TSTP Solution File: NUN062+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n016.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 12:45:20 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 : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 09:43:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 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 0.050000s
% 0.19/0.67 % Output :CNFRefutation 0.050000s
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 % File : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.19/0.67 % Domain : Number Theory
% 0.19/0.67 % Problem : Robinson arithmetic: There exist infinite numbers
% 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 : infiniteNumbersid [Lam18]
% 0.19/0.67
% 0.19/0.67 % Status : Theorem
% 0.19/0.67 % Rating : 0.27 v8.1.0, 0.57 v7.5.0, 0.81 v7.4.0
% 0.19/0.67 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 0.19/0.67 % Number of atoms : 79 ( 0 equ)
% 0.19/0.67 % Maximal formula atoms : 7 ( 4 avg)
% 0.19/0.67 % Number of connectives : 96 ( 36 ~; 27 |; 33 &)
% 0.19/0.67 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.67 % Maximal formula depth : 13 ( 8 avg)
% 0.19/0.67 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.67 % Number of predicates : 5 ( 5 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 : 72 ( 49 !; 23 ?)
% 0.19/0.67 % SPC : FOF_THM_RFO_NEQ
% 0.19/0.67
% 0.19/0.67 % Comments : Translated to FOL without equality.
% 0.19/0.67 % Bugfixes : v7.4.0 - Bugfixes in formulae's use if the r1/3 predicate.
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 include('Axioms/NUM009+0.ax').
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 fof(infiniteNumbersid,conjecture,
% 0.19/0.67 ! [X1] :
% 0.19/0.67 ? [Y2,Y1] :
% 0.19/0.67 ( ! [Y4] :
% 0.19/0.67 ( ~ id(Y1,Y4)
% 0.19/0.67 | ~ r1(Y4) )
% 0.19/0.67 & ? [Y3] :
% 0.19/0.67 ( id(Y3,Y2)
% 0.19/0.67 & r3(X1,Y1,Y3) ) ) ).
% 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
% 0.19/0.67 %ClaNum:44(EqnAxiom:0)
% 0.19/0.67 %VarNum:214(SingletonVarNum:104)
% 0.19/0.67 %MaxLitNum:5
% 0.19/0.67 %MaxfuncDepth:1
% 0.19/0.67 %SharedTerms:2
% 0.19/0.67 %goalClause: 39 40
% 0.19/0.67 [4]P2(x41,x41)
% 0.19/0.68 [1]P1(f1(x11))
% 0.19/0.68 [2]P1(f6(x21))
% 0.19/0.68 [3]P1(f8(x31))
% 0.19/0.68 [5]P2(f2(x51),x51)
% 0.19/0.68 [6]P2(f7(x61),f8(x61))
% 0.19/0.68 [12]P4(x121,f1(x121),f2(x121))
% 0.19/0.68 [13]P5(x131,f6(x131),f7(x131))
% 0.19/0.68 [7]P3(x71,f9(x72,x71))
% 0.19/0.68 [8]P3(x81,f3(x82,x81))
% 0.19/0.68 [9]P2(f10(x91,x92),f11(x91,x92))
% 0.19/0.68 [10]P2(f4(x101,x102),f21(x101,x102))
% 0.19/0.68 [11]P3(f22(x111,x112),f11(x111,x112))
% 0.19/0.68 [14]P4(x141,x142,f22(x141,x142))
% 0.19/0.68 [15]P5(x151,x152,f5(x151,x152))
% 0.19/0.68 [16]P4(x161,f9(x161,x162),f10(x161,x162))
% 0.19/0.68 [17]P5(x171,f3(x171,x172),f4(x171,x172))
% 0.19/0.68 [18]P4(f5(x181,x182),x181,f21(x181,x182))
% 0.19/0.68 [19]~P1(x191)+P2(x191,a12)
% 0.19/0.68 [20]P1(x201)+~P2(x201,a12)
% 0.19/0.68 [21]P2(x211,f15(x211))+P1(f13(x211))
% 0.19/0.68 [25]P3(f14(x251),f15(x251))+P1(f13(x251))
% 0.19/0.68 [26]P2(x261,f15(x261))+P2(x261,f13(x261))
% 0.19/0.68 [29]P3(f14(x291),f15(x291))+P2(x291,f13(x291))
% 0.19/0.68 [24]~P2(x242,x241)+P2(x241,x242)
% 0.19/0.68 [27]~P3(x272,x271)+P2(x271,f16(x272))
% 0.19/0.68 [28]P3(x281,x282)+~P2(x282,f16(x281))
% 0.19/0.68 [35]P4(x351,x352,x353)+~P2(x353,f19(x351,x352))
% 0.19/0.68 [36]P5(x361,x362,x363)+~P2(x363,f20(x361,x362))
% 0.19/0.68 [37]~P4(x372,x373,x371)+P2(x371,f19(x372,x373))
% 0.19/0.68 [38]~P5(x382,x383,x381)+P2(x381,f20(x382,x383))
% 0.19/0.68 [22]~P2(x222,x221)+P1(x221)+~P1(x222)
% 0.19/0.68 [23]~P2(x231,x232)+P1(x231)+~P1(x232)
% 0.19/0.68 [30]~P1(x301)+~P2(x301,x302)+~P3(x303,x302)
% 0.19/0.68 [31]~P2(x311,x313)+P2(x311,x312)+~P2(x313,x312)
% 0.19/0.68 [39]~P2(x393,x391)+~P4(a18,x392,x393)+P1(f17(x391,x392))
% 0.19/0.68 [40]~P2(x403,x402)+~P4(a18,x401,x403)+P2(x401,f17(x402,x401))
% 0.19/0.68 [32]~P3(x322,x324)+~P3(x321,x323)+P2(x321,x322)+~P2(x323,x324)
% 0.19/0.68 [33]~P3(x334,x333)+P3(x331,x332)+~P2(x333,x332)+~P2(x334,x331)
% 0.19/0.68 [34]~P3(x344,x343)+P3(x341,x342)+~P2(x342,x343)+~P2(x341,x344)
% 0.19/0.68 [41]~P4(x416,x415,x414)+P4(x411,x412,x413)+~P2(x414,x413)+~P2(x415,x412)+~P2(x416,x411)
% 0.19/0.68 [42]~P4(x426,x425,x424)+P4(x421,x422,x423)+~P2(x423,x424)+~P2(x422,x425)+~P2(x421,x426)
% 0.19/0.68 [43]~P5(x436,x435,x434)+P5(x431,x432,x433)+~P2(x434,x433)+~P2(x435,x432)+~P2(x436,x431)
% 0.19/0.68 [44]~P5(x446,x445,x444)+P5(x441,x442,x443)+~P2(x443,x444)+~P2(x442,x445)+~P2(x441,x446)
% 0.19/0.68 %EqnAxiom
% 0.19/0.68
% 0.19/0.68 %-------------------------------------------
% 0.19/0.68 cnf(46,plain,
% 0.19/0.68 (P2(x461,x461)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(48,plain,
% 0.19/0.68 (P2(x481,x481)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(50,plain,
% 0.19/0.68 (P5(x501,x502,f20(x501,x502))),
% 0.19/0.68 inference(scs_inference,[],[4,46,48,20,28,36])).
% 0.19/0.68 cnf(51,plain,
% 0.19/0.68 (P2(x511,x511)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(54,plain,
% 0.19/0.68 (P2(x541,x541)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(56,plain,
% 0.19/0.68 (~P3(x561,f1(x562))),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,20,28,36,35,30])).
% 0.19/0.68 cnf(59,plain,
% 0.19/0.68 (P2(f2(x591),x591)),
% 0.19/0.68 inference(rename_variables,[],[5])).
% 0.19/0.68 cnf(60,plain,
% 0.19/0.68 (P2(x601,x601)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(63,plain,
% 0.19/0.68 (P2(f2(x631),x631)),
% 0.19/0.68 inference(rename_variables,[],[5])).
% 0.19/0.68 cnf(65,plain,
% 0.19/0.68 (P2(x651,x651)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(66,plain,
% 0.19/0.68 (P5(x661,x662,f5(x661,x662))),
% 0.19/0.68 inference(rename_variables,[],[15])).
% 0.19/0.68 cnf(69,plain,
% 0.19/0.68 (P2(f2(x691),x691)),
% 0.19/0.68 inference(rename_variables,[],[5])).
% 0.19/0.68 cnf(70,plain,
% 0.19/0.68 (P2(x701,x701)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(71,plain,
% 0.19/0.68 (P2(x711,x711)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(72,plain,
% 0.19/0.68 (P4(x721,x722,f22(x721,x722))),
% 0.19/0.68 inference(rename_variables,[],[14])).
% 0.19/0.68 cnf(74,plain,
% 0.19/0.68 (P2(x741,f2(x741))),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,60,65,14,15,5,59,63,69,20,28,36,35,30,33,44,42,24])).
% 0.19/0.68 cnf(76,plain,
% 0.19/0.68 (P2(f1(x761),a12)),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,60,65,14,15,5,59,63,69,20,28,36,35,30,33,44,42,24,19])).
% 0.19/0.68 cnf(78,plain,
% 0.19/0.68 (P2(f9(x781,x782),f16(x782))),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,60,65,14,15,5,59,63,69,7,20,28,36,35,30,33,44,42,24,19,27])).
% 0.19/0.68 cnf(84,plain,
% 0.19/0.68 (P2(x841,f17(f22(a18,x841),x841))),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,60,65,71,14,72,15,66,5,59,63,69,7,20,28,36,35,30,33,44,42,24,19,27,38,37,40])).
% 0.19/0.68 cnf(86,plain,
% 0.19/0.68 (P1(f17(f22(a18,x861),x861))),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,60,65,71,14,72,15,66,5,59,63,69,7,20,28,36,35,30,33,44,42,24,19,27,38,37,40,39])).
% 0.19/0.68 cnf(88,plain,
% 0.19/0.68 (~P2(f1(x881),f9(x882,f1(x881)))),
% 0.19/0.68 inference(scs_inference,[],[1,4,46,48,51,54,60,65,71,70,14,72,15,66,5,59,63,69,7,20,28,36,35,30,33,44,42,24,19,27,38,37,40,39,34])).
% 0.19/0.68 cnf(111,plain,
% 0.19/0.68 (P2(x1111,f2(x1111))),
% 0.19/0.68 inference(rename_variables,[],[74])).
% 0.19/0.68 cnf(117,plain,
% 0.19/0.68 (P2(x1171,x1171)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(118,plain,
% 0.19/0.68 (P4(x1181,f1(x1181),f2(x1181))),
% 0.19/0.68 inference(rename_variables,[],[12])).
% 0.19/0.68 cnf(122,plain,
% 0.19/0.68 (P2(x1221,x1221)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(126,plain,
% 0.19/0.68 (P2(x1261,x1261)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(129,plain,
% 0.19/0.68 (P2(x1291,x1291)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(131,plain,
% 0.19/0.68 (P2(x1311,f2(x1311))),
% 0.19/0.68 inference(rename_variables,[],[74])).
% 0.19/0.68 cnf(134,plain,
% 0.19/0.68 (P2(x1341,x1341)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(135,plain,
% 0.19/0.68 (P4(x1351,f1(x1351),f2(x1351))),
% 0.19/0.68 inference(rename_variables,[],[12])).
% 0.19/0.68 cnf(148,plain,
% 0.19/0.68 (~P2(f3(x1481,f4(x1482,x1483)),f1(x1484))),
% 0.19/0.68 inference(scs_inference,[],[8,3,12,118,135,13,10,6,4,117,122,126,129,134,14,15,5,74,111,131,88,56,31,23,39,44,42,43,41,24,28,30,40,33])).
% 0.19/0.68 cnf(155,plain,
% 0.19/0.68 (P2(f2(x1551),x1551)),
% 0.19/0.68 inference(rename_variables,[],[5])).
% 0.19/0.68 cnf(159,plain,
% 0.19/0.68 (P2(x1591,x1591)),
% 0.19/0.68 inference(rename_variables,[],[4])).
% 0.19/0.68 cnf(164,plain,
% 0.19/0.68 (P2(f10(x1641,x1642),f11(x1641,x1642))),
% 0.19/0.68 inference(rename_variables,[],[9])).
% 0.19/0.68 cnf(167,plain,
% 0.19/0.68 (P2(f11(x1671,x1672),f10(x1671,x1672))),
% 0.19/0.68 inference(scs_inference,[],[16,17,9,164,4,159,5,155,78,76,31,44,41,24])).
% 0.19/0.68 cnf(169,plain,
% 0.19/0.68 (~P1(f10(x1691,x1692))),
% 0.19/0.68 inference(scs_inference,[],[16,17,11,9,164,4,159,5,155,78,76,31,44,41,24,30])).
% 0.19/0.68 cnf(197,plain,
% 0.19/0.68 (P2(f2(x1971),x1971)),
% 0.19/0.68 inference(rename_variables,[],[5])).
% 0.19/0.68 cnf(207,plain,
% 0.19/0.68 ($false),
% 0.19/0.68 inference(scs_inference,[],[11,4,5,197,50,167,148,169,84,86,20,24,44,33,23]),
% 0.19/0.68 ['proof']).
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time :0.050000s
%------------------------------------------------------------------------------