TPTP Problem File: NUM845+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUM845+2 : TPTP v8.2.0. Released v4.1.0.
% Domain : Number Theory
% Problem : qu(ind(267),imp(267))
% 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 : 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.10 v7.4.0, 0.12 v7.3.0, 0.15 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, 0.25 v5.5.0, 0.50 v5.4.0, 0.33 v5.2.0, 0.29 v5.0.0, 0.38 v4.1.0
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 26 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 0 ~; 0 |; 2 &)
% ( 0 <=>; 9 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 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(267), imp(267))',conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) ).
fof('ass(cond(conseq(263), 1), 0)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) = vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413)) ) ).
fof('ass(cond(conseq(263), 1), 1)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) = vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) ) ).
fof('ass(cond(conseq(263), 1), 2)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) = vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) ) ).
fof('ass(cond(conseq(263), 1), 3)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) = vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) ) ).
fof('ass(cond(conseq(263), 1), 4)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) = vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) ) ).
fof('ass(cond(conseq(263), 1), 5)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)) = vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) ) ).
fof('ass(cond(conseq(263), 1), 6)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)) ) ).
fof('ass(cond(conseq(263), 1), 7)',axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) ) ).
fof('holds(264, 412, 2)',axiom,
vsucc(vmul(vd411,v1)) = vplus(vmul(vd411,v1),v1) ).
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('ass(cond(43, 0), 0)',axiom,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59) ).
fof('ass(cond(33, 0), 0)',axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
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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