TSTP Solution File: NUM423+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 12:26:33 EDT 2022

% Result   : Theorem 2.92s 3.08s
% Output   : CNFRefutation 2.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (  12 unt;   0 def)
%            Number of atoms       :   94 (  47 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   96 (  44   ~;  29   |;  19   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn  13   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mIntZero,axiom,
    aInteger0(sz00) ).

fof(mAddNeg,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).

fof(mMulZero,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( sdtasdt0(W0,sz00) = sz00
        & sz00 = sdtasdt0(sz00,W0) ) ) ).

fof(m__671,hypothesis,
    ( aInteger0(xa)
    & aInteger0(xq)
    & xq != sz00 ) ).

fof(m__,conjecture,
    ( ? [W0] :
        ( aInteger0(W0)
        & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) )
    | aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
    | sdteqdtlpzmzozddtrp0(xa,xa,xq) ) ).

fof(subgoal_0,plain,
    ( ( ~ ? [W0] :
            ( aInteger0(W0)
            & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) )
      & ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
   => sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ( ( ~ ? [W0] :
              ( aInteger0(W0)
              & sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) )
        & ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
     => sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
    & ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
    & ! [W0] :
        ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
        | ~ aInteger0(W0) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [W0] :
      ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
      | ~ aInteger0(W0) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [W0] :
      ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
      | ~ aInteger0(W0) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( xq != sz00
    & aInteger0(xa)
    & aInteger0(xq) ),
    inference(canonicalize,[],[m__671]) ).

fof(normalize_0_4,plain,
    aInteger0(xa),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    inference(canonicalize,[],[mAddNeg]) ).

fof(normalize_0_6,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [W0] :
      ( ( ~ aInteger0(W0)
        | sdtpldt0(W0,smndt0(W0)) = sz00 )
      & ( ~ aInteger0(W0)
        | sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | sdtpldt0(W0,smndt0(W0)) = sz00 ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    aInteger0(xq),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_10,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtasdt0(W0,sz00) = sz00
        & sz00 = sdtasdt0(sz00,W0) ) ),
    inference(canonicalize,[],[mMulZero]) ).

fof(normalize_0_11,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtasdt0(W0,sz00) = sz00
        & sz00 = sdtasdt0(sz00,W0) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [W0] :
      ( ( ~ aInteger0(W0)
        | sdtasdt0(W0,sz00) = sz00 )
      & ( ~ aInteger0(W0)
        | sz00 = sdtasdt0(sz00,W0) ) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | sdtasdt0(W0,sz00) = sz00 ),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    aInteger0(sz00),
    inference(canonicalize,[],[mIntZero]) ).

cnf(refute_0_0,plain,
    ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
    | ~ aInteger0(W0) ),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    aInteger0(xa),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ aInteger0(W0)
    | sdtpldt0(W0,smndt0(W0)) = sz00 ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_3,plain,
    ( ~ aInteger0(xa)
    | sdtpldt0(xa,smndt0(xa)) = sz00 ),
    inference(subst,[],[refute_0_2:[bind(W0,$fot(xa))]]) ).

cnf(refute_0_4,plain,
    sdtpldt0(xa,smndt0(xa)) = sz00,
    inference(resolve,[$cnf( aInteger0(xa) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( sdtasdt0(xq,W0) != sz00
    | sdtpldt0(xa,smndt0(xa)) != sz00
    | sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xq,W0),sdtpldt0(xa,smndt0(xa))) ),[1],$fot(sz00)]]) ).

cnf(refute_0_6,plain,
    ( sdtasdt0(xq,W0) != sz00
    | sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ),
    inference(resolve,[$cnf( $equal(sdtpldt0(xa,smndt0(xa)),sz00) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( sdtasdt0(xq,W0) != sz00
    | ~ aInteger0(W0) ),
    inference(resolve,[$cnf( $equal(sdtasdt0(xq,W0),sdtpldt0(xa,smndt0(xa))) )],[refute_0_6,refute_0_0]) ).

cnf(refute_0_8,plain,
    ( sdtasdt0(xq,sz00) != sz00
    | ~ aInteger0(sz00) ),
    inference(subst,[],[refute_0_7:[bind(W0,$fot(sz00))]]) ).

cnf(refute_0_9,plain,
    aInteger0(xq),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_10,plain,
    ( ~ aInteger0(W0)
    | sdtasdt0(W0,sz00) = sz00 ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_11,plain,
    ( ~ aInteger0(xq)
    | sdtasdt0(xq,sz00) = sz00 ),
    inference(subst,[],[refute_0_10:[bind(W0,$fot(xq))]]) ).

cnf(refute_0_12,plain,
    sdtasdt0(xq,sz00) = sz00,
    inference(resolve,[$cnf( aInteger0(xq) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( sdtasdt0(xq,sz00) != sz00
    | sz00 != sz00
    | sdtasdt0(xq,sz00) = sz00 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xq,sz00),sz00) ),[0],$fot(sz00)]]) ).

cnf(refute_0_14,plain,
    ( sz00 != sz00
    | sdtasdt0(xq,sz00) = sz00 ),
    inference(resolve,[$cnf( $equal(sdtasdt0(xq,sz00),sz00) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( sz00 != sz00
    | ~ aInteger0(sz00) ),
    inference(resolve,[$cnf( $equal(sdtasdt0(xq,sz00),sz00) )],[refute_0_14,refute_0_8]) ).

cnf(refute_0_16,plain,
    sz00 = sz00,
    introduced(tautology,[refl,[$fot(sz00)]]) ).

cnf(refute_0_17,plain,
    ~ aInteger0(sz00),
    inference(resolve,[$cnf( $equal(sz00,sz00) )],[refute_0_16,refute_0_15]) ).

cnf(refute_0_18,plain,
    aInteger0(sz00),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( aInteger0(sz00) )],[refute_0_18,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jul  5 18:46:33 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.92/3.08  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/3.08  
% 2.92/3.08  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.92/3.08  
%------------------------------------------------------------------------------