TPTP Problem File: NUM849+2.p
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- Solve Problem
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% File : NUM849+2 : TPTP v8.2.0. Released v4.1.0.
% Domain : Number Theory
% Problem : qu(ind(296),imp(296))
% Version : Especial: Reduced > Especial.
% English :
% Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% Source : [Kue09]
% Names :
% Status : Theorem
% Rating : 0.15 v8.2.0, 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
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 19 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 0 ~; 0 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% SPC : FOF_THM_RFO_PEQ
% Comments : From the Landau in Naproche 0.45 collection.
% : This version uses a filtered set of axioms.
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fof('qu(ind(296), imp(296))',conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ) ).
fof('ass(cond(conseq(292), 1), 0)',axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) = vmul(vd448,vmul(vd449,vsucc(Vd451))) ) ).
fof('ass(cond(conseq(292), 1), 1)',axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) ) ).
fof('ass(cond(conseq(292), 1), 2)',axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) ) ).
fof('ass(cond(conseq(292), 1), 3)',axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vmul(vmul(vd448,vd449),vsucc(Vd451)) = vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) ) ).
fof('holds(293, 450, 1)',axiom,
vmul(vd448,vd449) = vmul(vd448,vmul(vd449,v1)) ).
fof('ass(cond(281, 0), 0)',axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
fof('ass(cond(270, 0), 0)',axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
fof('ass(cond(261, 0), 0)',axiom,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [Vd396,Vd397] :
( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& vmul(Vd396,v1) = Vd396 ) ).
fof('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ) ).
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