%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL506+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 : Sun Jul 17 12:52:48 EDT 2022

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   22 (  12 unt;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   29 (  15   ~;   8   |;   2   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   3 prp; 0-1 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   2 sgn  10   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(and_1,axiom,
    ( and_1
  <=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ) ).

fof(kn2,axiom,
    ( kn2
  <=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).

fof(rosser_kn2,axiom,
    kn2 ).

fof(hilbert_and_1,conjecture,
    and_1 ).

fof(subgoal_0,plain,
    and_1,
    inference(strip,[],[hilbert_and_1]) ).

fof(negate_0_0,plain,
    ~ and_1,
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ and_1
  <=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) ),
    inference(canonicalize,[],[and_1]) ).

fof(normalize_0_1,plain,
    ! [X,Y] :
      ( ( ~ and_1
        | is_a_theorem(implies(and(X,Y),X)) )
      & ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6))
        | and_1 ) ),
    inference(clausify,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6))
    | and_1 ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ~ kn2
  <=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
    inference(canonicalize,[],[kn2]) ).

fof(normalize_0_4,plain,
    ! [P,Q] :
      ( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
        | kn2 )
      & ( ~ kn2
        | is_a_theorem(implies(and(P,Q),P)) ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [P,Q] :
      ( ~ kn2
      | is_a_theorem(implies(and(P,Q),P)) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    kn2,
    inference(canonicalize,[],[rosser_kn2]) ).

fof(normalize_0_7,plain,
    ~ and_1,
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6))
    | and_1 ),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ kn2
    | is_a_theorem(implies(and(P,Q),P)) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    kn2,
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    is_a_theorem(implies(and(P,Q),P)),
    inference(resolve,[$cnf( kn2 )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6)),
    inference(subst,[],[refute_0_3:[bind(P,$fot(skolemFOFtoCNF_X_6)),bind(Q,$fot(skolemFOFtoCNF_Y_6))]]) ).

cnf(refute_0_5,plain,
    and_1,
    inference(resolve,[$cnf( is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6)) )],[refute_0_4,refute_0_0]) ).

cnf(refute_0_6,plain,
    ~ and_1,
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( and_1 )],[refute_0_5,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL506+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n020.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 : Mon Jul  4 21:40:29 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39  
% 0.13/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39  
%------------------------------------------------------------------------------