 0 equ)
% 1.45/1.51 % Maximal formula atoms : 7 ( 4 avg)
% 1.45/1.51 % Number of connectives : 96 ( 36 ~; 27 |; 33 &)
% 1.45/1.51 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 1.45/1.51 % Maximal formula depth : 13 ( 8 avg)
% 1.45/1.51 % Maximal term depth : 1 ( 1 avg)
% 1.45/1.51 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 1.45/1.51 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 1.45/1.51 % Number of variables : 72 ( 49 !; 23 ?)
% 1.45/1.51 % SPC : FOF_THM_RFO_NEQ
% 1.45/1.51
% 1.45/1.51 % Comments : Translated to FOL without equality.
% 1.45/1.51 % Bugfixes : v7.4.0 - Bugfixes in formulae's use if the r1/3 predicate.
% 1.45/1.51 %------------------------------------------------------------------------------
% 1.45/1.51 include('Axioms/NUM009+0.ax').
% 1.45/1.51 %------------------------------------------------------------------------------
% 1.45/1.51 fof(infiniteNumbersid,conjecture,
% 1.45/1.51 ! [X1] :
% 1.45/1.51 ? [Y2,Y1] :
% 1.45/1.51 ( ! [Y4] :
% 1.45/1.51 ( ~ id(Y1,Y4)
% 1.45/1.51 | ~ r1(Y4) )
% 1.45/1.51 & ? [Y3] :
% 1.45/1.51 ( id(Y3,Y2)
% 1.45/1.51 & r3(X1,Y1,Y3) ) ) ).
% 1.45/1.51
% 1.45/1.51 %------------------------------------------------------------------------------
% 1.45/1.51 %-------------------------------------------
% 1.45/1.51 % Proof found
% 1.45/1.51 % SZS status Theorem for theBenchmark
% 1.45/1.51 % SZS output start Proof
% 1.45/1.51 %ClaNum:44(EqnAxiom:0)
% 1.45/1.51 %VarNum:214(SingletonVarNum:104)
% 1.45/1.51 %MaxLitNum:5
% 1.45/1.51 %MaxfuncDepth:1
% 1.45/1.51 %SharedTerms:2
% 1.45/1.51 %goalClause: 39 40
% 1.45/1.51 [4]P2(x41,x41)
% 1.45/1.51 [1]P1(f1(x11))
% 1.45/1.51 [2]P1(f6(x21))
% 1.45/1.51 [3]P1(f8(x31))
% 1.45/1.51 [5]P2(f2(x51),x51)
% 1.45/1.51 [6]P2(f7(x61),f8(x61))
% 1.45/1.51 [12]P4(x121,f1(x121),f2(x121))
% 1.45/1.51 [13]P5(x131,f6(x131),f7(x131))
% 1.45/1.51 [7]P3(x71,f9(x72,x71))
% 1.45/1.51 [8]P3(x81,f3(x82,x81))
% 1.45/1.51 [9]P2(f10(x91,x92),f11(x91,x92))
% 1.45/1.51 [10]P2(f4(x101,x102),f21(x101,x102))
% 1.45/1.51 [11]P3(f22(x111,x112),f11(x111,x112))
% 1.45/1.51 [14]P4(x141,x142,f22(x141,x142))
% 1.45/1.51 [15]P5(x151,x152,f5(x151,x152))
% 1.45/1.51 [16]P4(x161,f9(x161,x162),f10(x161,x162))
% 1.45/1.51 [17]P5(x171,f3(x171,x172),f4(x171,x172))
% 1.45/1.51 [18]P4(f5(x181,x182),x181,f21(x181,x182))
% 1.45/1.51 [19]~P1(x191)+P2(x191,a12)
% 1.45/1.51 [20]P1(x201)+~P2(x201,a12)
% 1.45/1.51 [21]P2(x211,f15(x211))+P1(f13(x211))
% 1.45/1.51 [25]P3(f14(x251),f15(x251))+P1(f13(x251))
% 1.45/1.51 [26]P2(x261,f15(x261))+P2(x261,f13(x261))
% 1.45/1.51 [29]P3(f14(x291),f15(x291))+P2(x291,f13(x291))
% 1.45/1.51 [24]~P2(x242,x241)+P2(x241,x242)
% 1.45/1.51 [27]~P3(x272,x271)+P2(x271,f16(x272))
% 1.45/1.51 [28]P3(x281,x282)+~P2(x282,f16(x281))
% 1.45/1.51 [35]P4(x351,x352,x353)+~P2(x353,f19(x351,x352))
% 1.45/1.51 [36]P5(x361,x362,x363)+~P2(x363,f20(x361,x362))
% 1.45/1.51 [37]~P4(x372,x373,x371)+P2(x371,f19(x372,x373))
% 1.45/1.51 [38]~P5(x382,x383,x381)+P2(x381,f20(x382,x383))
% 1.45/1.51 [22]~P2(x222,x221)+P1(x221)+~P1(x222)
% 1.45/1.51 [23]~P2(x231,x232)+P1(x231)+~P1(x232)
% 1.45/1.51 [30]~P1(x301)+~P2(x301,x302)+~P3(x303,x302)
% 1.45/1.51 [31]~P2(x311,x313)+P2(x311,x312)+~P2(x313,x312)
% 1.45/1.51 [39]~P2(x393,x391)+~P4(a18,x392,x393)+P1(f17(x391,x392))
% 1.45/1.51 [40]~P2(x403,x402)+~P4(a18,x401,x403)+P2(x401,f17(x402,x401))
% 1.45/1.51 [32]~P3(x322,x324)+~P3(x321,x323)+P2(x321,x322)+~P2(x323,x324)
% 1.45/1.51 [33]~P3(x334,x333)+P3(x331,x332)+~P2(x333,x332)+~P2(x334,x331)
% 1.45/1.51 [34]~P3(x344,x343)+P3(x341,x342)+~P2(x342,x343)+~P2(x341,x344)
% 1.45/1.51 [41]~P4(x416,x415,x414)+P4(x411,x412,x413)+~P2(x414,x413)+~P2(x415,x412)+~P2(x416,x411)
% 1.45/1.51 [42]~P4(x426,x425,x424)+P4(x421,x422,x423)+~P2(x423,x424)+~P2(x422,x425)+~P2(x421,x426)
% 1.45/1.51 [43]~P5(x436,x435,x434)+P5(x431,x432,x433)+~P2(x434,x433)+~P2(x435,x432)+~P2(x436,x431)
% 1.45/1.51 [44]~P5(x446,x445,x444)+P5(x441,x442,x443)+~P2(x443,x444)+~P2(x442,x445)+~P2(x441,x446)
% 1.45/1.51 %EqnAxiom
% 1.45/1.51
% 1.45/1.51 %-------------------------------------------
% 1.45/1.52 cnf(45,plain,
% 1.45/1.52 (P1(a12)),
% 1.45/1.52 inference(scs_inference,[],[4,20])).
% 1.45/1.52 cnf(46,plain,
% 1.45/1.52 (P2(x461,x461)),
% 1.45/1.52 inference(rename_variables,[],[4])).
% 1.45/1.52 cnf(49,plain,
% 1.45/1.52 (P2(x491,x491)),
% 1.45/1.52 inference(rename_variables,[],[4])).
% 1.45/1.52 cnf(51,plain,
% 1.45/1.52 (P4(x511,x512,f19(x511,x512))),
% 1.45/1.52 inference(scs_inference,[],[4,46,49,20,28,35])).
% 1.45/1.52 cnf(266,plain,
% 1.45/1.52 (P2(f1(x2661),a12)),
% 1.45/1.52 inference(scs_inference,[],[1,4,19,22])).
% 1.45/1.52 cnf(281,plain,
% 1.45/1.52 (P1(f17(f19(a18,x2811),x2811))),
% 1.45/1.52 inference(scs_inference,[],[4,51,24,39])).
% 1.45/1.52 cnf(506,plain,
% 1.45/1.52 (P3(f1(x5061),f3(x5062,a12))),
% 1.45/1.52 inference(scs_inference,[],[266,4,8,34])).
% 1.45/1.52 cnf(561,plain,
% 1.45/1.52 (P3(f1(x5611),f2(f3(x5612,a12)))),
% 1.45/1.52 inference(scs_inference,[],[506,4,5,34])).
% 1.45/1.52 cnf(604,plain,
% 1.45/1.52 (~P1(f2(f3(x6041,a12)))),
% 1.45/1.52 inference(scs_inference,[],[561,45,30,24,19])).
% 1.45/1.52 cnf(625,plain,
% 1.45/1.52 (P2(x6251,f17(f19(a18,x6251),x6251))),
% 1.45/1.52 inference(scs_inference,[],[4,51,24,40])).
% 1.45/1.52 cnf(626,plain,
% 1.45/1.52 ($false),
% 1.45/1.52 inference(scs_inference,[],[281,625,604,23]),
% 1.45/1.52 ['proof']).
% 1.45/1.52 % SZS output end Proof
% 1.45/1.52 % Total time :0.900000s
%------------------------------------------------------------------------------