TSTP Solution File: NUM840+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM840+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 : n003.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 10:25:19 EDT 2023
% Result : Theorem 0.16s 0.57s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM840+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Aug 25 08:14:53 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.51 start to proof:theBenchmark
% 0.16/0.56 %-------------------------------------------
% 0.16/0.56 % File :CSE---1.6
% 0.16/0.56 % Problem :theBenchmark
% 0.16/0.56 % Transform :cnf
% 0.16/0.56 % Format :tptp:raw
% 0.16/0.56 % Command :java -jar mcs_scs.jar %d %s
% 0.16/0.56
% 0.16/0.56 % Result :Theorem 0.010000s
% 0.16/0.56 % Output :CNFRefutation 0.010000s
% 0.16/0.56 %-------------------------------------------
% 0.16/0.56 %------------------------------------------------------------------------------
% 0.16/0.56 % File : NUM840+2 : TPTP v8.1.2. Released v4.1.0.
% 0.16/0.56 % Domain : Number Theory
% 0.16/0.57 % Problem : holds(conseq(conjunct2(conjunct2(204))),336,0)
% 0.16/0.57 % Version : Especial: Reduced > Especial.
% 0.16/0.57 % English :
% 0.16/0.57
% 0.16/0.57 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.16/0.57 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 0.16/0.57 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 0.16/0.57 % Source : [Kue09]
% 0.16/0.57 % Names :
% 0.16/0.57
% 0.16/0.57 % Status : Theorem
% 0.16/0.57 % Rating : 0.19 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.20 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.26 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.27 v6.0.0, 0.30 v5.4.0, 0.29 v5.3.0, 0.37 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0
% 0.16/0.57 % Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% 0.16/0.57 % Number of atoms : 47 ( 27 equ)
% 0.16/0.57 % Maximal formula atoms : 3 ( 1 avg)
% 0.16/0.57 % Number of connectives : 36 ( 15 ~; 10 |; 1 &)
% 0.16/0.57 % ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% 0.16/0.57 % Maximal formula depth : 6 ( 4 avg)
% 0.16/0.57 % Maximal term depth : 3 ( 1 avg)
% 0.16/0.57 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.16/0.57 % Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% 0.16/0.57 % Number of variables : 56 ( 48 !; 8 ?)
% 0.16/0.57 % SPC : FOF_THM_RFO_SEQ
% 0.16/0.57
% 0.16/0.57 % Comments : From the Landau in Naproche 0.45 collection.
% 0.16/0.57 % : This version uses a filtered set of axioms.
% 0.16/0.57 %------------------------------------------------------------------------------
% 0.16/0.57 fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)',conjecture,
% 0.16/0.57 less(vd328,vd329) ).
% 0.16/0.57
% 0.16/0.57 fof('holds(antec(conjunct2(conjunct2(204))), 335, 0)',axiom,
% 0.16/0.57 less(vplus(vd328,vd330),vplus(vd329,vd330)) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(conjunct1(conjunct2(204)), 0), 0)',axiom,
% 0.16/0.57 ( vplus(vd328,vd330) = vplus(vd329,vd330)
% 0.16/0.57 => vd328 = vd329 ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(conjunct1(204), 0), 0)',axiom,
% 0.16/0.57 ( greater(vplus(vd328,vd330),vplus(vd329,vd330))
% 0.16/0.57 => greater(vd328,vd329) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(193), 0), 0)',axiom,
% 0.16/0.57 ! [Vd301,Vd302,Vd303] :
% 0.16/0.57 ( less(Vd301,Vd302)
% 0.16/0.57 => less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(193), 0), 1)',axiom,
% 0.16/0.57 ! [Vd301,Vd302,Vd303] :
% 0.16/0.57 ( Vd301 = Vd302
% 0.16/0.57 => vplus(Vd301,Vd303) = vplus(Vd302,Vd303) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(193), 0), 2)',axiom,
% 0.16/0.57 ! [Vd301,Vd302,Vd303] :
% 0.16/0.57 ( greater(Vd301,Vd302)
% 0.16/0.57 => greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(147, 0), 0)',axiom,
% 0.16/0.57 ! [Vd226,Vd227] :
% 0.16/0.57 ( less(Vd226,Vd227)
% 0.16/0.57 => greater(Vd227,Vd226) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(140, 0), 0)',axiom,
% 0.16/0.57 ! [Vd208,Vd209] :
% 0.16/0.57 ( greater(Vd208,Vd209)
% 0.16/0.57 => less(Vd209,Vd208) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(130), 0), 0)',axiom,
% 0.16/0.57 ! [Vd203,Vd204] :
% 0.16/0.57 ( Vd203 = Vd204
% 0.16/0.57 | greater(Vd203,Vd204)
% 0.16/0.57 | less(Vd203,Vd204) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(130), 0), 1)',axiom,
% 0.16/0.57 ! [Vd203,Vd204] :
% 0.16/0.57 ( Vd203 != Vd204
% 0.16/0.57 | ~ less(Vd203,Vd204) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(130), 0), 2)',axiom,
% 0.16/0.57 ! [Vd203,Vd204] :
% 0.16/0.57 ( ~ greater(Vd203,Vd204)
% 0.16/0.57 | ~ less(Vd203,Vd204) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(130), 0), 3)',axiom,
% 0.16/0.57 ! [Vd203,Vd204] :
% 0.16/0.57 ( Vd203 != Vd204
% 0.16/0.57 | ~ greater(Vd203,Vd204) ) ).
% 0.16/0.57
% 0.16/0.57 fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
% 0.16/0.57 ! [Vd198,Vd199] :
% 0.16/0.57 ( less(Vd199,Vd198)
% 0.16/0.57 <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
% 0.16/0.57
% 0.16/0.57 fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
% 0.16/0.57 ! [Vd193,Vd194] :
% 0.16/0.57 ( greater(Vd194,Vd193)
% 0.16/0.57 <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(88), 0), 0)',axiom,
% 0.16/0.57 ! [Vd120,Vd121] :
% 0.16/0.57 ( Vd120 = Vd121
% 0.16/0.57 | ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.16/0.57 | ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(88), 0), 1)',axiom,
% 0.16/0.57 ! [Vd120,Vd121] :
% 0.16/0.57 ( Vd120 != Vd121
% 0.16/0.57 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(88), 0), 2)',axiom,
% 0.16/0.57 ! [Vd120,Vd121] :
% 0.16/0.57 ( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.16/0.57 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(goal(88), 0), 3)',axiom,
% 0.16/0.57 ! [Vd120,Vd121] :
% 0.16/0.57 ( Vd120 != Vd121
% 0.16/0.57 | ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(81, 0), 0)',axiom,
% 0.16/0.57 ! [Vd104,Vd105] :
% 0.16/0.57 ( Vd104 != Vd105
% 0.16/0.57 => ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(73, 0), 0)',axiom,
% 0.16/0.57 ! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(61, 0), 0)',axiom,
% 0.16/0.57 ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(52, 0), 0)',axiom,
% 0.16/0.57 ! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(43, 0), 0)',axiom,
% 0.16/0.57 ! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59) ).
% 0.16/0.57
% 0.16/0.57 fof('ass(cond(33, 0), 0)',axiom,
% 0.16/0.57 ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
% 0.16/0.57
% 0.16/0.57 fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
% 0.16/0.57 ! [Vd42,Vd43] :
% 0.16/0.57 ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
% 0.16/0.57 & vplus(Vd42,v1) = vsucc(Vd42) ) ).
% 0.16/0.57
% 0.16/0.57 %------------------------------------------------------------------------------
% 0.16/0.57 %-------------------------------------------
% 0.16/0.57 % Proof found
% 0.16/0.57 % SZS status Theorem for theBenchmark
% 0.16/0.57 % SZS output start Proof
% 0.16/0.57 %ClaNum:44(EqnAxiom:17)
% 0.16/0.57 %VarNum:109(SingletonVarNum:52)
% 0.16/0.57 %MaxLitNum:3
% 0.16/0.57 %MaxfuncDepth:2
% 0.16/0.57 %SharedTerms:12
% 0.16/0.57 %goalClause: 24
% 0.16/0.57 %singleGoalClaCount:1
% 0.16/0.57 [24]~P1(a7,a9)
% 0.16/0.57 [20]P1(f6(a7,a8),f6(a9,a8))
% 0.16/0.57 [19]E(f6(x191,x192),f6(x192,x191))
% 0.16/0.57 [25]~E(f6(x251,x252),x252)
% 0.16/0.57 [22]E(f6(f6(x221,a1),x222),f6(f6(x221,x222),a1))
% 0.16/0.57 [23]E(f6(f6(x231,x232),x233),f6(x231,f6(x232,x233)))
% 0.16/0.57 [31]~E(f6(a9,a8),f6(a7,a8))+E(a9,a7)
% 0.16/0.57 [44]~P2(f6(a7,a8),f6(a9,a8))+P2(a7,a9)
% 0.16/0.57 [26]~P1(x261,x262)+~E(x261,x262)
% 0.16/0.57 [27]~P2(x271,x272)+~E(x271,x272)
% 0.16/0.57 [32]~P2(x322,x321)+P1(x321,x322)
% 0.16/0.57 [33]~P1(x332,x331)+P2(x331,x332)
% 0.16/0.57 [36]~P2(x361,x362)+~P1(x361,x362)
% 0.16/0.57 [39]~P1(x391,x392)+E(f6(x391,f2(x392,x391)),x392)
% 0.16/0.57 [40]~P2(x402,x401)+E(f6(x401,f3(x401,x402)),x402)
% 0.16/0.57 [28]~E(x281,x282)+~E(x282,f6(x281,x283))
% 0.16/0.57 [29]~E(x291,x292)+~E(x291,f6(x292,x293))
% 0.16/0.57 [34]P1(x341,x342)+~E(x342,f6(x341,x343))
% 0.16/0.57 [35]P2(x351,x352)+~E(x351,f6(x352,x353))
% 0.16/0.57 [37]E(x371,x372)+~E(f6(x373,x371),f6(x373,x372))
% 0.16/0.57 [42]~P1(x421,x423)+P1(f6(x421,x422),f6(x423,x422))
% 0.16/0.57 [43]~P2(x431,x433)+P2(f6(x431,x432),f6(x433,x432))
% 0.16/0.57 [38]~E(x381,f6(x382,x383))+~E(x382,f6(x381,x384))
% 0.16/0.57 [30]P1(x301,x302)+P2(x301,x302)+E(x301,x302)
% 0.16/0.57 [41]E(x411,x412)+E(f6(x411,f4(x411,x412)),x412)+E(f6(x412,f5(x411,x412)),x411)
% 0.16/0.57 %EqnAxiom
% 0.16/0.57 [1]E(x11,x11)
% 0.16/0.57 [2]E(x22,x21)+~E(x21,x22)
% 0.16/0.57 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.16/0.57 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.16/0.57 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.16/0.57 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.16/0.57 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.16/0.57 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83))
% 0.16/0.57 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92))
% 0.16/0.57 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103))
% 0.16/0.57 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112))
% 0.16/0.57 [12]~E(x121,x122)+E(f2(x121,x123),f2(x122,x123))
% 0.16/0.57 [13]~E(x131,x132)+E(f2(x133,x131),f2(x133,x132))
% 0.16/0.57 [14]P1(x142,x143)+~E(x141,x142)+~P1(x141,x143)
% 0.16/0.57 [15]P1(x153,x152)+~E(x151,x152)+~P1(x153,x151)
% 0.16/0.57 [16]P2(x162,x163)+~E(x161,x162)+~P2(x161,x163)
% 0.16/0.57 [17]P2(x173,x172)+~E(x171,x172)+~P2(x173,x171)
% 0.16/0.57
% 0.16/0.57 %-------------------------------------------
% 0.16/0.57 cnf(56,plain,
% 0.16/0.57 (P2(f6(x561,x562),x562)),
% 0.16/0.57 inference(scs_inference,[],[24,20,19,23,2,36,33,32,27,26,35])).
% 0.16/0.57 cnf(60,plain,
% 0.16/0.57 (~E(f6(f6(x601,x602),x603),x601)),
% 0.16/0.57 inference(scs_inference,[],[24,20,19,23,2,36,33,32,27,26,35,34,29])).
% 0.16/0.57 cnf(62,plain,
% 0.16/0.57 (~E(x621,f6(x622,x621))),
% 0.16/0.57 inference(scs_inference,[],[24,20,19,23,2,36,33,32,27,26,35,34,29,28])).
% 0.16/0.57 cnf(84,plain,
% 0.16/0.57 (E(f6(a9,x841),f6(a7,x841))),
% 0.16/0.57 inference(scs_inference,[],[24,20,19,23,2,36,33,32,27,26,35,34,29,28,43,42,38,40,16,30,13,12,11,10,9,8,7,6,5,4])).
% 0.16/0.57 cnf(108,plain,
% 0.16/0.57 (~E(f6(f6(x1081,x1082),x1083),x1081)),
% 0.16/0.57 inference(rename_variables,[],[60])).
% 0.16/0.57 cnf(118,plain,
% 0.16/0.57 ($false),
% 0.16/0.57 inference(scs_inference,[],[22,20,19,56,62,60,108,84,36,42,38,40,39,41,29,33,27]),
% 0.16/0.57 ['proof']).
% 0.16/0.57 % SZS output end Proof
% 0.16/0.57 % Total time :0.010000s
%------------------------------------------------------------------------------