TSTP Solution File: COM018+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COM018+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.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 : Fri Jul 15 01:32:33 EDT 2022

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (  16 unt;   0 def)
%            Number of atoms       :   57 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   52 (  24   ~;  19   |;   7   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   22 (   1 sgn  10   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mTermNF,axiom,
    ! [W0] :
      ( ( aRewritingSystem0(W0)
        & isTerminating0(W0) )
     => ! [W1] :
          ( aElement0(W1)
         => ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ) ).

fof(m__656,hypothesis,
    aRewritingSystem0(xR) ).

fof(m__656_01,hypothesis,
    ( isLocallyConfluent0(xR)
    & isTerminating0(xR) ) ).

fof(m__799,hypothesis,
    ( aElement0(xw)
    & sdtmndtasgtdt0(xu,xR,xw)
    & sdtmndtasgtdt0(xv,xR,xw) ) ).

fof(m__,conjecture,
    ? [W0] : aNormalFormOfIn0(W0,xw,xR) ).

fof(subgoal_0,plain,
    ? [W0] : aNormalFormOfIn0(W0,xw,xR),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ? [W0] : aNormalFormOfIn0(W0,xw,xR),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( aElement0(xw)
    & sdtmndtasgtdt0(xu,xR,xw)
    & sdtmndtasgtdt0(xv,xR,xw) ),
    inference(canonicalize,[],[m__799]) ).

fof(normalize_0_1,plain,
    aElement0(xw),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( isLocallyConfluent0(xR)
    & isTerminating0(xR) ),
    inference(canonicalize,[],[m__656_01]) ).

fof(normalize_0_3,plain,
    isTerminating0(xR),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [W0] :
      ( ~ aRewritingSystem0(W0)
      | ~ isTerminating0(W0)
      | ! [W1] :
          ( ~ aElement0(W1)
          | ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
    inference(canonicalize,[],[mTermNF]) ).

fof(normalize_0_5,plain,
    ! [W0] :
      ( ~ aRewritingSystem0(W0)
      | ~ isTerminating0(W0)
      | ! [W1] :
          ( ~ aElement0(W1)
          | ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [W0,W1] :
      ( ~ aElement0(W1)
      | ~ aRewritingSystem0(W0)
      | ~ isTerminating0(W0)
      | aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W0,W1),W1,W0) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    aRewritingSystem0(xR),
    inference(canonicalize,[],[m__656]) ).

fof(normalize_0_8,plain,
    ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_9,plain,
    ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
    inference(specialize,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
    aElement0(xw),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    isTerminating0(xR),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    ( ~ aElement0(W1)
    | ~ aRewritingSystem0(W0)
    | ~ isTerminating0(W0)
    | aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W0,W1),W1,W0) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ aElement0(X_22)
    | ~ aRewritingSystem0(xR)
    | ~ isTerminating0(xR)
    | aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,X_22),X_22,xR) ),
    inference(subst,[],[refute_0_2:[bind(W0,$fot(xR)),bind(W1,$fot(X_22))]]) ).

cnf(refute_0_4,plain,
    ( ~ aElement0(X_22)
    | ~ aRewritingSystem0(xR)
    | aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,X_22),X_22,xR) ),
    inference(resolve,[$cnf( isTerminating0(xR) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    aRewritingSystem0(xR),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_6,plain,
    ( ~ aElement0(X_22)
    | aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,X_22),X_22,xR) ),
    inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_5,refute_0_4]) ).

cnf(refute_0_7,plain,
    ( ~ aElement0(xw)
    | aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR) ),
    inference(subst,[],[refute_0_6:[bind(X_22,$fot(xw))]]) ).

cnf(refute_0_8,plain,
    aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR),
    inference(resolve,[$cnf( aElement0(xw) )],[refute_0_0,refute_0_7]) ).

cnf(refute_0_9,plain,
    ~ aNormalFormOfIn0(W0,xw,xR),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_10,plain,
    ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR),
    inference(subst,[],[refute_0_9:[bind(W0,$fot(skolemFOFtoCNF_W2_3(xR,xw)))]]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR) )],[refute_0_8,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : COM018+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 18:15:26 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37  
% 0.12/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37  
%------------------------------------------------------------------------------