TSTP Solution File: NUM844+2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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  : 600s
% DateTime : Mon Jul 18 12:30:53 EDT 2022

% Result   : Theorem 0.19s 0.37s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  124 (  69 unt;   0 def)
%            Number of atoms       :  204 ( 203 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  162 (  82   ~;  78   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   54 (   0 sgn  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof('holds(266, 415, 3)',conjecture,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ).

fof('holds(266, 415, 2)',axiom,
    vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ).

fof('holds(266, 415, 1)',axiom,
    vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) ).

fof('holds(266, 415, 0)',axiom,
    vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) ).

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) ) ).

fof(subgoal_0,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    inference(strip,[],['holds(266, 415, 3)']) ).

fof(negate_0_0,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
    inference(canonicalize,[],['holds(266, 415, 2)']) ).

fof(normalize_0_2,plain,
    ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
    inference(canonicalize,[],['ass(cond(61, 0), 0)']) ).

fof(normalize_0_3,plain,
    ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
    inference(canonicalize,[],['ass(cond(33, 0), 0)']) ).

fof(normalize_0_5,plain,
    ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42)
    & ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
    inference(canonicalize,[],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).

fof(normalize_0_7,plain,
    ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
    inference(canonicalize,[],['holds(266, 415, 1)']) ).

fof(normalize_0_10,plain,
    vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
    inference(canonicalize,[],['holds(266, 415, 0)']) ).

fof(normalize_0_11,plain,
    ! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
    inference(canonicalize,[],['ass(cond(52, 0), 0)']) ).

fof(normalize_0_12,plain,
    ! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
    inference(specialize,[],[normalize_0_11]) ).

cnf(refute_0_0,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_2,plain,
    vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_4,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_5,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( vplus(Vd79,Vd78) != vplus(Vd78,Vd79)
    | vplus(Vd78,Vd79) = vplus(Vd79,Vd78) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(vplus(Vd79,Vd78))),bind(Y,$fot(vplus(Vd78,Vd79)))]]) ).

cnf(refute_0_7,plain,
    vplus(Vd78,Vd79) = vplus(Vd79,Vd78),
    inference(resolve,[$cnf( $equal(vplus(Vd79,Vd78),vplus(Vd78,Vd79)) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    vplus(vd413,vd411) = vplus(vd411,vd413),
    inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vd413)),bind(Vd79,$fot(vd411))]]) ).

cnf(refute_0_9,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vd411)),
    introduced(tautology,[refl,[$fot(vplus(vmul(vd411,vd413),vplus(vd413,vd411)))]]) ).

cnf(refute_0_10,plain,
    ( vplus(vd413,vd411) != vplus(vd411,vd413)
    | vplus(vmul(vd411,vd413),vplus(vd413,vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vd411))
    | vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
    introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vd411))) ),[1,1],$fot(vplus(vd411,vd413))]]) ).

cnf(refute_0_11,plain,
    ( vplus(vd413,vd411) != vplus(vd411,vd413)
    | vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vd411))) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)),
    inference(resolve,[$cnf( $equal(vplus(vd413,vd411),vplus(vd411,vd413)) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_14,plain,
    vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd413,vd411)),
    inference(subst,[],[refute_0_13:[bind(Vd46,$fot(vmul(vd411,vd413))),bind(Vd47,$fot(vd413)),bind(Vd48,$fot(vd411))]]) ).

cnf(refute_0_15,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_16,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_5,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( vplus(vmul(vd411,vd413),vplus(vd413,vd411)) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
    | vplus(vplus(vmul(vd411,vd413),vd413),vd411) != vplus(vmul(vd411,vd413),vplus(vd413,vd411))
    | vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vplus(vmul(vd411,vd413),vd413),vd411))),bind(Y,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vd411)))),bind(Z,$fot(vplus(vmul(vd411,vd413),vplus(vd411,vd413))))]]) ).

cnf(refute_0_18,plain,
    ( vplus(vmul(vd411,vd413),vplus(vd413,vd411)) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
    | vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vd411),vplus(vmul(vd411,vd413),vplus(vd413,vd411))) )],[refute_0_14,refute_0_17]) ).

cnf(refute_0_19,plain,
    vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vd411)),vplus(vmul(vd411,vd413),vplus(vd411,vd413))) )],[refute_0_12,refute_0_18]) ).

cnf(refute_0_20,plain,
    vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),
    introduced(tautology,[refl,[$fot(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)))]]) ).

cnf(refute_0_21,plain,
    ( vplus(vplus(vmul(vd411,vd413),vd413),vd411) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
    | vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) != vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))
    | vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
    introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))) ),[1,0],$fot(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))]]) ).

cnf(refute_0_22,plain,
    ( vplus(vplus(vmul(vd411,vd413),vd413),vd411) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
    | vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),
    inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vd411),vplus(vmul(vd411,vd413),vplus(vd411,vd413))) )],[refute_0_19,refute_0_22]) ).

cnf(refute_0_24,plain,
    vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_25,plain,
    vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),
    inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vplus(vmul(vd411,vd413),vd413))),bind(Vd43,$fot(vd411))]]) ).

cnf(refute_0_26,plain,
    ( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))
    | vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
    | vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)))),bind(Y,$fot(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)))),bind(Z,$fot(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))))]]) ).

cnf(refute_0_27,plain,
    ( vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
    | vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))) )],[refute_0_23,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
    introduced(tautology,[equality,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[0],$fot(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))))]]) ).

cnf(refute_0_30,plain,
    ( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
    inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))) )],[refute_0_28,refute_0_29]) ).

cnf(refute_0_31,plain,
    vplus(vmul(vsucc(vd411),vd413),vd411) = vplus(vd411,vmul(vsucc(vd411),vd413)),
    inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vmul(vsucc(vd411),vd413))),bind(Vd79,$fot(vd411))]]) ).

cnf(refute_0_32,plain,
    vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),
    introduced(tautology,[refl,[$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)))]]) ).

cnf(refute_0_33,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vd411) != vplus(vd411,vmul(vsucc(vd411),vd413))
    | vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
    | vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) ),[1,0],$fot(vplus(vd411,vmul(vsucc(vd411),vd413)))]]) ).

cnf(refute_0_34,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vd411) != vplus(vd411,vmul(vsucc(vd411),vd413))
    | vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
    inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vd411),vplus(vd411,vmul(vsucc(vd411),vd413))) )],[refute_0_31,refute_0_34]) ).

cnf(refute_0_36,plain,
    vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),
    inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vmul(vsucc(vd411),vd413))),bind(Vd43,$fot(vd411))]]) ).

cnf(refute_0_37,plain,
    vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_38,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411))
    | vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[0],$fot(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)))]]) ).

cnf(refute_0_39,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411))
    | vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
    inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_1,refute_0_38]) ).

cnf(refute_0_40,plain,
    vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
    inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411))) )],[refute_0_37,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))),bind(Y,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))))]]) ).

cnf(refute_0_42,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
    inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))
    | vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))),bind(Y,$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))),bind(Z,$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))))]]) ).

cnf(refute_0_44,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),
    inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_36,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
    | vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))),bind(Y,$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)))),bind(Z,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))))]]) ).

cnf(refute_0_47,plain,
    ( vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_45,refute_0_46]) ).

cnf(refute_0_48,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_35,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[1],$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))))]]) ).

cnf(refute_0_50,plain,
    ( vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_30,refute_0_50]) ).

cnf(refute_0_52,plain,
    vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
    inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_1,refute_0_51]) ).

cnf(refute_0_53,plain,
    vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_54,plain,
    ( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
    | vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))),bind(Y,$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)))),bind(Z,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))))]]) ).

cnf(refute_0_55,plain,
    ( vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_36,refute_0_54]) ).

cnf(refute_0_56,plain,
    vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_35,refute_0_55]) ).

cnf(refute_0_57,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))
    | vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vmul(vsucc(vd411),vsucc(vd413)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(vd411),vsucc(vd413)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) ),[0],$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))]]) ).

cnf(refute_0_58,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))
    | vmul(vsucc(vd411),vsucc(vd413)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    vmul(vsucc(vd411),vsucc(vd413)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
    inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))) )],[refute_0_53,refute_0_58]) ).

cnf(refute_0_60,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(vmul(vsucc(vd411),vsucc(vd413)))),bind(Y,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))))]]) ).

cnf(refute_0_61,plain,
    vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) = vmul(vsucc(vd411),vsucc(vd413)),
    inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    ( vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) ),[1],$fot(vmul(vsucc(vd411),vsucc(vd413)))]]) ).

cnf(refute_0_63,plain,
    ( vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_52,refute_0_63]) ).

cnf(refute_0_65,plain,
    vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),
    inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vmul(vd411,vd413))),bind(Vd43,$fot(vplus(vd411,vd413)))]]) ).

cnf(refute_0_66,plain,
    ( vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
    | vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))))),bind(Y,$fot(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(vd413))))]]) ).

cnf(refute_0_67,plain,
    ( vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_64,refute_0_67]) ).

cnf(refute_0_69,plain,
    vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd413,vd411)),
    introduced(tautology,[refl,[$fot(vsucc(vplus(vd413,vd411)))]]) ).

cnf(refute_0_70,plain,
    ( vplus(vd413,vd411) != vplus(vd411,vd413)
    | vsucc(vplus(vd413,vd411)) != vsucc(vplus(vd413,vd411))
    | vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd411,vd413)) ),
    introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vd413,vd411)),vsucc(vplus(vd413,vd411))) ),[1,0],$fot(vplus(vd411,vd413))]]) ).

cnf(refute_0_71,plain,
    ( vplus(vd413,vd411) != vplus(vd411,vd413)
    | vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd411,vd413)) ),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vd413,vd411)),vsucc(vplus(vd413,vd411))) )],[refute_0_69,refute_0_70]) ).

cnf(refute_0_72,plain,
    vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd411,vd413)),
    inference(resolve,[$cnf( $equal(vplus(vd413,vd411),vplus(vd411,vd413)) )],[refute_0_8,refute_0_71]) ).

cnf(refute_0_73,plain,
    vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd413,vd411)),
    inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vd413)),bind(Vd43,$fot(vd411))]]) ).

cnf(refute_0_74,plain,
    ( vplus(vd413,vsucc(vd411)) != vsucc(vplus(vd413,vd411))
    | vsucc(vplus(vd413,vd411)) != vsucc(vplus(vd411,vd413))
    | vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd411,vd413)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vd413,vsucc(vd411)))),bind(Y,$fot(vsucc(vplus(vd413,vd411)))),bind(Z,$fot(vsucc(vplus(vd411,vd413))))]]) ).

cnf(refute_0_75,plain,
    ( vsucc(vplus(vd413,vd411)) != vsucc(vplus(vd411,vd413))
    | vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd411,vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vd413,vsucc(vd411)),vsucc(vplus(vd413,vd411))) )],[refute_0_73,refute_0_74]) ).

cnf(refute_0_76,plain,
    vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd411,vd413)),
    inference(resolve,[$cnf( $equal(vsucc(vplus(vd413,vd411)),vsucc(vplus(vd411,vd413))) )],[refute_0_72,refute_0_75]) ).

cnf(refute_0_77,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
    introduced(tautology,[refl,[$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))]]) ).

cnf(refute_0_78,plain,
    ( vplus(vd413,vsucc(vd411)) != vsucc(vplus(vd411,vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
    introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[1,1],$fot(vsucc(vplus(vd411,vd413)))]]) ).

cnf(refute_0_79,plain,
    ( vplus(vd413,vsucc(vd411)) != vsucc(vplus(vd411,vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_77,refute_0_78]) ).

cnf(refute_0_80,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),
    inference(resolve,[$cnf( $equal(vplus(vd413,vsucc(vd411)),vsucc(vplus(vd411,vd413))) )],[refute_0_76,refute_0_79]) ).

cnf(refute_0_81,plain,
    ( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))
    | vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))),bind(Y,$fot(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(vd413))))]]) ).

cnf(refute_0_82,plain,
    ( vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))) )],[refute_0_80,refute_0_81]) ).

cnf(refute_0_83,plain,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vmul(vsucc(vd411),vsucc(vd413)),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_68,refute_0_82]) ).

cnf(refute_0_84,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
    introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vmul(vsucc(vd411),vsucc(vd413))) ),[1],$fot(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)))]]) ).

cnf(refute_0_85,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_87,plain,
    vplus(vsucc(vd411),vd413) = vsucc(vplus(vd411,vd413)),
    inference(subst,[],[refute_0_86:[bind(Vd68,$fot(vd411)),bind(Vd69,$fot(vd413))]]) ).

cnf(refute_0_88,plain,
    vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    introduced(tautology,[refl,[$fot(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)))]]) ).

cnf(refute_0_89,plain,
    ( vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))
    | vplus(vsucc(vd411),vd413) != vsucc(vplus(vd411,vd413))
    | vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
    introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) ),[1,1],$fot(vsucc(vplus(vd411,vd413)))]]) ).

cnf(refute_0_90,plain,
    ( vplus(vsucc(vd411),vd413) != vsucc(vplus(vd411,vd413))
    | vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) )],[refute_0_88,refute_0_89]) ).

cnf(refute_0_91,plain,
    vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),
    inference(resolve,[$cnf( $equal(vplus(vsucc(vd411),vd413),vsucc(vplus(vd411,vd413))) )],[refute_0_87,refute_0_90]) ).

cnf(refute_0_92,plain,
    ( vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))
    | vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)))),bind(Y,$fot(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(vd413))))]]) ).

cnf(refute_0_93,plain,
    ( vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_68,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vmul(vsucc(vd411),vsucc(vd413))
    | vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(vd411),vsucc(vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) ),[1],$fot(vmul(vsucc(vd411),vsucc(vd413)))]]) ).

cnf(refute_0_96,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413))
    | vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    ( vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413))
    | vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
    inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) )],[refute_0_96,refute_0_85]) ).

cnf(refute_0_98,plain,
    vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413)),
    inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) )],[refute_0_97,refute_0_0]) ).

cnf(refute_0_99,plain,
    vmul(vsucc(vd411),vsucc(vd413)) = vmul(vsucc(vd411),vsucc(vd413)),
    introduced(tautology,[refl,[$fot(vmul(vsucc(vd411),vsucc(vd413)))]]) ).

cnf(refute_0_100,plain,
    $false,
    inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_99,refute_0_98]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul  5 04:58:27 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37  
% 0.19/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39  
%------------------------------------------------------------------------------