%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN370+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 : Thu Jul 21 09:01:51 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   16 (   8 unt;   0 def)
%            Number of atoms       :   30 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   23 (   9   ~;   8   |;   3   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   27 (   1 sgn  14   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(x2121,conjecture,
    ? [V] :
    ! [Y] :
    ? [Z] :
      ( ( big_p(a,Y,h(Y))
        | big_p(V,Y,f(Y)) )
     => big_p(V,Y,Z) ) ).

fof(subgoal_0,plain,
    ? [V] :
    ! [Y] :
    ? [Z] :
      ( ( big_p(a,Y,h(Y))
        | big_p(V,Y,f(Y)) )
     => big_p(V,Y,Z) ),
    inference(strip,[],[x2121]) ).

fof(negate_0_0,plain,
    ~ ? [V] :
      ! [Y] :
      ? [Z] :
        ( ( big_p(a,Y,h(Y))
          | big_p(V,Y,f(Y)) )
       => big_p(V,Y,Z) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [V] :
    ? [Y] :
      ( ( big_p(V,Y,f(Y))
        | big_p(a,Y,h(Y)) )
      & ! [Z] : ~ big_p(V,Y,Z) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [V] :
    ? [Y] :
      ( ( big_p(V,Y,f(Y))
        | big_p(a,Y,h(Y)) )
      & ! [Z] : ~ big_p(V,Y,Z) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [V] :
      ( ( big_p(V,skolemFOFtoCNF_Y(V),f(skolemFOFtoCNF_Y(V)))
        | big_p(a,skolemFOFtoCNF_Y(V),h(skolemFOFtoCNF_Y(V))) )
      & ! [Z] : ~ big_p(V,skolemFOFtoCNF_Y(V),Z) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [V] :
      ( big_p(V,skolemFOFtoCNF_Y(V),f(skolemFOFtoCNF_Y(V)))
      | big_p(a,skolemFOFtoCNF_Y(V),h(skolemFOFtoCNF_Y(V))) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [V,Z] : ~ big_p(V,skolemFOFtoCNF_Y(V),Z),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_5,plain,
    ! [V,Z] : ~ big_p(V,skolemFOFtoCNF_Y(V),Z),
    inference(specialize,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    ( big_p(V,skolemFOFtoCNF_Y(V),f(skolemFOFtoCNF_Y(V)))
    | big_p(a,skolemFOFtoCNF_Y(V),h(skolemFOFtoCNF_Y(V))) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ~ big_p(V,skolemFOFtoCNF_Y(V),Z),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ~ big_p(V,skolemFOFtoCNF_Y(V),f(skolemFOFtoCNF_Y(V))),
    inference(subst,[],[refute_0_1:[bind(Z,$fot(f(skolemFOFtoCNF_Y(V))))]]) ).

cnf(refute_0_3,plain,
    big_p(a,skolemFOFtoCNF_Y(V),h(skolemFOFtoCNF_Y(V))),
    inference(resolve,[$cnf( big_p(V,skolemFOFtoCNF_Y(V),f(skolemFOFtoCNF_Y(V))) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    big_p(a,skolemFOFtoCNF_Y(a),h(skolemFOFtoCNF_Y(a))),
    inference(subst,[],[refute_0_3:[bind(V,$fot(a))]]) ).

cnf(refute_0_5,plain,
    ~ big_p(a,skolemFOFtoCNF_Y(a),h(skolemFOFtoCNF_Y(a))),
    inference(subst,[],[refute_0_1:[bind(V,$fot(a)),bind(Z,$fot(h(skolemFOFtoCNF_Y(a))))]]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( big_p(a,skolemFOFtoCNF_Y(a),h(skolemFOFtoCNF_Y(a))) )],[refute_0_4,refute_0_5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN370+1 : TPTP v8.1.0. Released v2.0.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 18:32:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.34  
%------------------------------------------------------------------------------