%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUM851+2 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : Mon Jun 24 12:26:46 EDT 2024
% Result : Theorem 30.78s 30.84s
% Output : CNFRefutation 30.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM851+2 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n018.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 : Sat Jun 22 20:30:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.52/0.58 start to proof:theBenchmark
% 30.78/30.83 %-------------------------------------------
% 30.78/30.83 % File :CSE---1.7
% 30.78/30.83 % Problem :theBenchmark
% 30.78/30.83 % Transform :cnf
% 30.78/30.83 % Format :tptp:raw
% 30.78/30.83 % Command :java -jar mcs_scs.jar %d %s
% 30.78/30.83
% 30.78/30.83 % Result :Theorem 30.190000s
% 30.78/30.83 % Output :CNFRefutation 30.190000s
% 30.78/30.83 %-------------------------------------------
% 30.78/30.84 %------------------------------------------------------------------------------
% 30.78/30.84 % File : NUM851+2 : TPTP v8.2.0. Released v4.1.0.
% 30.78/30.84 % Domain : Number Theory
% 30.78/30.84 % Problem : holds(conseq_conjunct2(conseq(302)),475,1)
% 30.78/30.84 % Version : Especial: Reduced > Especial.
% 30.78/30.84 % English :
% 30.78/30.84
% 30.78/30.84 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 30.78/30.84 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 30.78/30.84 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 30.78/30.84 % Source : [Kue09]
% 30.78/30.84 % Names :
% 30.78/30.84
% 30.78/30.84 % Status : Theorem
% 30.78/30.84 % Rating : 0.22 v8.2.0, 0.25 v7.5.0, 0.28 v7.4.0, 0.23 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.30 v7.0.0, 0.27 v6.4.0, 0.35 v6.3.0, 0.29 v6.2.0, 0.32 v6.1.0, 0.40 v6.0.0, 0.35 v5.5.0, 0.26 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.29 v5.0.0, 0.38 v4.1.0
% 30.78/30.84 % Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% 30.78/30.84 % Number of atoms : 40 ( 34 equ)
% 30.78/30.84 % Maximal formula atoms : 3 ( 1 avg)
% 30.78/30.84 % Number of connectives : 26 ( 13 ~; 5 |; 2 &)
% 30.78/30.84 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 30.78/30.84 % Maximal formula depth : 6 ( 4 avg)
% 30.78/30.84 % Maximal term depth : 3 ( 1 avg)
% 30.78/30.84 % Number of predicates : 5 ( 4 usr; 0 prp; 2-2 aty)
% 30.78/30.84 % Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% 30.78/30.84 % Number of variables : 53 ( 46 !; 7 ?)
% 30.78/30.84 % SPC : FOF_THM_RFO_SEQ
% 30.78/30.84
% 30.78/30.84 % Comments : From the Landau in Naproche 0.45 collection.
% 30.78/30.84 % : This version uses a filtered set of axioms.
% 30.78/30.84 %------------------------------------------------------------------------------
% 30.78/30.84 fof('holds(conseq_conjunct2(conseq(302)), 475, 1)',conjecture,
% 30.78/30.84 vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ).
% 30.78/30.84
% 30.78/30.84 fof('holds(conseq_conjunct2(conseq(302)), 475, 0)',axiom,
% 30.78/30.84 vmul(vd470,vd469) = vmul(vplus(vd471,vd473),vd469) ).
% 30.78/30.84
% 30.78/30.84 fof('holds(conseq_conjunct1(conseq(302)), 474, 0)',axiom,
% 30.78/30.84 vd470 = vplus(vd471,vd473) ).
% 30.78/30.84
% 30.78/30.84 fof('holds(antec(302), 472, 0)',axiom,
% 30.78/30.84 greater(vd470,vd471) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(290, 0), 0)',axiom,
% 30.78/30.84 ! [Vd444,Vd445,Vd446] : vmul(vmul(Vd444,Vd445),Vd446) = vmul(Vd444,vmul(Vd445,Vd446)) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(281, 0), 0)',axiom,
% 30.78/30.84 ! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(270, 0), 0)',axiom,
% 30.78/30.84 ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(261, 0), 0)',axiom,
% 30.78/30.84 ! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(253, 0), 0)',axiom,
% 30.78/30.84 ! [Vd400] : vmul(v1,Vd400) = Vd400 ).
% 30.78/30.84
% 30.78/30.84 fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
% 30.78/30.84 ! [Vd396,Vd397] :
% 30.78/30.84 ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
% 30.78/30.84 & vmul(Vd396,v1) = Vd396 ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(241, 0), 0)',axiom,
% 30.78/30.84 ! [Vd386,Vd387] :
% 30.78/30.84 ( less(Vd386,vplus(Vd387,v1))
% 30.78/30.84 => leq(Vd386,Vd387) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(234, 0), 0)',axiom,
% 30.78/30.84 ! [Vd375,Vd376] :
% 30.78/30.84 ( greater(Vd375,Vd376)
% 30.78/30.84 => geq(Vd375,vplus(Vd376,v1)) ) ).
% 30.78/30.84
% 30.78/30.84 fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
% 30.78/30.84 ! [Vd193,Vd194] :
% 30.78/30.84 ( greater(Vd194,Vd193)
% 30.78/30.84 <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(goal(88), 0), 0)',axiom,
% 30.78/30.84 ! [Vd120,Vd121] :
% 30.78/30.84 ( Vd120 = Vd121
% 30.78/30.84 | ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 30.78/30.84 | ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(goal(88), 0), 1)',axiom,
% 30.78/30.84 ! [Vd120,Vd121] :
% 30.78/30.84 ( Vd120 != Vd121
% 30.78/30.84 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(goal(88), 0), 2)',axiom,
% 30.78/30.84 ! [Vd120,Vd121] :
% 30.78/30.84 ( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 30.78/30.84 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(goal(88), 0), 3)',axiom,
% 30.78/30.84 ! [Vd120,Vd121] :
% 30.78/30.84 ( Vd120 != Vd121
% 30.78/30.84 | ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(81, 0), 0)',axiom,
% 30.78/30.84 ! [Vd104,Vd105] :
% 30.78/30.84 ( Vd104 != Vd105
% 30.78/30.84 => ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(73, 0), 0)',axiom,
% 30.78/30.84 ! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(61, 0), 0)',axiom,
% 30.78/30.84 ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(52, 0), 0)',axiom,
% 30.78/30.84 ! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(43, 0), 0)',axiom,
% 30.78/30.84 ! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(33, 0), 0)',axiom,
% 30.78/30.84 ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
% 30.78/30.84
% 30.78/30.84 fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
% 30.78/30.84 ! [Vd42,Vd43] :
% 30.78/30.84 ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
% 30.78/30.84 & vplus(Vd42,v1) = vsucc(Vd42) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(20, 0), 0)',axiom,
% 30.78/30.84 ! [Vd24] :
% 30.78/30.84 ( Vd24 != v1
% 30.78/30.84 => Vd24 = vsucc(vskolem2(Vd24)) ) ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(12, 0), 0)',axiom,
% 30.78/30.84 ! [Vd16] : vsucc(Vd16) != Vd16 ).
% 30.78/30.84
% 30.78/30.84 fof('ass(cond(6, 0), 0)',axiom,
% 30.78/30.84 ! [Vd7,Vd8] :
% 30.78/30.84 ( Vd7 != Vd8
% 30.78/30.84 => vsucc(Vd7) != vsucc(Vd8) ) ).
% 30.78/30.84
% 30.78/30.84 %------------------------------------------------------------------------------
% 30.78/30.84 %-------------------------------------------
% 30.78/30.84 % Proof found
% 30.78/30.84 % SZS status Theorem for theBenchmark
% 30.78/30.84 % SZS output start Proof
% 30.78/30.84 %ClaNum:51(EqnAxiom:22)
% 30.78/30.84 %VarNum:108(SingletonVarNum:51)
% 30.78/30.84 %MaxLitNum:3
% 30.78/30.84 %MaxfuncDepth:2
% 30.78/30.84 %SharedTerms:15
% 30.78/30.84 %goalClause: 40
% 30.78/30.84 %singleGoalClaCount:1
% 30.78/30.84 [24]P1(a2,a1)
% 30.78/30.84 [23]E(f9(a1,a8),a2)
% 30.78/30.84 [30]E(f10(f9(a1,a8),a7),f10(a2,a7))
% 30.78/30.84 [40]~E(f9(f10(a1,a7),f10(a8,a7)),f10(f9(a1,a8),a7))
% 30.78/30.84 [25]E(f10(x251,a3),x251)
% 30.78/30.84 [26]E(f10(a3,x261),x261)
% 30.78/30.84 [38]~E(f9(x381,a3),x381)
% 30.78/30.84 [28]E(f9(x281,x282),f9(x282,x281))
% 30.78/30.84 [29]E(f10(x291,x292),f10(x292,x291))
% 30.78/30.84 [39]~E(f9(x391,x392),x392)
% 30.78/30.84 [32]E(f9(f9(x321,a3),x322),f9(f9(x321,x322),a3))
% 30.78/30.84 [33]E(f9(f10(x331,x332),x331),f10(x331,f9(x332,a3)))
% 30.78/30.84 [34]E(f9(f10(x341,x342),x342),f10(f9(x341,a3),x342))
% 30.78/30.84 [35]E(f9(f9(x351,x352),x353),f9(x351,f9(x352,x353)))
% 30.78/30.84 [36]E(f10(f10(x361,x362),x363),f10(x361,f10(x362,x363)))
% 30.78/30.84 [37]E(f9(f10(x371,x372),f10(x371,x373)),f10(x371,f9(x372,x373)))
% 30.78/30.84 [41]E(x411,a3)+E(f9(f11(x411),a3),x411)
% 30.78/30.84 [45]E(x451,x452)+~E(f9(x451,a3),f9(x452,a3))
% 30.78/30.84 [48]~P1(x481,x482)+P2(x481,f9(x482,a3))
% 30.78/30.84 [50]P3(x501,x502)+~P4(x501,f9(x502,a3))
% 30.78/30.84 [49]~P1(x492,x491)+E(f9(x491,f4(x491,x492)),x492)
% 30.78/30.84 [42]~E(x421,x422)+~E(x422,f9(x421,x423))
% 30.78/30.84 [43]~E(x431,x432)+~E(x431,f9(x432,x433))
% 30.78/30.84 [44]P1(x441,x442)+~E(x441,f9(x442,x443))
% 30.78/30.84 [46]E(x461,x462)+~E(f9(x463,x461),f9(x463,x462))
% 30.78/30.84 [47]~E(x471,f9(x472,x473))+~E(x472,f9(x471,x474))
% 30.78/30.84 [51]E(x511,x512)+E(f9(x511,f5(x511,x512)),x512)+E(f9(x512,f6(x511,x512)),x511)
% 30.78/30.84 %EqnAxiom
% 30.78/30.84 [1]E(x11,x11)
% 30.78/30.84 [2]E(x22,x21)+~E(x21,x22)
% 30.78/30.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 30.78/30.84 [4]~E(x41,x42)+E(f9(x41,x43),f9(x42,x43))
% 30.78/30.84 [5]~E(x51,x52)+E(f9(x53,x51),f9(x53,x52))
% 30.78/30.84 [6]~E(x61,x62)+E(f10(x61,x63),f10(x62,x63))
% 30.78/30.84 [7]~E(x71,x72)+E(f10(x73,x71),f10(x73,x72))
% 30.78/30.84 [8]~E(x81,x82)+E(f11(x81),f11(x82))
% 30.78/30.84 [9]~E(x91,x92)+E(f6(x91,x93),f6(x92,x93))
% 30.78/30.84 [10]~E(x101,x102)+E(f6(x103,x101),f6(x103,x102))
% 30.78/30.84 [11]~E(x111,x112)+E(f5(x111,x113),f5(x112,x113))
% 30.78/30.84 [12]~E(x121,x122)+E(f5(x123,x121),f5(x123,x122))
% 30.78/30.84 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 30.78/30.84 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 30.78/30.84 [15]P1(x152,x153)+~E(x151,x152)+~P1(x151,x153)
% 30.78/30.85 [16]P1(x163,x162)+~E(x161,x162)+~P1(x163,x161)
% 30.78/30.85 [17]P4(x172,x173)+~E(x171,x172)+~P4(x171,x173)
% 30.78/30.85 [18]P4(x183,x182)+~E(x181,x182)+~P4(x183,x181)
% 30.78/30.85 [19]P2(x192,x193)+~E(x191,x192)+~P2(x191,x193)
% 30.78/30.85 [20]P2(x203,x202)+~E(x201,x202)+~P2(x203,x201)
% 30.78/30.85 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213)
% 30.78/30.85 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221)
% 30.78/30.85
% 30.78/30.85 %-------------------------------------------
% 30.85/30.85 cnf(52,plain,
% 30.85/30.85 (P1(f9(x521,x522),x521)),
% 30.85/30.85 inference(equality_inference,[],[44])).
% 30.85/30.85 cnf(55,plain,
% 30.85/30.85 (E(x551,f10(x551,a3))),
% 30.85/30.85 inference(scs_inference,[],[25,2])).
% 30.85/30.85 cnf(61,plain,
% 30.85/30.85 (P1(f9(x611,x612),x612)),
% 30.85/30.85 inference(scs_inference,[],[28,25,2,42,43,44])).
% 30.85/30.85 cnf(67,plain,
% 30.85/30.85 (~P1(x671,f10(x671,a3))),
% 30.85/30.85 inference(scs_inference,[],[28,25,2,42,43,44,47,4,6,49])).
% 30.85/30.85 cnf(69,plain,
% 30.85/30.85 (~E(f9(f10(a1,a7),f10(a8,a7)),f10(a7,f9(a1,a8)))),
% 30.85/30.85 inference(scs_inference,[],[40,28,29,25,2,42,43,44,47,4,6,49,3])).
% 30.85/30.85 cnf(71,plain,
% 30.85/30.85 (~E(x711,f10(f9(x711,x712),a3))),
% 30.85/30.85 inference(scs_inference,[],[40,52,28,29,25,2,42,43,44,47,4,6,49,3,16])).
% 30.85/30.85 cnf(72,plain,
% 30.85/30.85 (P1(x721,a1)+~E(a2,x721)),
% 30.85/30.85 inference(scs_inference,[],[40,52,28,29,25,24,2,42,43,44,47,4,6,49,3,16,15])).
% 30.85/30.85 cnf(77,plain,
% 30.85/30.85 (E(f10(a3,x771),x771)),
% 30.85/30.85 inference(rename_variables,[],[26])).
% 30.85/30.85 cnf(80,plain,
% 30.85/30.85 (E(f10(a3,x801),x801)),
% 30.85/30.85 inference(rename_variables,[],[26])).
% 30.85/30.85 cnf(83,plain,
% 30.85/30.85 (E(f10(a3,x831),x831)),
% 30.85/30.85 inference(rename_variables,[],[26])).
% 30.85/30.85 cnf(86,plain,
% 30.85/30.85 (E(f10(a3,x861),x861)),
% 30.85/30.85 inference(rename_variables,[],[26])).
% 30.85/30.85 cnf(93,plain,
% 30.85/30.85 (~E(f9(f10(a1,a7),f10(a8,a7)),f9(f10(a7,a1),f10(a7,a8)))),
% 30.85/30.85 inference(scs_inference,[],[55,69,61,71,67,26,77,80,83,86,37,72,44,43,42,47,6,2,16,3])).
% 30.85/30.85 cnf(488,plain,
% 30.85/30.85 (E(f9(x4881,f10(x4882,x4883)),f9(x4881,f10(x4883,x4882)))),
% 30.85/30.85 inference(scs_inference,[],[29,2,5])).
% 30.85/30.85 cnf(1635,plain,
% 30.85/30.85 ($false),
% 30.85/30.85 inference(scs_inference,[],[93,488,29,3,4]),
% 30.85/30.85 ['proof']).
% 30.85/30.85 % SZS output end Proof
% 30.85/30.85 % Total time :30.190000s
%------------------------------------------------------------------------------