TSTP Solution File: NUM849+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM849+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 : n011.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 10:25:23 EDT 2023
% Result : Theorem 0.97s 1.07s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM849+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 17:29:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.97/1.06 %-------------------------------------------
% 0.97/1.06 % File :CSE---1.6
% 0.97/1.06 % Problem :theBenchmark
% 0.97/1.06 % Transform :cnf
% 0.97/1.06 % Format :tptp:raw
% 0.97/1.06 % Command :java -jar mcs_scs.jar %d %s
% 0.97/1.06
% 0.97/1.06 % Result :Theorem 0.460000s
% 0.97/1.06 % Output :CNFRefutation 0.460000s
% 0.97/1.06 %-------------------------------------------
% 0.97/1.07 %------------------------------------------------------------------------------
% 0.97/1.07 % File : NUM849+2 : TPTP v8.1.2. Released v4.1.0.
% 0.97/1.07 % Domain : Number Theory
% 0.97/1.07 % Problem : qu(ind(296),imp(296))
% 0.97/1.07 % Version : Especial: Reduced > Especial.
% 0.97/1.07 % English :
% 0.97/1.07
% 0.97/1.07 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.97/1.07 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 0.97/1.07 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 0.97/1.07 % Source : [Kue09]
% 0.97/1.07 % Names :
% 0.97/1.07
% 0.97/1.07 % Status : Theorem
% 0.97/1.07 % Rating : 0.12 v8.1.0, 0.13 v7.5.0, 0.14 v7.4.0, 0.18 v7.3.0, 0.23 v7.2.0, 0.17 v7.1.0, 0.18 v7.0.0, 0.13 v6.4.0, 0.14 v6.2.0, 0.18 v6.1.0, 0.17 v5.5.0, 0.25 v5.4.0, 0.11 v5.3.0, 0.17 v5.2.0, 0.14 v5.0.0, 0.25 v4.1.0
% 0.97/1.07 % Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% 0.97/1.07 % Number of atoms : 19 ( 19 equ)
% 0.97/1.07 % Maximal formula atoms : 2 ( 1 avg)
% 0.97/1.07 % Number of connectives : 7 ( 0 ~; 0 |; 2 &)
% 0.97/1.07 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.97/1.07 % Maximal formula depth : 4 ( 3 avg)
% 0.97/1.07 % Maximal term depth : 4 ( 2 avg)
% 0.97/1.07 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.97/1.07 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.97/1.07 % Number of variables : 18 ( 18 !; 0 ?)
% 0.97/1.07 % SPC : FOF_THM_RFO_PEQ
% 0.97/1.07
% 0.97/1.07 % Comments : From the Landau in Naproche 0.45 collection.
% 0.97/1.07 % : This version uses a filtered set of axioms.
% 0.97/1.07 %------------------------------------------------------------------------------
% 0.97/1.07 fof('qu(ind(296), imp(296))',conjecture,
% 0.97/1.07 ! [Vd454] :
% 0.97/1.07 ( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
% 0.97/1.07 => vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(conseq(292), 1), 0)',axiom,
% 0.97/1.07 ! [Vd451] :
% 0.97/1.07 ( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
% 0.97/1.07 => vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) = vmul(vd448,vmul(vd449,vsucc(Vd451))) ) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(conseq(292), 1), 1)',axiom,
% 0.97/1.07 ! [Vd451] :
% 0.97/1.07 ( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
% 0.97/1.07 => vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) ) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(conseq(292), 1), 2)',axiom,
% 0.97/1.07 ! [Vd451] :
% 0.97/1.07 ( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
% 0.97/1.07 => vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) ) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(conseq(292), 1), 3)',axiom,
% 0.97/1.07 ! [Vd451] :
% 0.97/1.07 ( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
% 0.97/1.07 => vmul(vmul(vd448,vd449),vsucc(Vd451)) = vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) ) ).
% 0.97/1.07
% 0.97/1.07 fof('holds(293, 450, 1)',axiom,
% 0.97/1.07 vmul(vd448,vd449) = vmul(vd448,vmul(vd449,v1)) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(281, 0), 0)',axiom,
% 0.97/1.07 ! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(270, 0), 0)',axiom,
% 0.97/1.07 ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(261, 0), 0)',axiom,
% 0.97/1.07 ! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
% 0.97/1.07
% 0.97/1.07 fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
% 0.97/1.07 ! [Vd396,Vd397] :
% 0.97/1.07 ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
% 0.97/1.07 & vmul(Vd396,v1) = Vd396 ) ).
% 0.97/1.07
% 0.97/1.07 fof('ass(cond(61, 0), 0)',axiom,
% 0.97/1.07 ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
% 0.97/1.07
% 0.97/1.07 fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
% 0.97/1.07 ! [Vd42,Vd43] :
% 0.97/1.07 ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
% 0.97/1.07 & vplus(Vd42,v1) = vsucc(Vd42) ) ).
% 0.97/1.07
% 0.97/1.07 %------------------------------------------------------------------------------
% 0.97/1.07 %-------------------------------------------
% 0.97/1.07 % Proof found
% 0.97/1.07 % SZS status Theorem for theBenchmark
% 0.97/1.07 % SZS output start Proof
% 0.97/1.07 %ClaNum:20(EqnAxiom:7)
% 0.97/1.07 %VarNum:35(SingletonVarNum:15)
% 0.97/1.07 %MaxLitNum:2
% 0.97/1.07 %MaxfuncDepth:3
% 0.97/1.07 %SharedTerms:17
% 0.97/1.07 %goalClause: 12 17
% 0.97/1.07 %singleGoalClaCount:2
% 0.97/1.07 [11]E(f3(a4,f3(a5,a1)),f3(a4,a5))
% 0.97/1.07 [12]E(f3(f3(a4,a5),a2),f3(a4,f3(a5,a2)))
% 0.97/1.07 [17]~E(f3(f3(a4,a5),f6(a2,a1)),f3(a4,f3(a5,f6(a2,a1))))
% 0.97/1.07 [8]E(f3(x81,a1),x81)
% 0.97/1.07 [9]E(f3(x91,x92),f3(x92,x91))
% 0.97/1.07 [10]E(f6(x101,x102),f6(x102,x101))
% 0.97/1.07 [13]E(f6(f6(x131,x132),a1),f6(x131,f6(x132,a1)))
% 0.97/1.07 [14]E(f6(f3(x141,x142),x141),f3(x141,f6(x142,a1)))
% 0.97/1.07 [15]E(f6(f3(x151,x152),x152),f3(f6(x151,a1),x152))
% 0.97/1.07 [16]E(f6(f3(x161,x162),f3(x161,x163)),f3(x161,f6(x162,x163)))
% 0.97/1.07 [19]~E(f3(f3(a4,a5),x191),f3(a4,f3(a5,x191)))+E(f3(a4,f6(f3(a5,x191),a5)),f3(a4,f3(a5,f6(x191,a1))))
% 0.97/1.07 %EqnAxiom
% 0.97/1.07 [1]E(x11,x11)
% 0.97/1.07 [2]E(x22,x21)+~E(x21,x22)
% 0.97/1.07 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.97/1.07 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.97/1.07 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.97/1.07 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.97/1.07 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.97/1.07
% 0.97/1.07 %-------------------------------------------
% 0.97/1.08 cnf(25,plain,
% 0.97/1.08 (E(f6(f3(f3(a4,a5),a2),x251),f6(f3(a4,f3(a5,a2)),x251))),
% 0.97/1.08 inference(scs_inference,[],[12,8,2,3,7,6])).
% 0.97/1.08 cnf(28,plain,
% 0.97/1.08 (E(f3(a4,f6(f3(a5,a2),a5)),f3(a4,f3(a5,f6(a2,a1))))),
% 0.97/1.08 inference(scs_inference,[],[12,8,2,3,7,6,5,4,19])).
% 0.97/1.08 cnf(30,plain,
% 0.97/1.08 (~E(f3(f6(a2,a1),f3(a4,a5)),f3(a4,f3(a5,f6(a2,a1))))),
% 0.97/1.08 inference(scs_inference,[],[17,9,3])).
% 0.97/1.08 cnf(32,plain,
% 0.97/1.08 (~E(f3(a4,f3(a5,f6(a2,a1))),f3(f3(a4,a5),f6(a2,a1)))),
% 0.97/1.08 inference(scs_inference,[],[17,9,3,2])).
% 0.97/1.08 cnf(36,plain,
% 0.97/1.08 (~E(f3(a4,f3(a5,f6(a2,a1))),f6(f3(f3(a4,a5),a2),f3(a4,a5)))),
% 0.97/1.08 inference(scs_inference,[],[14,32,3])).
% 0.97/1.08 cnf(38,plain,
% 0.97/1.08 (~E(f3(a4,f3(a5,f6(a2,a1))),f3(f6(a2,a1),f3(a4,a5)))),
% 0.97/1.08 inference(scs_inference,[],[14,30,32,3,2])).
% 0.97/1.08 cnf(39,plain,
% 0.97/1.08 (~E(f3(f3(a5,f6(a2,a1)),a4),f3(f6(a2,a1),f3(a4,a5)))),
% 0.97/1.08 inference(scs_inference,[],[9,38,3])).
% 0.97/1.08 cnf(41,plain,
% 0.97/1.08 (E(x411,f3(x411,a1))),
% 0.97/1.08 inference(scs_inference,[],[8,9,38,3,2])).
% 0.97/1.08 cnf(46,plain,
% 0.97/1.08 (~E(f6(f3(f3(a4,a5),a2),f3(a4,a5)),f3(a4,f3(a5,f6(a2,a1))))),
% 0.97/1.08 inference(scs_inference,[],[36,2])).
% 0.97/1.08 cnf(50,plain,
% 0.97/1.08 (~E(f6(f3(f3(a4,a5),a2),f3(a4,a5)),f3(f3(a5,f6(a2,a1)),a4))),
% 0.97/1.08 inference(scs_inference,[],[9,46,3])).
% 0.97/1.08 cnf(54,plain,
% 0.97/1.08 (~E(f6(f3(a4,f3(a5,a2)),f3(a4,a5)),f3(f3(a5,f6(a2,a1)),a4))),
% 0.97/1.08 inference(scs_inference,[],[25,50,2,3])).
% 0.97/1.08 cnf(64,plain,
% 0.97/1.08 (~E(f3(f3(a5,f6(a2,a1)),a4),f6(f3(a4,f3(a5,a2)),f3(a4,a5)))),
% 0.97/1.08 inference(scs_inference,[],[54,2])).
% 0.97/1.08 cnf(78,plain,
% 0.97/1.08 (E(f3(f6(f3(x781,x782),x781),x783),f3(f3(x781,f6(x782,a1)),x783))),
% 0.97/1.08 inference(scs_inference,[],[14,28,46,3,2,7,6,4])).
% 0.97/1.08 cnf(91,plain,
% 0.97/1.08 (E(f3(x911,f6(x912,x913)),f6(f3(x911,x912),f3(x911,x913)))),
% 0.97/1.08 inference(scs_inference,[],[16,32,41,3,2])).
% 0.97/1.08 cnf(128,plain,
% 0.97/1.08 (~E(f3(f3(a5,f6(a2,a1)),a4),f3(f3(a4,a5),f6(a2,a1)))),
% 0.97/1.08 inference(scs_inference,[],[39,32,9,2,3])).
% 0.97/1.08 cnf(135,plain,
% 0.97/1.08 (~E(f3(f3(a5,f6(a2,a1)),a4),f3(a4,f6(f3(a5,a2),a5)))),
% 0.97/1.08 inference(scs_inference,[],[91,128,64,2,3])).
% 0.97/1.08 cnf(144,plain,
% 0.97/1.08 (~E(f3(a4,f6(f3(a5,a2),a5)),f3(f3(a5,f6(a2,a1)),a4))),
% 0.97/1.08 inference(scs_inference,[],[135,2])).
% 0.97/1.08 cnf(431,plain,
% 0.97/1.08 ($false),
% 0.97/1.08 inference(scs_inference,[],[78,144,9,3]),
% 0.97/1.08 ['proof']).
% 0.97/1.08 % SZS output end Proof
% 0.97/1.08 % Total time :0.460000s
%------------------------------------------------------------------------------