TSTP Solution File: NUN060+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN060+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 12:45:19 EDT 2023
% Result : Theorem 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN060+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 10:18:28 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.61 start to proof:theBenchmark
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 % File :CSE---1.6
% 0.19/0.70 % Problem :theBenchmark
% 0.19/0.70 % Transform :cnf
% 0.19/0.70 % Format :tptp:raw
% 0.19/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.70
% 0.19/0.70 % Result :Theorem 0.030000s
% 0.19/0.70 % Output :CNFRefutation 0.030000s
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 %------------------------------------------------------------------------------
% 0.19/0.70 % File : NUN060+1 : TPTP v8.1.2. Released v7.3.0.
% 0.19/0.70 % Domain : Number Theory
% 0.19/0.70 % Problem : Robinson arithmetic: There exists X > 4
% 0.19/0.71 % Version : Especial.
% 0.19/0.71 % English :
% 0.19/0.71
% 0.19/0.71 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.19/0.71 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.19/0.71 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.19/0.71 % Source : [Lam18]
% 0.19/0.71 % Names : greq4id [Lam18]
% 0.19/0.71
% 0.19/0.71 % Status : Theorem
% 0.19/0.71 % Rating : 0.27 v8.1.0, 0.36 v7.5.0, 0.33 v7.4.0, 0.31 v7.3.0
% 0.19/0.71 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 0.19/0.71 % Number of atoms : 82 ( 0 equ)
% 0.19/0.71 % Maximal formula atoms : 7 ( 4 avg)
% 0.19/0.71 % Number of connectives : 97 ( 34 ~; 26 |; 37 &)
% 0.19/0.71 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.71 % Maximal formula depth : 15 ( 8 avg)
% 0.19/0.71 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.71 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.19/0.71 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.71 % Number of variables : 75 ( 47 !; 28 ?)
% 0.19/0.71 % SPC : FOF_THM_RFO_NEQ
% 0.19/0.71
% 0.19/0.71 % Comments : Translated to FOL without equality.
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 include('Axioms/NUM009+0.ax').
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 fof(greq4id,conjecture,
% 0.19/0.71 ? [Y1,Y2,Y3] :
% 0.19/0.71 ( id(Y3,Y1)
% 0.19/0.71 & ? [Y4] :
% 0.19/0.71 ( r3(Y2,Y4,Y3)
% 0.19/0.71 & ? [Y5] :
% 0.19/0.71 ( r2(Y5,Y4)
% 0.19/0.71 & ? [Y6] :
% 0.19/0.71 ( r2(Y6,Y5)
% 0.19/0.71 & ? [Y7] :
% 0.19/0.71 ( r2(Y7,Y6)
% 0.19/0.71 & ? [Y8] :
% 0.19/0.71 ( r1(Y8)
% 0.19/0.71 & r2(Y8,Y7) ) ) ) ) ) ) ).
% 0.19/0.71
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark
% 0.19/0.71 % SZS output start Proof
% 0.19/0.71 %ClaNum:43(EqnAxiom:0)
% 0.19/0.71 %VarNum:215(SingletonVarNum:106)
% 0.19/0.71 %MaxLitNum:7
% 0.19/0.71 %MaxfuncDepth:1
% 0.19/0.71 %SharedTerms:1
% 0.19/0.71 %goalClause: 39
% 0.19/0.71 [4]P2(x41,x41)
% 0.19/0.71 [1]P1(f1(x11))
% 0.19/0.71 [2]P1(f6(x21))
% 0.19/0.71 [3]P1(f8(x31))
% 0.19/0.71 [5]P2(f2(x51),x51)
% 0.19/0.71 [6]P2(f7(x61),f8(x61))
% 0.19/0.71 [12]P4(x121,f1(x121),f2(x121))
% 0.19/0.71 [13]P5(x131,f6(x131),f7(x131))
% 0.19/0.71 [7]P3(x71,f9(x72,x71))
% 0.19/0.71 [8]P3(x81,f3(x82,x81))
% 0.19/0.71 [9]P2(f10(x91,x92),f11(x91,x92))
% 0.19/0.71 [10]P2(f4(x101,x102),f19(x101,x102))
% 0.19/0.71 [11]P3(f20(x111,x112),f11(x111,x112))
% 0.19/0.71 [14]P4(x141,x142,f20(x141,x142))
% 0.19/0.71 [15]P5(x151,x152,f5(x151,x152))
% 0.19/0.71 [16]P4(x161,f9(x161,x162),f10(x161,x162))
% 0.19/0.71 [17]P5(x171,f3(x171,x172),f4(x171,x172))
% 0.19/0.71 [18]P4(f5(x181,x182),x181,f19(x181,x182))
% 0.19/0.71 [19]~P1(x191)+P2(x191,a12)
% 0.19/0.71 [20]P1(x201)+~P2(x201,a12)
% 0.19/0.71 [21]P2(x211,f15(x211))+P1(f13(x211))
% 0.19/0.71 [25]P3(f14(x251),f15(x251))+P1(f13(x251))
% 0.19/0.71 [26]P2(x261,f15(x261))+P2(x261,f13(x261))
% 0.19/0.71 [29]P3(f14(x291),f15(x291))+P2(x291,f13(x291))
% 0.19/0.71 [24]~P2(x242,x241)+P2(x241,x242)
% 0.19/0.71 [27]~P3(x272,x271)+P2(x271,f16(x272))
% 0.19/0.71 [28]P3(x281,x282)+~P2(x282,f16(x281))
% 0.19/0.71 [35]P4(x351,x352,x353)+~P2(x353,f17(x351,x352))
% 0.19/0.71 [36]P5(x361,x362,x363)+~P2(x363,f18(x361,x362))
% 0.19/0.71 [37]~P4(x372,x373,x371)+P2(x371,f17(x372,x373))
% 0.19/0.71 [38]~P5(x382,x383,x381)+P2(x381,f18(x382,x383))
% 0.19/0.71 [22]~P2(x222,x221)+P1(x221)+~P1(x222)
% 0.19/0.71 [23]~P2(x231,x232)+P1(x231)+~P1(x232)
% 0.19/0.71 [30]~P1(x301)+~P2(x301,x302)+~P3(x303,x302)
% 0.19/0.71 [31]~P2(x311,x313)+P2(x311,x312)+~P2(x313,x312)
% 0.19/0.71 [32]~P3(x322,x324)+~P3(x321,x323)+P2(x321,x322)+~P2(x323,x324)
% 0.19/0.71 [33]~P3(x334,x333)+P3(x331,x332)+~P2(x333,x332)+~P2(x334,x331)
% 0.19/0.71 [34]~P3(x344,x343)+P3(x341,x342)+~P2(x342,x343)+~P2(x341,x344)
% 0.19/0.71 [40]~P4(x406,x405,x404)+P4(x401,x402,x403)+~P2(x404,x403)+~P2(x405,x402)+~P2(x406,x401)
% 0.19/0.71 [41]~P4(x416,x415,x414)+P4(x411,x412,x413)+~P2(x413,x414)+~P2(x412,x415)+~P2(x411,x416)
% 0.19/0.71 [42]~P5(x426,x425,x424)+P5(x421,x422,x423)+~P2(x424,x423)+~P2(x425,x422)+~P2(x426,x421)
% 0.19/0.71 [43]~P5(x436,x435,x434)+P5(x431,x432,x433)+~P2(x433,x434)+~P2(x432,x435)+~P2(x431,x436)
% 0.19/0.71 [39]~P1(x391)+~P2(x392,x393)+~P3(x391,x394)+~P3(x394,x395)+~P4(x398,x397,x392)+~P3(x395,x396)+~P3(x396,x397)
% 0.19/0.71 %EqnAxiom
% 0.19/0.71
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 cnf(45,plain,
% 0.19/0.71 (P2(x451,x451)),
% 0.19/0.71 inference(rename_variables,[],[4])).
% 0.19/0.71 cnf(46,plain,
% 0.19/0.71 (P3(x461,f16(x461))),
% 0.19/0.71 inference(scs_inference,[],[4,45,20,28])).
% 0.19/0.71 cnf(47,plain,
% 0.19/0.71 (P2(x471,x471)),
% 0.19/0.71 inference(rename_variables,[],[4])).
% 0.19/0.71 cnf(50,plain,
% 0.19/0.71 (P2(x501,x501)),
% 0.19/0.71 inference(rename_variables,[],[4])).
% 0.19/0.71 cnf(53,plain,
% 0.19/0.71 (P2(x531,x531)),
% 0.19/0.71 inference(rename_variables,[],[4])).
% 0.19/0.71 cnf(55,plain,
% 0.19/0.71 (~P3(x551,f1(x552))),
% 0.19/0.71 inference(scs_inference,[],[1,4,45,47,50,53,20,28,36,35,30])).
% 0.19/0.71 cnf(58,plain,
% 0.19/0.71 (P2(f2(x581),x581)),
% 0.19/0.71 inference(rename_variables,[],[5])).
% 0.19/0.71 cnf(59,plain,
% 0.19/0.71 (P2(x591,x591)),
% 0.19/0.71 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(62,plain,
% 0.19/0.72 (P2(f2(x621),x621)),
% 0.19/0.72 inference(rename_variables,[],[5])).
% 0.19/0.72 cnf(64,plain,
% 0.19/0.72 (P2(x641,x641)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(65,plain,
% 0.19/0.72 (P5(x651,x652,f5(x651,x652))),
% 0.19/0.72 inference(rename_variables,[],[15])).
% 0.19/0.72 cnf(68,plain,
% 0.19/0.72 (P2(f2(x681),x681)),
% 0.19/0.72 inference(rename_variables,[],[5])).
% 0.19/0.72 cnf(70,plain,
% 0.19/0.72 (P2(x701,x701)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(71,plain,
% 0.19/0.72 (P4(x711,x712,f20(x711,x712))),
% 0.19/0.72 inference(rename_variables,[],[14])).
% 0.19/0.72 cnf(73,plain,
% 0.19/0.72 (P2(x731,f2(x731))),
% 0.19/0.72 inference(scs_inference,[],[1,4,45,47,50,53,59,64,14,15,5,58,62,68,20,28,36,35,30,33,43,41,24])).
% 0.19/0.72 cnf(83,plain,
% 0.19/0.72 (~P2(f1(x831),f9(x832,f1(x831)))),
% 0.19/0.72 inference(scs_inference,[],[1,4,45,47,50,53,59,64,70,14,71,15,65,5,58,62,68,7,20,28,36,35,30,33,43,41,24,19,27,38,37,34])).
% 0.19/0.72 cnf(105,plain,
% 0.19/0.72 (P2(x1051,f2(x1051))),
% 0.19/0.72 inference(rename_variables,[],[73])).
% 0.19/0.72 cnf(112,plain,
% 0.19/0.72 (P2(x1121,x1121)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(120,plain,
% 0.19/0.72 (P2(x1201,x1201)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(123,plain,
% 0.19/0.72 (P2(x1231,x1231)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(125,plain,
% 0.19/0.72 (P2(x1251,f2(x1251))),
% 0.19/0.72 inference(rename_variables,[],[73])).
% 0.19/0.72 cnf(131,plain,
% 0.19/0.72 (P2(x1311,x1311)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(134,plain,
% 0.19/0.72 (P2(x1341,x1341)),
% 0.19/0.72 inference(rename_variables,[],[4])).
% 0.19/0.72 cnf(138,plain,
% 0.19/0.72 (~P3(f1(x1381),x1382)),
% 0.19/0.72 inference(scs_inference,[],[1,8,12,13,18,10,4,112,120,123,131,134,14,15,5,6,7,46,73,105,125,83,55,31,24,28,30,23,22,41,42,20,43,40,39])).
% 0.19/0.72 cnf(148,plain,
% 0.19/0.72 ($false),
% 0.19/0.72 inference(scs_inference,[],[138,7]),
% 0.19/0.72 ['proof']).
% 0.19/0.72 % SZS output end Proof
% 0.19/0.72 % Total time :0.030000s
%------------------------------------------------------------------------------