TPTP Problem File: NUM838+2.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : NUM838+2 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Number Theory
% Problem  : holds(conseq(195),305,0)
% 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   : 0.11 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.13 v7.3.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.16 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0
% Syntax   : Number of formulae    :   30 (   6 unt;   0 def)
%            Number of atoms       :   57 (  26 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   39 (  12   ~;  10   |;   2   &)
%                                         (   2 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 2-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   76 (  68   !;   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(195), 305, 0)',conjecture,
    greater(vplus(vd301,vd303),vplus(vd302,vd303)) ).

fof('holds(antec(195), 304, 0)',axiom,
    greater(vd301,vd302) ).

fof('ass(cond(proof(196), 0), 0)',axiom,
    ! [Vd310,Vd322,Vd323] :
      ( less(Vd322,Vd323)
     => less(vplus(Vd322,Vd310),vplus(Vd323,Vd310)) ) ).

fof('ass(cond(proof(196), 0), 1)',axiom,
    ! [Vd310,Vd322,Vd323] :
      ( less(Vd322,Vd323)
     => greater(vplus(Vd323,Vd310),vplus(Vd322,Vd310)) ) ).

fof('ass(cond(proof(196), 0), 2)',axiom,
    ! [Vd310,Vd322,Vd323] :
      ( less(Vd322,Vd323)
     => greater(Vd323,Vd322) ) ).

fof('ass(cond(proof(196), 0), 3)',axiom,
    ! [Vd310,Vd318,Vd319] :
      ( Vd318 = Vd319
     => vplus(Vd318,Vd310) = vplus(Vd319,Vd310) ) ).

fof('ass(cond(proof(196), 0), 4)',axiom,
    ! [Vd310,Vd311,Vd312] :
      ( greater(Vd311,Vd312)
     => greater(vplus(Vd311,Vd310),vplus(Vd312,Vd310)) ) ).

fof('ass(cond(proof(196), 0), 5)',axiom,
    ! [Vd310,Vd311,Vd312] :
      ( greater(Vd311,Vd312)
     => vplus(vskolem7(Vd311,Vd312),vplus(Vd312,Vd310)) = vplus(vplus(Vd312,Vd310),vskolem7(Vd311,Vd312)) ) ).

fof('ass(cond(proof(196), 0), 6)',axiom,
    ! [Vd310,Vd311,Vd312] :
      ( greater(Vd311,Vd312)
     => vplus(vplus(vskolem7(Vd311,Vd312),Vd312),Vd310) = vplus(vskolem7(Vd311,Vd312),vplus(Vd312,Vd310)) ) ).

fof('ass(cond(proof(196), 0), 7)',axiom,
    ! [Vd310,Vd311,Vd312] :
      ( greater(Vd311,Vd312)
     => vplus(vplus(Vd312,vskolem7(Vd311,Vd312)),Vd310) = vplus(vplus(vskolem7(Vd311,Vd312),Vd312),Vd310) ) ).

fof('ass(cond(proof(196), 0), 8)',axiom,
    ! [Vd310,Vd311,Vd312] :
      ( greater(Vd311,Vd312)
     => vplus(Vd311,Vd310) = vplus(vplus(Vd312,vskolem7(Vd311,Vd312)),Vd310) ) ).

fof('ass(cond(proof(196), 0), 9)',axiom,
    ! [Vd310,Vd311,Vd312] :
      ( greater(Vd311,Vd312)
     => Vd311 = vplus(Vd312,vskolem7(Vd311,Vd312)) ) ).

fof('ass(cond(189, 0), 0)',axiom,
    ! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295) ).

fof('ass(cond(184, 0), 0)',axiom,
    ! [Vd289,Vd290,Vd292] :
      ( ( leq(Vd290,Vd292)
        & leq(Vd289,Vd290) )
     => leq(Vd289,Vd292) ) ).

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(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(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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