TSTP Solution File: NUM837+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM837+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n018.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 10:25:17 EDT 2023
% Result : Theorem 0.20s 0.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM837+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n018.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
% 0.13/0.35 % DateTime : Fri Aug 25 12:48:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 start to proof:theBenchmark
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % File :CSE---1.6
% 0.20/0.66 % Problem :theBenchmark
% 0.20/0.66 % Transform :cnf
% 0.20/0.66 % Format :tptp:raw
% 0.20/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.66
% 0.20/0.66 % Result :Theorem 0.000000s
% 0.20/0.66 % Output :CNFRefutation 0.000000s
% 0.20/0.66 %-------------------------------------------
% 0.20/0.67 %------------------------------------------------------------------------------
% 0.20/0.67 % File : NUM837+2 : TPTP v8.1.2. Released v4.1.0.
% 0.20/0.67 % Domain : Number Theory
% 0.20/0.67 % Problem : qe(171)
% 0.20/0.67 % Version : Especial: Reduced > Especial.
% 0.20/0.67 % English :
% 0.20/0.67
% 0.20/0.67 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.67 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 0.20/0.67 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 0.20/0.67 % Source : [Kue09]
% 0.20/0.67 % Names :
% 0.20/0.67
% 0.20/0.67 % Status : Theorem
% 0.20/0.67 % Rating : 0.17 v7.5.0, 0.16 v7.4.0, 0.17 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.29 v6.2.0, 0.24 v6.1.0, 0.17 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0
% 0.20/0.67 % Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% 0.20/0.67 % Number of atoms : 44 ( 22 equ)
% 0.20/0.67 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.67 % Number of connectives : 36 ( 14 ~; 12 |; 1 &)
% 0.20/0.67 % ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.67 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.67 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.67 % Number of predicates : 5 ( 4 usr; 0 prp; 2-2 aty)
% 0.20/0.67 % Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% 0.20/0.67 % Number of variables : 49 ( 40 !; 9 ?)
% 0.20/0.67 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.67
% 0.20/0.67 % Comments : From the Landau in Naproche 0.45 collection.
% 0.20/0.67 % : This version uses a filtered set of axioms.
% 0.20/0.67 %------------------------------------------------------------------------------
% 0.20/0.67 fof('qe(171)',conjecture,
% 0.20/0.67 ? [Vd273] : vd269 = vplus(vd268,Vd273) ).
% 0.20/0.67
% 0.20/0.67 fof('(conjunct2(170),272,0)',axiom,
% 0.20/0.67 less(vd269,vd271) ).
% 0.20/0.67
% 0.20/0.67 fof('holds(conjunct1(170), 270, 0)',axiom,
% 0.20/0.67 less(vd268,vd269) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(163, 0), 0)',axiom,
% 0.20/0.67 ! [Vd258,Vd259] :
% 0.20/0.67 ( leq(Vd258,Vd259)
% 0.20/0.67 => geq(Vd259,Vd258) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(158, 0), 0)',axiom,
% 0.20/0.67 ! [Vd254,Vd255] :
% 0.20/0.67 ( geq(Vd254,Vd255)
% 0.20/0.67 => leq(Vd255,Vd254) ) ).
% 0.20/0.67
% 0.20/0.67 fof('def(cond(conseq(axiom(3)), 17), 1)',axiom,
% 0.20/0.67 ! [Vd249,Vd250] :
% 0.20/0.67 ( leq(Vd250,Vd249)
% 0.20/0.67 <=> ( less(Vd250,Vd249)
% 0.20/0.67 | Vd250 = Vd249 ) ) ).
% 0.20/0.67
% 0.20/0.67 fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
% 0.20/0.67 ! [Vd244,Vd245] :
% 0.20/0.67 ( geq(Vd245,Vd244)
% 0.20/0.67 <=> ( greater(Vd245,Vd244)
% 0.20/0.67 | Vd245 = Vd244 ) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(147, 0), 0)',axiom,
% 0.20/0.67 ! [Vd226,Vd227] :
% 0.20/0.67 ( less(Vd226,Vd227)
% 0.20/0.67 => greater(Vd227,Vd226) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(140, 0), 0)',axiom,
% 0.20/0.67 ! [Vd208,Vd209] :
% 0.20/0.67 ( greater(Vd208,Vd209)
% 0.20/0.67 => less(Vd209,Vd208) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(130), 0), 0)',axiom,
% 0.20/0.67 ! [Vd203,Vd204] :
% 0.20/0.67 ( Vd203 = Vd204
% 0.20/0.67 | greater(Vd203,Vd204)
% 0.20/0.67 | less(Vd203,Vd204) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(130), 0), 1)',axiom,
% 0.20/0.67 ! [Vd203,Vd204] :
% 0.20/0.67 ( Vd203 != Vd204
% 0.20/0.67 | ~ less(Vd203,Vd204) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(130), 0), 2)',axiom,
% 0.20/0.67 ! [Vd203,Vd204] :
% 0.20/0.67 ( ~ greater(Vd203,Vd204)
% 0.20/0.67 | ~ less(Vd203,Vd204) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(130), 0), 3)',axiom,
% 0.20/0.67 ! [Vd203,Vd204] :
% 0.20/0.67 ( Vd203 != Vd204
% 0.20/0.67 | ~ greater(Vd203,Vd204) ) ).
% 0.20/0.67
% 0.20/0.67 fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
% 0.20/0.67 ! [Vd198,Vd199] :
% 0.20/0.67 ( less(Vd199,Vd198)
% 0.20/0.67 <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
% 0.20/0.67
% 0.20/0.67 fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
% 0.20/0.67 ! [Vd193,Vd194] :
% 0.20/0.67 ( greater(Vd194,Vd193)
% 0.20/0.67 <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(88), 0), 0)',axiom,
% 0.20/0.67 ! [Vd120,Vd121] :
% 0.20/0.67 ( Vd120 = Vd121
% 0.20/0.67 | ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.20/0.67 | ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(88), 0), 1)',axiom,
% 0.20/0.67 ! [Vd120,Vd121] :
% 0.20/0.67 ( Vd120 != Vd121
% 0.20/0.67 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(88), 0), 2)',axiom,
% 0.20/0.67 ! [Vd120,Vd121] :
% 0.20/0.67 ( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.20/0.67 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(goal(88), 0), 3)',axiom,
% 0.20/0.67 ! [Vd120,Vd121] :
% 0.20/0.67 ( Vd120 != Vd121
% 0.20/0.67 | ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(81, 0), 0)',axiom,
% 0.20/0.67 ! [Vd104,Vd105] :
% 0.20/0.67 ( Vd104 != Vd105
% 0.20/0.67 => ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ) ).
% 0.20/0.67
% 0.20/0.67 fof('ass(cond(33, 0), 0)',axiom,
% 0.20/0.67 ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
% 0.20/0.67
% 0.20/0.67 fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
% 0.20/0.67 ! [Vd42,Vd43] :
% 0.20/0.67 ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
% 0.20/0.67 & vplus(Vd42,v1) = vsucc(Vd42) ) ).
% 0.20/0.67
% 0.20/0.67 %------------------------------------------------------------------------------
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 % Proof found
% 0.20/0.67 % SZS status Theorem for theBenchmark
% 0.20/0.67 % SZS output start Proof
% 0.20/0.67 %ClaNum:49(EqnAxiom:21)
% 0.20/0.67 %VarNum:123(SingletonVarNum:57)
% 0.20/0.67 %MaxLitNum:3
% 0.20/0.67 %MaxfuncDepth:2
% 0.20/0.67 %SharedTerms:6
% 0.20/0.67 %goalClause: 26
% 0.20/0.67 %singleGoalClaCount:1
% 0.20/0.67 [22]P1(a1,a8)
% 0.20/0.67 [23]P1(a2,a1)
% 0.20/0.67 [26]~E(f9(a2,x261),a1)
% 0.20/0.67 [25]E(f9(f9(x251,x252),x253),f9(x251,f9(x252,x253)))
% 0.20/0.67 [27]~E(x271,x272)+P2(x271,x272)
% 0.20/0.67 [28]~E(x281,x282)+P3(x281,x282)
% 0.20/0.67 [29]~P1(x291,x292)+~E(x291,x292)
% 0.20/0.67 [30]~P4(x301,x302)+~E(x301,x302)
% 0.20/0.67 [34]~P4(x342,x341)+P1(x341,x342)
% 0.20/0.67 [35]~P3(x352,x351)+P2(x351,x352)
% 0.20/0.67 [36]~P1(x361,x362)+P2(x361,x362)
% 0.20/0.67 [37]~P2(x372,x371)+P3(x371,x372)
% 0.20/0.67 [38]~P4(x381,x382)+P3(x381,x382)
% 0.20/0.67 [39]~P1(x392,x391)+P4(x391,x392)
% 0.20/0.67 [44]~P4(x441,x442)+~P1(x441,x442)
% 0.20/0.67 [47]~P1(x471,x472)+E(f9(x471,f4(x472,x471)),x472)
% 0.20/0.67 [48]~P4(x482,x481)+E(f9(x481,f5(x481,x482)),x482)
% 0.20/0.67 [31]~E(x311,x312)+~E(x312,f9(x311,x313))
% 0.20/0.67 [32]~E(x321,x322)+~E(x321,f9(x322,x323))
% 0.20/0.67 [40]P1(x401,x402)+~E(x402,f9(x401,x403))
% 0.20/0.67 [41]P4(x411,x412)+~E(x411,f9(x412,x413))
% 0.20/0.67 [45]E(x451,x452)+~E(f9(x453,x451),f9(x453,x452))
% 0.20/0.67 [46]~E(x461,f9(x462,x463))+~E(x462,f9(x461,x464))
% 0.20/0.67 [33]P1(x331,x332)+P4(x331,x332)+E(x331,x332)
% 0.20/0.67 [42]P1(x421,x422)+~P2(x421,x422)+E(x421,x422)
% 0.20/0.67 [43]P4(x431,x432)+~P3(x431,x432)+E(x431,x432)
% 0.20/0.67 [49]E(x491,x492)+E(f9(x491,f6(x491,x492)),x492)+E(f9(x492,f7(x491,x492)),x491)
% 0.20/0.67 %EqnAxiom
% 0.20/0.67 [1]E(x11,x11)
% 0.20/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.67 [4]~E(x41,x42)+E(f9(x41,x43),f9(x42,x43))
% 0.20/0.67 [5]~E(x51,x52)+E(f9(x53,x51),f9(x53,x52))
% 0.20/0.67 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.20/0.67 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.20/0.67 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.20/0.67 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.20/0.67 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 0.20/0.67 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 0.20/0.67 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.20/0.67 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.20/0.67 [14]P1(x142,x143)+~E(x141,x142)+~P1(x141,x143)
% 0.20/0.67 [15]P1(x153,x152)+~E(x151,x152)+~P1(x153,x151)
% 0.20/0.67 [16]P4(x162,x163)+~E(x161,x162)+~P4(x161,x163)
% 0.20/0.67 [17]P4(x173,x172)+~E(x171,x172)+~P4(x173,x171)
% 0.20/0.67 [18]P2(x182,x183)+~E(x181,x182)+~P2(x181,x183)
% 0.20/0.67 [19]P2(x193,x192)+~E(x191,x192)+~P2(x193,x191)
% 0.20/0.67 [20]P3(x202,x203)+~E(x201,x202)+~P3(x201,x203)
% 0.20/0.67 [21]P3(x213,x212)+~E(x211,x212)+~P3(x213,x211)
% 0.20/0.67
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 cnf(70,plain,
% 0.20/0.67 (~E(f9(a2,x701),a1)),
% 0.20/0.67 inference(rename_variables,[],[26])).
% 0.20/0.67 cnf(72,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[26,70,22,23,25,2,44,39,30,29,41,40,32,31,46,48,47]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------