%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUM852+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 : n001.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 36.45s 36.65s
% Output : CNFRefutation 36.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM852+2 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Jun 22 21:26:39 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.18/0.57 start to proof:theBenchmark
% 36.45/36.64 %-------------------------------------------
% 36.45/36.64 % File :CSE---1.7
% 36.45/36.64 % Problem :theBenchmark
% 36.45/36.64 % Transform :cnf
% 36.45/36.64 % Format :tptp:raw
% 36.45/36.64 % Command :java -jar mcs_scs.jar %d %s
% 36.45/36.64
% 36.45/36.64 % Result :Theorem 35.930000s
% 36.45/36.64 % Output :CNFRefutation 35.930000s
% 36.45/36.64 %-------------------------------------------
% 36.45/36.64 %------------------------------------------------------------------------------
% 36.45/36.64 % File : NUM852+2 : TPTP v8.2.0. Released v4.1.0.
% 36.45/36.65 % Domain : Number Theory
% 36.45/36.65 % Problem : holds(conseq_conjunct1(conseq_conjunct2(conseq(304))),484,0)
% 36.45/36.65 % Version : Especial: Reduced > Especial.
% 36.45/36.65 % English :
% 36.45/36.65
% 36.45/36.65 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 36.45/36.65 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 36.45/36.65 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 36.45/36.65 % Source : [Kue09]
% 36.45/36.65 % Names :
% 36.45/36.65
% 36.45/36.65 % Status : Theorem
% 36.45/36.65 % Rating : 0.22 v8.1.0, 0.25 v7.5.0, 0.28 v7.4.0, 0.23 v7.3.0, 0.24 v7.1.0, 0.26 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.27 v6.0.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0
% 36.45/36.65 % Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% 36.45/36.65 % Number of atoms : 34 ( 14 equ)
% 36.45/36.65 % Maximal formula atoms : 3 ( 1 avg)
% 36.45/36.65 % Number of connectives : 20 ( 6 ~; 5 |; 0 &)
% 36.45/36.65 % ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% 36.45/36.65 % Maximal formula depth : 5 ( 4 avg)
% 36.45/36.65 % Maximal term depth : 4 ( 1 avg)
% 36.45/36.65 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 36.45/36.65 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 36.45/36.65 % Number of variables : 38 ( 36 !; 2 ?)
% 36.45/36.65 % SPC : FOF_THM_RFO_SEQ
% 36.45/36.65
% 36.45/36.65 % Comments : From the Landau in Naproche 0.45 collection.
% 36.45/36.65 % : This version uses a filtered set of axioms.
% 36.45/36.65 %------------------------------------------------------------------------------
% 36.45/36.65 fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)',conjecture,
% 36.45/36.65 greater(vmul(vd481,vd469),vmul(vd480,vd469)) ).
% 36.45/36.65
% 36.45/36.65 fof('holds(conseq_conjunct1(conseq(304)), 483, 0)',axiom,
% 36.45/36.65 greater(vd481,vd480) ).
% 36.45/36.65
% 36.45/36.65 fof('holds(antec(304), 482, 0)',axiom,
% 36.45/36.65 less(vd480,vd481) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(303, 0), 0)',axiom,
% 36.45/36.65 ! [Vd476,Vd477] :
% 36.45/36.65 ( Vd476 = Vd477
% 36.45/36.65 => vmul(Vd476,vd469) = vmul(Vd477,vd469) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(302, 0), 0)',axiom,
% 36.45/36.65 ! [Vd470,Vd471] :
% 36.45/36.65 ( greater(Vd470,Vd471)
% 36.45/36.65 => greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469)) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(302, 0), 1)',axiom,
% 36.45/36.65 ! [Vd470,Vd471] :
% 36.45/36.65 ( greater(Vd470,Vd471)
% 36.45/36.65 => vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(302, 0), 2)',axiom,
% 36.45/36.65 ! [Vd470,Vd471] :
% 36.45/36.65 ( greater(Vd470,Vd471)
% 36.45/36.65 => vmul(Vd470,vd469) = vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(302, 0), 3)',axiom,
% 36.45/36.65 ! [Vd470,Vd471] :
% 36.45/36.65 ( greater(Vd470,Vd471)
% 36.45/36.65 => Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471)) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(290, 0), 0)',axiom,
% 36.45/36.65 ! [Vd444,Vd445,Vd446] : vmul(vmul(Vd444,Vd445),Vd446) = vmul(Vd444,vmul(Vd445,Vd446)) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(281, 0), 0)',axiom,
% 36.45/36.65 ! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(270, 0), 0)',axiom,
% 36.45/36.65 ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(261, 0), 0)',axiom,
% 36.45/36.65 ! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(147, 0), 0)',axiom,
% 36.45/36.65 ! [Vd226,Vd227] :
% 36.45/36.65 ( less(Vd226,Vd227)
% 36.45/36.65 => greater(Vd227,Vd226) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(140, 0), 0)',axiom,
% 36.45/36.65 ! [Vd208,Vd209] :
% 36.45/36.65 ( greater(Vd208,Vd209)
% 36.45/36.65 => less(Vd209,Vd208) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(goal(130), 0), 0)',axiom,
% 36.45/36.65 ! [Vd203,Vd204] :
% 36.45/36.65 ( Vd203 = Vd204
% 36.45/36.65 | greater(Vd203,Vd204)
% 36.45/36.65 | less(Vd203,Vd204) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(goal(130), 0), 1)',axiom,
% 36.45/36.65 ! [Vd203,Vd204] :
% 36.45/36.65 ( Vd203 != Vd204
% 36.45/36.65 | ~ less(Vd203,Vd204) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(goal(130), 0), 2)',axiom,
% 36.45/36.65 ! [Vd203,Vd204] :
% 36.45/36.65 ( ~ greater(Vd203,Vd204)
% 36.45/36.65 | ~ less(Vd203,Vd204) ) ).
% 36.45/36.65
% 36.45/36.65 fof('ass(cond(goal(130), 0), 3)',axiom,
% 36.45/36.65 ! [Vd203,Vd204] :
% 36.45/36.65 ( Vd203 != Vd204
% 36.45/36.65 | ~ greater(Vd203,Vd204) ) ).
% 36.45/36.65
% 36.45/36.65 fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
% 36.45/36.65 ! [Vd198,Vd199] :
% 36.45/36.65 ( less(Vd199,Vd198)
% 36.45/36.65 <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
% 36.45/36.65
% 36.45/36.65 fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
% 36.45/36.65 ! [Vd193,Vd194] :
% 36.45/36.65 ( greater(Vd194,Vd193)
% 36.45/36.65 <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
% 36.45/36.65
% 36.45/36.65 %------------------------------------------------------------------------------
% 36.45/36.65 %-------------------------------------------
% 36.45/36.65 % Proof found
% 36.45/36.65 % SZS status Theorem for theBenchmark
% 36.45/36.65 % SZS output start Proof
% 36.45/36.65 %ClaNum:39(EqnAxiom:18)
% 36.45/36.65 %VarNum:96(SingletonVarNum:40)
% 36.45/36.65 %MaxLitNum:3
% 36.45/36.65 %MaxfuncDepth:3
% 36.45/36.65 %SharedTerms:8
% 36.45/36.65 %goalClause: 25
% 36.45/36.65 %singleGoalClaCount:1
% 36.45/36.65 [19]P1(a1,a2)
% 36.45/36.65 [20]P2(a2,a1)
% 36.45/36.65 [25]~P1(f6(a1,a3),f6(a2,a3))
% 36.45/36.65 [21]E(f6(x211,x212),f6(x212,x211))
% 36.45/36.65 [22]E(f7(f6(x221,x222),x222),f6(f8(x221),x222))
% 36.45/36.65 [23]E(f6(f6(x231,x232),x233),f6(x231,f6(x232,x233)))
% 36.45/36.65 [24]E(f7(f6(x241,x242),f6(x241,x243)),f6(x241,f7(x242,x243)))
% 36.45/36.65 [26]~P1(x261,x262)+~E(x261,x262)
% 36.45/36.65 [27]~P2(x271,x272)+~E(x271,x272)
% 36.45/36.65 [29]~P2(x292,x291)+P1(x291,x292)
% 36.45/36.65 [30]~P1(x302,x301)+P2(x301,x302)
% 36.45/36.65 [33]~P2(x331,x332)+~P1(x331,x332)
% 36.45/36.65 [34]~P2(x341,x342)+E(f7(x341,f4(x342,x341)),x342)
% 36.45/36.65 [35]~P1(x352,x351)+E(f7(x351,f9(x352,x351)),x352)
% 36.45/36.65 [36]~P1(x362,x361)+E(f7(x361,f5(x361,x362)),x362)
% 36.45/36.65 [37]~P1(x372,x371)+E(f6(f7(x371,f9(x372,x371)),a3),f6(x372,a3))
% 36.45/36.65 [38]~P1(x382,x381)+E(f7(f6(x381,a3),f6(f9(x382,x381),a3)),f6(f7(x381,f9(x382,x381)),a3))
% 36.45/36.65 [39]~P1(x392,x391)+P1(f7(f6(x391,a3),f6(f9(x392,x391),a3)),f6(x391,a3))
% 36.45/36.65 [31]P1(x311,x312)+~E(x311,f7(x312,x313))
% 36.45/36.65 [32]P2(x321,x322)+~E(x322,f7(x321,x323))
% 36.45/36.65 [28]P1(x281,x282)+P2(x281,x282)+E(x281,x282)
% 36.45/36.65 %EqnAxiom
% 36.45/36.65 [1]E(x11,x11)
% 36.45/36.65 [2]E(x22,x21)+~E(x21,x22)
% 36.45/36.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 36.45/36.65 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 36.45/36.65 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 36.45/36.65 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 36.45/36.65 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 36.45/36.65 [8]~E(x81,x82)+E(f9(x81,x83),f9(x82,x83))
% 36.45/36.65 [9]~E(x91,x92)+E(f9(x93,x91),f9(x93,x92))
% 36.45/36.65 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 36.45/36.65 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 36.45/36.65 [12]~E(x121,x122)+E(f8(x121),f8(x122))
% 36.45/36.65 [13]~E(x131,x132)+E(f5(x131,x133),f5(x132,x133))
% 36.45/36.65 [14]~E(x141,x142)+E(f5(x143,x141),f5(x143,x142))
% 36.45/36.65 [15]P1(x152,x153)+~E(x151,x152)+~P1(x151,x153)
% 36.45/36.65 [16]P1(x163,x162)+~E(x161,x162)+~P1(x163,x161)
% 36.45/36.65 [17]P2(x172,x173)+~E(x171,x172)+~P2(x171,x173)
% 36.45/36.65 [18]P2(x183,x182)+~E(x181,x182)+~P2(x183,x181)
% 36.45/36.65
% 36.45/36.65 %-------------------------------------------
% 36.45/36.66 cnf(42,plain,
% 36.45/36.66 (P1(f7(x421,x422),x421)),
% 36.45/36.66 inference(equality_inference,[],[31])).
% 36.45/36.66 cnf(53,plain,
% 36.45/36.66 (~E(f7(f6(a2,a3),x531),f6(a1,a3))),
% 36.45/36.66 inference(scs_inference,[],[25,42,21,22,29,26,27,33,2,15])).
% 36.45/36.66 cnf(1730,plain,
% 36.45/36.66 (E(f6(f7(a2,f9(a1,a2)),a3),f6(a1,a3))),
% 36.45/36.66 inference(scs_inference,[],[20,29,37])).
% 36.45/36.66 cnf(1739,plain,
% 36.45/36.66 ($false),
% 36.45/36.66 inference(scs_inference,[],[53,19,1730,27,26,30,2,3,38]),
% 36.45/36.66 ['proof']).
% 36.45/36.66 % SZS output end Proof
% 36.45/36.66 % Total time :35.930000s
%------------------------------------------------------------------------------