TSTP Solution File: NUM854+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n004.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 10:25:25 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n004.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 : Fri Aug 25 14:02:23 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % File :CSE---1.6
% 0.20/0.61 % Problem :theBenchmark
% 0.20/0.61 % Transform :cnf
% 0.20/0.61 % Format :tptp:raw
% 0.20/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.61
% 0.20/0.61 % Result :Theorem 0.000000s
% 0.20/0.61 % Output :CNFRefutation 0.000000s
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 % File : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% 0.20/0.61 % Domain : Number Theory
% 0.20/0.61 % Problem : holds(conjunct1(315),514,0)
% 0.20/0.61 % Version : Especial: Reduced > Especial.
% 0.20/0.61 % English :
% 0.20/0.61
% 0.20/0.61 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.61 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 0.20/0.61 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 0.20/0.61 % Source : [Kue09]
% 0.20/0.61 % Names :
% 0.20/0.61
% 0.20/0.61 % Status : Theorem
% 0.20/0.61 % Rating : 0.11 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0
% 0.20/0.61 % Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% 0.20/0.61 % Number of atoms : 48 ( 25 equ)
% 0.20/0.61 % Maximal formula atoms : 3 ( 1 avg)
% 0.20/0.61 % Number of connectives : 33 ( 12 ~; 10 |; 1 &)
% 0.20/0.61 % ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% 0.20/0.61 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.61 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.20/0.61 % Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% 0.20/0.61 % Number of variables : 63 ( 55 !; 8 ?)
% 0.20/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.61
% 0.20/0.61 % Comments : From the Landau in Naproche 0.45 collection.
% 0.20/0.61 % : This version uses a filtered set of axioms.
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 fof('holds(conjunct1(315), 514, 0)',conjecture,
% 0.20/0.61 greater(vmul(vd508,vd511),vmul(vd509,vd511)) ).
% 0.20/0.61
% 0.20/0.61 fof('holds(conjunct2(314), 513, 0)',axiom,
% 0.20/0.61 greater(vd511,vd512) ).
% 0.20/0.61
% 0.20/0.61 fof('holds(conjunct1(314), 510, 0)',axiom,
% 0.20/0.62 greater(vd508,vd509) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(conjunct2(conjunct2(307)), 0), 0)',axiom,
% 0.20/0.62 ! [Vd496,Vd497,Vd498] :
% 0.20/0.62 ( less(vmul(Vd496,Vd497),vmul(Vd498,Vd497))
% 0.20/0.62 => less(Vd496,Vd498) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(conjunct1(conjunct2(307)), 0), 0)',axiom,
% 0.20/0.62 ! [Vd491,Vd492,Vd493] :
% 0.20/0.62 ( vmul(Vd491,Vd492) = vmul(Vd493,Vd492)
% 0.20/0.62 => Vd491 = Vd493 ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(conjunct1(307), 0), 0)',axiom,
% 0.20/0.62 ! [Vd486,Vd487,Vd488] :
% 0.20/0.62 ( greater(vmul(Vd486,Vd487),vmul(Vd488,Vd487))
% 0.20/0.62 => greater(Vd486,Vd488) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(299, 0), 0)',axiom,
% 0.20/0.62 ! [Vd456,Vd465,Vd466] :
% 0.20/0.62 ( less(Vd465,Vd466)
% 0.20/0.62 => less(vmul(Vd465,Vd456),vmul(Vd466,Vd456)) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(299, 0), 1)',axiom,
% 0.20/0.62 ! [Vd456,Vd461,Vd462] :
% 0.20/0.62 ( Vd461 = Vd462
% 0.20/0.62 => vmul(Vd461,Vd456) = vmul(Vd462,Vd456) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(299, 0), 2)',axiom,
% 0.20/0.62 ! [Vd456,Vd457,Vd458] :
% 0.20/0.62 ( greater(Vd457,Vd458)
% 0.20/0.62 => greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(290, 0), 0)',axiom,
% 0.20/0.62 ! [Vd444,Vd445,Vd446] : vmul(vmul(Vd444,Vd445),Vd446) = vmul(Vd444,vmul(Vd445,Vd446)) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(281, 0), 0)',axiom,
% 0.20/0.62 ! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(270, 0), 0)',axiom,
% 0.20/0.62 ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(261, 0), 0)',axiom,
% 0.20/0.62 ! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(253, 0), 0)',axiom,
% 0.20/0.62 ! [Vd400] : vmul(v1,Vd400) = Vd400 ).
% 0.20/0.62
% 0.20/0.62 fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
% 0.20/0.62 ! [Vd396,Vd397] :
% 0.20/0.62 ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
% 0.20/0.62 & vmul(Vd396,v1) = Vd396 ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(147, 0), 0)',axiom,
% 0.20/0.62 ! [Vd226,Vd227] :
% 0.20/0.62 ( less(Vd226,Vd227)
% 0.20/0.62 => greater(Vd227,Vd226) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(140, 0), 0)',axiom,
% 0.20/0.62 ! [Vd208,Vd209] :
% 0.20/0.62 ( greater(Vd208,Vd209)
% 0.20/0.62 => less(Vd209,Vd208) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(130), 0), 0)',axiom,
% 0.20/0.62 ! [Vd203,Vd204] :
% 0.20/0.62 ( Vd203 = Vd204
% 0.20/0.62 | greater(Vd203,Vd204)
% 0.20/0.62 | less(Vd203,Vd204) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(130), 0), 1)',axiom,
% 0.20/0.62 ! [Vd203,Vd204] :
% 0.20/0.62 ( Vd203 != Vd204
% 0.20/0.62 | ~ less(Vd203,Vd204) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(130), 0), 2)',axiom,
% 0.20/0.62 ! [Vd203,Vd204] :
% 0.20/0.62 ( ~ greater(Vd203,Vd204)
% 0.20/0.62 | ~ less(Vd203,Vd204) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(130), 0), 3)',axiom,
% 0.20/0.62 ! [Vd203,Vd204] :
% 0.20/0.62 ( Vd203 != Vd204
% 0.20/0.62 | ~ greater(Vd203,Vd204) ) ).
% 0.20/0.62
% 0.20/0.62 fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
% 0.20/0.62 ! [Vd198,Vd199] :
% 0.20/0.62 ( less(Vd199,Vd198)
% 0.20/0.62 <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
% 0.20/0.62
% 0.20/0.62 fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
% 0.20/0.62 ! [Vd193,Vd194] :
% 0.20/0.62 ( greater(Vd194,Vd193)
% 0.20/0.62 <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(88), 0), 0)',axiom,
% 0.20/0.62 ! [Vd120,Vd121] :
% 0.20/0.62 ( Vd120 = Vd121
% 0.20/0.62 | ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.20/0.62 | ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(88), 0), 1)',axiom,
% 0.20/0.62 ! [Vd120,Vd121] :
% 0.20/0.62 ( Vd120 != Vd121
% 0.20/0.62 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(88), 0), 2)',axiom,
% 0.20/0.62 ! [Vd120,Vd121] :
% 0.20/0.62 ( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.20/0.62 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.20/0.62
% 0.20/0.62 fof('ass(cond(goal(88), 0), 3)',axiom,
% 0.20/0.62 ! [Vd120,Vd121] :
% 0.20/0.62 ( Vd120 != Vd121
% 0.20/0.62 | ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).
% 0.20/0.62
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 %ClaNum:49(EqnAxiom:20)
% 0.20/0.62 %VarNum:135(SingletonVarNum:63)
% 0.20/0.62 %MaxLitNum:3
% 0.20/0.62 %MaxfuncDepth:2
% 0.20/0.62 %SharedTerms:10
% 0.20/0.62 %goalClause: 30
% 0.20/0.62 %singleGoalClaCount:1
% 0.20/0.62 [21]P1(a1,a7)
% 0.20/0.62 [22]P1(a8,a9)
% 0.20/0.62 [30]~P1(f10(a1,a8),f10(a7,a8))
% 0.20/0.62 [23]E(f10(x231,a2),x231)
% 0.20/0.62 [24]E(f10(a2,x241),x241)
% 0.20/0.62 [25]E(f10(x251,x252),f10(x252,x251))
% 0.20/0.62 [26]E(f11(f10(x261,x262),x261),f10(x261,f12(x262)))
% 0.20/0.62 [27]E(f11(f10(x271,x272),x272),f10(f12(x271),x272))
% 0.20/0.62 [28]E(f10(f10(x281,x282),x283),f10(x281,f10(x282,x283)))
% 0.20/0.62 [29]E(f11(f10(x291,x292),f10(x291,x293)),f10(x291,f11(x292,x293)))
% 0.20/0.62 [31]~P1(x311,x312)+~E(x311,x312)
% 0.20/0.62 [32]~P2(x321,x322)+~E(x321,x322)
% 0.20/0.62 [36]~P2(x362,x361)+P1(x361,x362)
% 0.20/0.62 [37]~P1(x372,x371)+P2(x371,x372)
% 0.20/0.62 [40]~P2(x401,x402)+~P1(x401,x402)
% 0.20/0.62 [43]~P2(x431,x432)+E(f11(x431,f3(x432,x431)),x432)
% 0.20/0.62 [44]~P1(x442,x441)+E(f11(x441,f4(x441,x442)),x442)
% 0.20/0.62 [33]~E(x331,x332)+~E(x332,f11(x331,x333))
% 0.20/0.62 [34]~E(x341,x342)+~E(x341,f11(x342,x343))
% 0.20/0.62 [38]P1(x381,x382)+~E(x381,f11(x382,x383))
% 0.20/0.62 [39]P2(x391,x392)+~E(x392,f11(x391,x393))
% 0.20/0.62 [41]E(x411,x412)+~E(f10(x411,x413),f10(x412,x413))
% 0.20/0.62 [46]~P1(x461,x463)+P1(f10(x461,x462),f10(x463,x462))
% 0.20/0.62 [47]~P2(x471,x473)+P2(f10(x471,x472),f10(x473,x472))
% 0.20/0.62 [48]P1(x481,x482)+~P1(f10(x481,x483),f10(x482,x483))
% 0.20/0.62 [49]P2(x491,x492)+~P2(f10(x491,x493),f10(x492,x493))
% 0.20/0.62 [42]~E(x421,f11(x422,x423))+~E(x422,f11(x421,x424))
% 0.20/0.62 [35]P1(x351,x352)+P2(x351,x352)+E(x351,x352)
% 0.20/0.62 [45]E(x451,x452)+E(f11(x451,f5(x451,x452)),x452)+E(f11(x452,f6(x451,x452)),x451)
% 0.20/0.62 %EqnAxiom
% 0.20/0.62 [1]E(x11,x11)
% 0.20/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.62 [4]~E(x41,x42)+E(f10(x41,x43),f10(x42,x43))
% 0.20/0.62 [5]~E(x51,x52)+E(f10(x53,x51),f10(x53,x52))
% 0.20/0.62 [6]~E(x61,x62)+E(f11(x61,x63),f11(x62,x63))
% 0.20/0.62 [7]~E(x71,x72)+E(f11(x73,x71),f11(x73,x72))
% 0.20/0.62 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.20/0.62 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.20/0.62 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103))
% 0.20/0.62 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112))
% 0.20/0.62 [12]~E(x121,x122)+E(f5(x121,x123),f5(x122,x123))
% 0.20/0.62 [13]~E(x131,x132)+E(f5(x133,x131),f5(x133,x132))
% 0.20/0.62 [14]~E(x141,x142)+E(f12(x141),f12(x142))
% 0.20/0.62 [15]~E(x151,x152)+E(f4(x151,x153),f4(x152,x153))
% 0.20/0.62 [16]~E(x161,x162)+E(f4(x163,x161),f4(x163,x162))
% 0.20/0.62 [17]P1(x172,x173)+~E(x171,x172)+~P1(x171,x173)
% 0.20/0.62 [18]P1(x183,x182)+~E(x181,x182)+~P1(x183,x181)
% 0.20/0.62 [19]P2(x192,x193)+~E(x191,x192)+~P2(x191,x193)
% 0.20/0.62 [20]P2(x203,x202)+~E(x201,x202)+~P2(x203,x201)
% 0.20/0.62
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 cnf(50,plain,
% 0.20/0.62 ($false),
% 0.20/0.62 inference(scs_inference,[],[21,30,46]),
% 0.20/0.62 ['proof']).
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------