%------------------------------------------------------------------------------
% File     : NUM840+2 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Number Theory
% Problem  : holds(conseq(conjunct2(conjunct2(204))),336,0)
% 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   : 0.19 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
% Syntax   : Number of formulae    :   26 (   7 unt;   0 def)
%            Number of atoms       :   47 (  27 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   36 (  15   ~;  10   |;   1   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   56 (  48   !;   8   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : From the Landau in Naproche 0.45 collection.
%          : This version uses a filtered set of axioms.
%------------------------------------------------------------------------------
fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)',conjecture,
    less(vd328,vd329) ).

fof('holds(antec(conjunct2(conjunct2(204))), 335, 0)',axiom,
    less(vplus(vd328,vd330),vplus(vd329,vd330)) ).

fof('ass(cond(conjunct1(conjunct2(204)), 0), 0)',axiom,
    ( vplus(vd328,vd330) = vplus(vd329,vd330)
   => vd328 = vd329 ) ).

fof('ass(cond(conjunct1(204), 0), 0)',axiom,
    ( greater(vplus(vd328,vd330),vplus(vd329,vd330))
   => greater(vd328,vd329) ) ).

fof('ass(cond(goal(193), 0), 0)',axiom,
    ! [Vd301,Vd302,Vd303] :
      ( less(Vd301,Vd302)
     => less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).

fof('ass(cond(goal(193), 0), 1)',axiom,
    ! [Vd301,Vd302,Vd303] :
      ( Vd301 = Vd302
     => vplus(Vd301,Vd303) = vplus(Vd302,Vd303) ) ).

fof('ass(cond(goal(193), 0), 2)',axiom,
    ! [Vd301,Vd302,Vd303] :
      ( greater(Vd301,Vd302)
     => greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).

fof('ass(cond(147, 0), 0)',axiom,
    ! [Vd226,Vd227] :
      ( less(Vd226,Vd227)
     => greater(Vd227,Vd226) ) ).

fof('ass(cond(140, 0), 0)',axiom,
    ! [Vd208,Vd209] :
      ( greater(Vd208,Vd209)
     => less(Vd209,Vd208) ) ).

fof('ass(cond(goal(130), 0), 0)',axiom,
    ! [Vd203,Vd204] :
      ( Vd203 = Vd204
      | greater(Vd203,Vd204)
      | less(Vd203,Vd204) ) ).

fof('ass(cond(goal(130), 0), 1)',axiom,
    ! [Vd203,Vd204] :
      ( Vd203 != Vd204
      | ~ less(Vd203,Vd204) ) ).

fof('ass(cond(goal(130), 0), 2)',axiom,
    ! [Vd203,Vd204] :
      ( ~ greater(Vd203,Vd204)
      | ~ less(Vd203,Vd204) ) ).

fof('ass(cond(goal(130), 0), 3)',axiom,
    ! [Vd203,Vd204] :
      ( Vd203 != Vd204
      | ~ greater(Vd203,Vd204) ) ).

fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
    ! [Vd198,Vd199] :
      ( less(Vd199,Vd198)
    <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).

fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
    ! [Vd193,Vd194] :
      ( greater(Vd194,Vd193)
    <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).

fof('ass(cond(goal(88), 0), 0)',axiom,
    ! [Vd120,Vd121] :
      ( Vd120 = Vd121
      | ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
      | ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).

fof('ass(cond(goal(88), 0), 1)',axiom,
    ! [Vd120,Vd121] :
      ( Vd120 != Vd121
      | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).

fof('ass(cond(goal(88), 0), 2)',axiom,
    ! [Vd120,Vd121] :
      ( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
      | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).

fof('ass(cond(goal(88), 0), 3)',axiom,
    ! [Vd120,Vd121] :
      ( Vd120 != Vd121
      | ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).

fof('ass(cond(81, 0), 0)',axiom,
    ! [Vd104,Vd105] :
      ( Vd104 != Vd105
     => ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ) ).

fof('ass(cond(73, 0), 0)',axiom,
    ! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93) ).

fof('ass(cond(61, 0), 0)',axiom,
    ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).

fof('ass(cond(52, 0), 0)',axiom,
    ! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ).

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) ) ).

%------------------------------------------------------------------------------