%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN081+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 : n012.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 13:29:41 EDT 2024
% Result : Theorem 0.55s 0.70s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN081+1 : TPTP v8.2.0. Released v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Jun 18 20:41:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.54/0.60 start to proof:theBenchmark
% 0.55/0.70 %-------------------------------------------
% 0.55/0.70 % File :CSE---1.7
% 0.55/0.70 % Problem :theBenchmark
% 0.55/0.70 % Transform :cnf
% 0.55/0.70 % Format :tptp:raw
% 0.55/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.70
% 0.55/0.70 % Result :Theorem 0.050000s
% 0.55/0.70 % Output :CNFRefutation 0.050000s
% 0.55/0.70 %-------------------------------------------
% 0.55/0.70 %------------------------------------------------------------------------------
% 0.55/0.70 % File : NUN081+1 : TPTP v8.2.0. Released v7.3.0.
% 0.55/0.70 % Domain : Number Theory
% 0.55/0.70 % Problem : Robinson arithmetic: There exists X + Y = 3
% 0.55/0.70 % Version : Especial.
% 0.55/0.70 % English :
% 0.55/0.70
% 0.55/0.70 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.55/0.70 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.55/0.70 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.55/0.70 % Source : [Lam18]
% 0.55/0.70 % Names : xplusyidthree [Lam18]
% 0.55/0.70
% 0.55/0.70 % Status : Theorem
% 0.55/0.70 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.36 v7.5.0, 0.33 v7.4.0, 0.25 v7.3.0
% 0.55/0.70 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 0.55/0.70 % Number of atoms : 81 ( 0 equ)
% 0.55/0.70 % Maximal formula atoms : 7 ( 4 avg)
% 0.55/0.70 % Number of connectives : 96 ( 34 ~; 26 |; 36 &)
% 0.55/0.70 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.55/0.70 % Maximal formula depth : 13 ( 8 avg)
% 0.55/0.70 % Maximal term depth : 1 ( 1 avg)
% 0.55/0.70 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.55/0.70 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.55/0.70 % Number of variables : 74 ( 47 !; 27 ?)
% 0.55/0.70 % SPC : FOF_THM_RFO_NEQ
% 0.55/0.70
% 0.55/0.70 % Comments : Translated to FOL without equality.
% 0.55/0.70 %------------------------------------------------------------------------------
% 0.55/0.70 include('Axioms/NUM009+0.ax').
% 0.55/0.70 %------------------------------------------------------------------------------
% 0.55/0.70 fof(xplusyidthree,conjecture,
% 0.55/0.70 ? [Y1,Y2,Y3] :
% 0.55/0.70 ( r3(Y1,Y2,Y3)
% 0.55/0.70 & ? [Y4] :
% 0.55/0.70 ( id(Y3,Y4)
% 0.55/0.70 & ? [Y5] :
% 0.55/0.70 ( r2(Y5,Y4)
% 0.55/0.70 & ? [Y6] :
% 0.55/0.70 ( r2(Y6,Y5)
% 0.55/0.70 & ? [Y7] :
% 0.55/0.70 ( r1(Y7)
% 0.55/0.70 & r2(Y7,Y6) ) ) ) ) ) ).
% 0.55/0.70
% 0.55/0.70 %------------------------------------------------------------------------------
% 0.55/0.70 %-------------------------------------------
% 0.55/0.70 % Proof found
% 0.55/0.70 % SZS status Theorem for theBenchmark
% 0.55/0.70 % SZS output start Proof
% 0.55/0.70 %ClaNum:43(EqnAxiom:0)
% 0.55/0.70 %VarNum:213(SingletonVarNum:105)
% 0.55/0.70 %MaxLitNum:6
% 0.55/0.70 %MaxfuncDepth:1
% 0.55/0.70 %SharedTerms:1
% 0.55/0.70 %goalClause: 39
% 0.55/0.70 [4]P2(x41,x41)
% 0.55/0.70 [1]P1(f1(x11))
% 0.55/0.70 [2]P1(f6(x21))
% 0.55/0.70 [3]P1(f8(x31))
% 0.55/0.70 [5]P2(f2(x51),x51)
% 0.55/0.70 [6]P2(f7(x61),f8(x61))
% 0.55/0.70 [12]P4(x121,f1(x121),f2(x121))
% 0.55/0.70 [13]P5(x131,f6(x131),f7(x131))
% 0.55/0.70 [7]P3(x71,f9(x72,x71))
% 0.55/0.70 [8]P3(x81,f3(x82,x81))
% 0.55/0.70 [9]P2(f10(x91,x92),f11(x91,x92))
% 0.55/0.70 [10]P2(f4(x101,x102),f19(x101,x102))
% 0.55/0.70 [11]P3(f20(x111,x112),f11(x111,x112))
% 0.55/0.70 [14]P4(x141,x142,f20(x141,x142))
% 0.55/0.70 [15]P5(x151,x152,f5(x151,x152))
% 0.55/0.70 [16]P4(x161,f9(x161,x162),f10(x161,x162))
% 0.55/0.70 [17]P5(x171,f3(x171,x172),f4(x171,x172))
% 0.55/0.70 [18]P4(f5(x181,x182),x181,f19(x181,x182))
% 0.55/0.70 [19]~P1(x191)+P2(x191,a12)
% 0.55/0.70 [20]P1(x201)+~P2(x201,a12)
% 0.55/0.70 [21]P2(x211,f15(x211))+P1(f13(x211))
% 0.55/0.70 [25]P3(f14(x251),f15(x251))+P1(f13(x251))
% 0.55/0.70 [26]P2(x261,f15(x261))+P2(x261,f13(x261))
% 0.55/0.70 [29]P3(f14(x291),f15(x291))+P2(x291,f13(x291))
% 0.55/0.70 [24]~P2(x242,x241)+P2(x241,x242)
% 0.55/0.70 [27]~P3(x272,x271)+P2(x271,f16(x272))
% 0.55/0.70 [28]P3(x281,x282)+~P2(x282,f16(x281))
% 0.55/0.70 [35]P4(x351,x352,x353)+~P2(x353,f17(x351,x352))
% 0.55/0.70 [36]P5(x361,x362,x363)+~P2(x363,f18(x361,x362))
% 0.55/0.70 [37]~P4(x372,x373,x371)+P2(x371,f17(x372,x373))
% 0.55/0.70 [38]~P5(x382,x383,x381)+P2(x381,f18(x382,x383))
% 0.55/0.70 [22]~P2(x222,x221)+P1(x221)+~P1(x222)
% 0.55/0.70 [23]~P2(x231,x232)+P1(x231)+~P1(x232)
% 0.55/0.70 [30]~P1(x301)+~P2(x301,x302)+~P3(x303,x302)
% 0.55/0.70 [31]~P2(x311,x313)+P2(x311,x312)+~P2(x313,x312)
% 0.55/0.70 [32]~P3(x322,x324)+~P3(x321,x323)+P2(x321,x322)+~P2(x323,x324)
% 0.55/0.70 [33]~P3(x334,x333)+P3(x331,x332)+~P2(x333,x332)+~P2(x334,x331)
% 0.55/0.70 [34]~P3(x344,x343)+P3(x341,x342)+~P2(x342,x343)+~P2(x341,x344)
% 0.55/0.70 [40]~P4(x406,x405,x404)+P4(x401,x402,x403)+~P2(x404,x403)+~P2(x405,x402)+~P2(x406,x401)
% 0.55/0.70 [41]~P4(x416,x415,x414)+P4(x411,x412,x413)+~P2(x413,x414)+~P2(x412,x415)+~P2(x411,x416)
% 0.55/0.70 [42]~P5(x426,x425,x424)+P5(x421,x422,x423)+~P2(x424,x423)+~P2(x425,x422)+~P2(x426,x421)
% 0.55/0.70 [43]~P5(x436,x435,x434)+P5(x431,x432,x433)+~P2(x433,x434)+~P2(x432,x435)+~P2(x431,x436)
% 0.55/0.70 [39]~P3(x395,x393)+~P1(x391)+~P2(x392,x393)+~P3(x391,x394)+~P4(x396,x397,x392)+~P3(x394,x395)
% 0.55/0.70 %EqnAxiom
% 0.55/0.70
% 0.55/0.70 %-------------------------------------------
% 0.56/0.71 cnf(45,plain,
% 0.56/0.71 (P2(x451,x451)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(48,plain,
% 0.56/0.71 (P2(x481,x481)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(51,plain,
% 0.56/0.71 (P2(x511,x511)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(54,plain,
% 0.56/0.71 (P2(x541,x541)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(57,plain,
% 0.56/0.71 (P2(x571,x571)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(60,plain,
% 0.56/0.71 (P2(f2(x601),x601)),
% 0.56/0.71 inference(rename_variables,[],[5])).
% 0.56/0.71 cnf(61,plain,
% 0.56/0.71 (P2(x611,x611)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(63,plain,
% 0.56/0.71 (P3(x631,f2(f9(x632,x631)))),
% 0.56/0.71 inference(scs_inference,[],[1,7,4,45,48,51,54,57,61,5,60,20,28,35,36,30,33,34])).
% 0.56/0.71 cnf(197,plain,
% 0.56/0.71 (P2(f2(x1971),x1971)),
% 0.56/0.71 inference(rename_variables,[],[5])).
% 0.56/0.71 cnf(200,plain,
% 0.56/0.71 (P2(x2001,x2001)),
% 0.56/0.71 inference(rename_variables,[],[4])).
% 0.56/0.71 cnf(201,plain,
% 0.56/0.71 (P3(x2011,f9(x2012,x2011))),
% 0.56/0.71 inference(rename_variables,[],[7])).
% 0.56/0.71 cnf(203,plain,
% 0.56/0.71 (P3(f2(x2031),f9(x2032,x2031))),
% 0.56/0.71 inference(scs_inference,[],[7,201,5,197,10,4,200,31,33,34])).
% 0.56/0.71 cnf(243,plain,
% 0.56/0.71 (P2(f2(x2431),x2431)),
% 0.56/0.71 inference(rename_variables,[],[5])).
% 0.56/0.71 cnf(245,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(scs_inference,[],[1,7,5,243,203,63,6,12,31,39]),
% 0.56/0.71 ['proof']).
% 0.56/0.71 % SZS output end Proof
% 0.56/0.71 % Total time :0.050000s
%------------------------------------------------------------------------------