%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN336+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 09:01:27 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   14 (   7 unt;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   36 (   8   ~;   0   |;  16   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   32 (   4 sgn  17   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_15_1,conjecture,
    ! [X] :
    ? [Y1,Y2] :
    ! [Z] :
      ( big_f(X,Z)
     => ( big_f(Y1,Z)
       => ( big_f(Y2,Z)
         => ( big_f(Y1,X)
           => big_f(Z,Y2) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [X] :
    ? [Y1,Y2] :
    ! [Z] :
      ( big_f(X,Z)
     => ( big_f(Y1,Z)
       => ( big_f(Y2,Z)
         => ( big_f(Y1,X)
           => big_f(Z,Y2) ) ) ) ),
    inference(strip,[],[church_46_15_1]) ).

fof(negate_0_0,plain,
    ~ ! [X] :
      ? [Y1,Y2] :
      ! [Z] :
        ( big_f(X,Z)
       => ( big_f(Y1,Z)
         => ( big_f(Y2,Z)
           => ( big_f(Y1,X)
             => big_f(Z,Y2) ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X] :
    ! [Y1,Y2] :
    ? [Z] :
      ( ~ big_f(Z,Y2)
      & big_f(X,Z)
      & big_f(Y1,X)
      & big_f(Y1,Z)
      & big_f(Y2,Z) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [Y1,Y2] :
    ? [Z] :
      ( ~ big_f(Z,Y2)
      & big_f(Y1,Z)
      & big_f(Y1,skolemFOFtoCNF_X)
      & big_f(Y2,Z)
      & big_f(skolemFOFtoCNF_X,Z) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Y1,Y2] :
    ? [Z] :
      ( ~ big_f(Z,Y2)
      & big_f(Y1,Z)
      & big_f(Y1,skolemFOFtoCNF_X)
      & big_f(Y2,Z)
      & big_f(skolemFOFtoCNF_X,Z) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Y1,Y2] :
      ( ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),Y2)
      & big_f(Y1,skolemFOFtoCNF_X)
      & big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
      & big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
      & big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Y1] : big_f(Y1,skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Y1,Y2] : ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),Y2),
    inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
    big_f(Y1,skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    big_f(skolemFOFtoCNF_Z(X_3,skolemFOFtoCNF_X),skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_0:[bind(Y1,$fot(skolemFOFtoCNF_Z(X_3,skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_2,plain,
    ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),Y2),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ~ big_f(skolemFOFtoCNF_Z(X_3,skolemFOFtoCNF_X),skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_2:[bind(Y1,$fot(X_3)),bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X_3,skolemFOFtoCNF_X),skolemFOFtoCNF_X) )],[refute_0_1,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN336+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n007.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 : Mon Jul 11 22:44:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------