%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUN070+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 13:29:38 EDT 2024
% Result : Theorem 2.59s 2.68s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN070+1 : TPTP v8.2.0. Released v7.3.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 21:17:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.45/0.57 start to proof:theBenchmark
% 2.59/2.67 %-------------------------------------------
% 2.59/2.67 % File :CSE---1.7
% 2.59/2.67 % Problem :theBenchmark
% 2.59/2.67 % Transform :cnf
% 2.59/2.67 % Format :tptp:raw
% 2.59/2.67 % Command :java -jar mcs_scs.jar %d %s
% 2.59/2.67
% 2.59/2.67 % Result :Theorem 2.070000s
% 2.59/2.67 % Output :CNFRefutation 2.070000s
% 2.59/2.67 %-------------------------------------------
% 2.59/2.68 %------------------------------------------------------------------------------
% 2.59/2.68 % File : NUN070+1 : TPTP v8.2.0. Released v7.3.0.
% 2.59/2.68 % Domain : Number Theory
% 2.59/2.68 % Problem : Robinson arithmetic: 1 + 0 = 1
% 2.59/2.68 % Version : Especial.
% 2.59/2.68 % English :
% 2.59/2.68
% 2.59/2.68 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 2.59/2.68 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 2.59/2.68 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 2.59/2.68 % Source : [Lam18]
% 2.59/2.68 % Names : onepluszeroidone [Lam18]
% 2.59/2.68
% 2.59/2.68 % Status : Theorem
% 2.59/2.68 % Rating : 0.25 v8.2.0, 0.20 v8.1.0, 0.21 v7.5.0, 0.29 v7.4.0, 0.12 v7.3.0
% 2.59/2.68 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 2.59/2.68 % Number of atoms : 82 ( 0 equ)
% 2.59/2.68 % Maximal formula atoms : 7 ( 4 avg)
% 2.59/2.68 % Number of connectives : 97 ( 34 ~; 26 |; 37 &)
% 2.59/2.68 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 2.59/2.68 % Maximal formula depth : 13 ( 8 avg)
% 2.59/2.68 % Maximal term depth : 1 ( 1 avg)
% 2.59/2.68 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 2.59/2.68 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 2.59/2.68 % Number of variables : 73 ( 47 !; 26 ?)
% 2.59/2.68 % SPC : FOF_THM_RFO_NEQ
% 2.59/2.68
% 2.59/2.68 % Comments : Translated to FOL without equality.
% 2.59/2.68 %------------------------------------------------------------------------------
% 2.59/2.68 include('Axioms/NUM009+0.ax').
% 2.59/2.68 %------------------------------------------------------------------------------
% 2.59/2.68 fof(onepluszeroidone,conjecture,
% 2.59/2.68 ? [Y1] :
% 2.59/2.68 ( ? [Y2] :
% 2.59/2.68 ( ? [Y4] :
% 2.59/2.68 ( r1(Y4)
% 2.59/2.68 & r3(Y2,Y4,Y1) )
% 2.59/2.68 & ? [Y5] :
% 2.59/2.68 ( r1(Y5)
% 2.59/2.68 & r2(Y5,Y2) ) )
% 2.59/2.68 & ? [Y3] :
% 2.59/2.68 ( id(Y1,Y3)
% 2.59/2.68 & ? [Y6] :
% 2.59/2.68 ( r1(Y6)
% 2.59/2.68 & r2(Y6,Y3) ) ) ) ).
% 2.59/2.68
% 2.59/2.68 %------------------------------------------------------------------------------
% 2.59/2.68 %-------------------------------------------
% 2.59/2.68 % Proof found
% 2.59/2.68 % SZS status Theorem for theBenchmark
% 2.59/2.68 % SZS output start Proof
% 2.59/2.68 %ClaNum:43(EqnAxiom:0)
% 2.59/2.68 %VarNum:213(SingletonVarNum:104)
% 2.59/2.68 %MaxLitNum:7
% 2.59/2.68 %MaxfuncDepth:1
% 2.59/2.68 %SharedTerms:1
% 2.59/2.68 %goalClause: 39
% 2.59/2.68 [4]P2(x41,x41)
% 2.59/2.68 [1]P1(f1(x11))
% 2.59/2.68 [2]P1(f6(x21))
% 2.59/2.68 [3]P1(f8(x31))
% 2.59/2.68 [5]P2(f2(x51),x51)
% 2.59/2.68 [6]P2(f7(x61),f8(x61))
% 2.59/2.68 [12]P4(x121,f1(x121),f2(x121))
% 2.59/2.68 [13]P5(x131,f6(x131),f7(x131))
% 2.59/2.68 [7]P3(x71,f9(x72,x71))
% 2.59/2.68 [8]P3(x81,f3(x82,x81))
% 2.59/2.68 [9]P2(f10(x91,x92),f11(x91,x92))
% 2.59/2.68 [10]P2(f4(x101,x102),f19(x101,x102))
% 2.59/2.68 [11]P3(f20(x111,x112),f11(x111,x112))
% 2.59/2.68 [14]P4(x141,x142,f20(x141,x142))
% 2.59/2.68 [15]P5(x151,x152,f5(x151,x152))
% 2.59/2.68 [16]P4(x161,f9(x161,x162),f10(x161,x162))
% 2.59/2.68 [17]P5(x171,f3(x171,x172),f4(x171,x172))
% 2.59/2.68 [18]P4(f5(x181,x182),x181,f19(x181,x182))
% 2.59/2.68 [19]~P1(x191)+P2(x191,a12)
% 2.59/2.68 [20]P1(x201)+~P2(x201,a12)
% 2.59/2.68 [21]P2(x211,f15(x211))+P1(f13(x211))
% 2.59/2.68 [25]P3(f14(x251),f15(x251))+P1(f13(x251))
% 2.59/2.68 [26]P2(x261,f15(x261))+P2(x261,f13(x261))
% 2.59/2.68 [29]P3(f14(x291),f15(x291))+P2(x291,f13(x291))
% 2.59/2.68 [24]~P2(x242,x241)+P2(x241,x242)
% 2.59/2.68 [27]~P3(x272,x271)+P2(x271,f16(x272))
% 2.59/2.68 [28]P3(x281,x282)+~P2(x282,f16(x281))
% 2.59/2.68 [35]P4(x351,x352,x353)+~P2(x353,f17(x351,x352))
% 2.59/2.68 [36]P5(x361,x362,x363)+~P2(x363,f18(x361,x362))
% 2.59/2.68 [37]~P4(x372,x373,x371)+P2(x371,f17(x372,x373))
% 2.59/2.68 [38]~P5(x382,x383,x381)+P2(x381,f18(x382,x383))
% 2.59/2.68 [22]~P2(x222,x221)+P1(x221)+~P1(x222)
% 2.59/2.68 [23]~P2(x231,x232)+P1(x231)+~P1(x232)
% 2.59/2.68 [30]~P1(x301)+~P2(x301,x302)+~P3(x303,x302)
% 2.59/2.68 [31]~P2(x311,x313)+P2(x311,x312)+~P2(x313,x312)
% 2.59/2.68 [32]~P3(x322,x324)+~P3(x321,x323)+P2(x321,x322)+~P2(x323,x324)
% 2.59/2.68 [33]~P3(x334,x333)+P3(x331,x332)+~P2(x333,x332)+~P2(x334,x331)
% 2.59/2.68 [34]~P3(x344,x343)+P3(x341,x342)+~P2(x342,x343)+~P2(x341,x344)
% 2.59/2.68 [40]~P4(x406,x405,x404)+P4(x401,x402,x403)+~P2(x404,x403)+~P2(x405,x402)+~P2(x406,x401)
% 2.59/2.68 [41]~P4(x416,x415,x414)+P4(x411,x412,x413)+~P2(x413,x414)+~P2(x412,x415)+~P2(x411,x416)
% 2.59/2.68 [42]~P5(x426,x425,x424)+P5(x421,x422,x423)+~P2(x424,x423)+~P2(x425,x422)+~P2(x426,x421)
% 2.59/2.68 [43]~P5(x436,x435,x434)+P5(x431,x432,x433)+~P2(x433,x434)+~P2(x432,x435)+~P2(x431,x436)
% 2.59/2.68 [39]~P3(x391,x395)+~P4(x396,x393,x394)+~P1(x391)+~P1(x392)+~P2(x394,x395)+~P1(x393)+~P3(x392,x396)
% 2.59/2.68 %EqnAxiom
% 2.59/2.68
% 2.59/2.68 %-------------------------------------------
% 2.59/2.68 cnf(44,plain,
% 2.59/2.68 (P1(a12)),
% 2.59/2.68 inference(scs_inference,[],[4,20])).
% 2.59/2.68 cnf(45,plain,
% 2.59/2.68 (P2(x451,x451)),
% 2.59/2.68 inference(rename_variables,[],[4])).
% 2.59/2.68 cnf(48,plain,
% 2.59/2.68 (P2(x481,x481)),
% 2.59/2.68 inference(rename_variables,[],[4])).
% 2.59/2.68 cnf(50,plain,
% 2.59/2.68 (P4(x501,x502,f17(x501,x502))),
% 2.59/2.68 inference(scs_inference,[],[4,45,48,20,28,35])).
% 2.59/2.68 cnf(51,plain,
% 2.59/2.68 (P2(x511,x511)),
% 2.59/2.68 inference(rename_variables,[],[4])).
% 2.59/2.68 cnf(53,plain,
% 2.59/2.68 (P5(x531,x532,f18(x531,x532))),
% 2.59/2.68 inference(scs_inference,[],[4,45,48,51,20,28,35,36])).
% 2.59/2.68 cnf(202,plain,
% 2.59/2.68 (P2(f2(x2021),x2021)),
% 2.59/2.68 inference(rename_variables,[],[5])).
% 2.59/2.68 cnf(205,plain,
% 2.59/2.69 (P2(x2051,x2051)),
% 2.59/2.69 inference(rename_variables,[],[4])).
% 2.59/2.69 cnf(206,plain,
% 2.59/2.69 (P2(f2(x2061),x2061)),
% 2.59/2.69 inference(rename_variables,[],[5])).
% 2.59/2.69 cnf(209,plain,
% 2.59/2.69 (P2(x2091,x2091)),
% 2.59/2.69 inference(rename_variables,[],[4])).
% 2.59/2.69 cnf(210,plain,
% 2.59/2.69 (P3(x2101,f9(x2102,x2101))),
% 2.59/2.69 inference(rename_variables,[],[7])).
% 2.59/2.69 cnf(213,plain,
% 2.59/2.69 (P2(x2131,x2131)),
% 2.59/2.69 inference(rename_variables,[],[4])).
% 2.59/2.69 cnf(220,plain,
% 2.59/2.69 (~P4(f9(x2201,a12),a12,f2(f9(x2201,a12)))),
% 2.59/2.69 inference(scs_inference,[],[7,210,5,202,206,44,50,4,205,209,213,10,53,31,34,33,42,40,39])).
% 2.59/2.69 cnf(881,plain,
% 2.59/2.69 (~P2(f1(f9(x8811,a12)),a12)+~P2(f9(x8811,a12),f9(x8811,a12))),
% 2.59/2.69 inference(scs_inference,[],[220,4,12,40])).
% 2.59/2.69 cnf(889,plain,
% 2.59/2.69 (~P2(a12,f1(f9(x8891,a12)))),
% 2.59/2.69 inference(scs_inference,[],[4,881,24])).
% 2.59/2.69 cnf(892,plain,
% 2.59/2.69 ($false),
% 2.59/2.69 inference(scs_inference,[],[1,889,24,19]),
% 2.59/2.69 ['proof']).
% 2.59/2.69 % SZS output end Proof
% 2.59/2.69 % Total time :2.070000s
%------------------------------------------------------------------------------