TSTP Solution File: SYN347+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN347+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 09:01:36 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   41 (   5 unt;   0 def)
%            Number of atoms       :  122 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  137 (  56   ~;  49   |;   8   &)
%                                         (  24 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   65 (   0 sgn  37   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(church_46_17_3,conjecture,
    ! [Z1,Z2] :
    ? [X1,X2] :
    ! [Y] :
      ( ( ( big_f(X1,Y)
        <=> big_f(X2,Y) )
      <=> big_f(Z1,Z2) )
      | ( big_f(Z1,Y)
      <=> big_f(Z2,Y) ) ) ).

fof(subgoal_0,plain,
    ! [Z1,Z2] :
    ? [X1,X2] :
    ! [Y] :
      ( ( ( big_f(X1,Y)
        <=> big_f(X2,Y) )
      <=> big_f(Z1,Z2) )
      | ( big_f(Z1,Y)
      <=> big_f(Z2,Y) ) ),
    inference(strip,[],[church_46_17_3]) ).

fof(negate_0_0,plain,
    ~ ! [Z1,Z2] :
      ? [X1,X2] :
      ! [Y] :
        ( ( ( big_f(X1,Y)
          <=> big_f(X2,Y) )
        <=> big_f(Z1,Z2) )
        | ( big_f(Z1,Y)
        <=> big_f(Z2,Y) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [Z1,Z2] :
    ! [X1,X2] :
    ? [Y] :
      ( ( ~ big_f(Z1,Y)
      <=> big_f(Z2,Y) )
      & ( ~ big_f(X1,Y)
      <=> ( ~ big_f(X2,Y)
        <=> ~ big_f(Z1,Z2) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [X1,X2] :
    ? [Y] :
      ( ( ~ big_f(skolemFOFtoCNF_Z1,Y)
      <=> big_f(skolemFOFtoCNF_Z2,Y) )
      & ( ~ big_f(X1,Y)
      <=> ( ~ big_f(X2,Y)
        <=> ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X1,X2] :
    ? [Y] :
      ( ( ~ big_f(skolemFOFtoCNF_Z1,Y)
      <=> big_f(skolemFOFtoCNF_Z2,Y) )
      & ( ~ big_f(X1,Y)
      <=> ( ~ big_f(X2,Y)
        <=> ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X1,X2] :
      ( ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
      <=> big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) )
      & ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
      <=> ( ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
        <=> ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ) ) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X1,X2] :
      ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
    <=> big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X1,X2] :
      ( ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
        | ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) )
      & ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
        | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X1,X2] :
      ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
      | ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X1,X2] :
      ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
    <=> ( ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
      <=> ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_8,plain,
    ! [X1,X2] :
      ( ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
        | ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
        | ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) )
      & ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
        | big_f(X2,skolemFOFtoCNF_Y(X1,X2))
        | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) )
      & ( ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
        | big_f(X1,skolemFOFtoCNF_Y(X1,X2))
        | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) )
      & ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
        | big_f(X1,skolemFOFtoCNF_Y(X1,X2))
        | big_f(X2,skolemFOFtoCNF_Y(X1,X2)) ) ),
    inference(clausify,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X1,X2] :
      ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
      | big_f(X1,skolemFOFtoCNF_Y(X1,X2))
      | big_f(X2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X1,X2] :
      ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
      | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_11,plain,
    ! [X1,X2] :
      ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
      | big_f(X2,skolemFOFtoCNF_Y(X1,X2))
      | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_12,plain,
    ! [X1,X2] :
      ( ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
      | big_f(X1,skolemFOFtoCNF_Y(X1,X2))
      | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_13,plain,
    ! [X1,X2] :
      ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
      | ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
      | ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(conjunct,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
    | ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_1,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2))
    | ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) ),
    inference(subst,[],[refute_0_0:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(skolemFOFtoCNF_Z2))]]) ).

cnf(refute_0_2,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
    | big_f(X1,skolemFOFtoCNF_Y(X1,X2))
    | big_f(X2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_3,plain,
    ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(X1,X2))
    | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_4,plain,
    ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6))
    | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6)) ),
    inference(subst,[],[refute_0_3:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(X_6))]]) ).

cnf(refute_0_5,plain,
    ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
    | big_f(X2,skolemFOFtoCNF_Y(X1,X2))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_6,plain,
    ( ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6))
    | big_f(X_6,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(subst,[],[refute_0_5:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(X_6))]]) ).

cnf(refute_0_7,plain,
    ( big_f(X_6,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,X_6)) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(subst,[],[refute_0_7:[bind(X_6,$fot(skolemFOFtoCNF_Z1))]]) ).

cnf(refute_0_9,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1))
    | ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1)) ),
    inference(subst,[],[refute_0_0:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(skolemFOFtoCNF_Z1))]]) ).

cnf(refute_0_10,plain,
    ( ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
    | big_f(X1,skolemFOFtoCNF_Y(X1,X2))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_11,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
    | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1)) ),
    inference(subst,[],[refute_0_10:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(skolemFOFtoCNF_Z1))]]) ).

cnf(refute_0_12,plain,
    ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
    | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1)) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1)) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1))
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1)) )],[refute_0_12,refute_0_9]) ).

cnf(refute_0_14,plain,
    big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z1)) )],[refute_0_8,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( big_f(X1,skolemFOFtoCNF_Y(X1,X2))
    | big_f(X2,skolemFOFtoCNF_Y(X1,X2)) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) )],[refute_0_14,refute_0_2]) ).

cnf(refute_0_16,plain,
    big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)),
    inference(subst,[],[refute_0_15:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(skolemFOFtoCNF_Z2))]]) ).

cnf(refute_0_17,plain,
    ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) )],[refute_0_16,refute_0_1]) ).

cnf(refute_0_18,plain,
    ( ~ big_f(X1,skolemFOFtoCNF_Y(X1,X2))
    | ~ big_f(X2,skolemFOFtoCNF_Y(X1,X2))
    | ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_19,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
    | ~ big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) ),
    inference(subst,[],[refute_0_18:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(skolemFOFtoCNF_Z2))]]) ).

cnf(refute_0_20,plain,
    ( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2))
    | big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) ),
    inference(subst,[],[refute_0_3:[bind(X1,$fot(skolemFOFtoCNF_Z2)),bind(X2,$fot(skolemFOFtoCNF_Z2))]]) ).

cnf(refute_0_21,plain,
    ( ~ big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2)
    | big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) )],[refute_0_20,refute_0_19]) ).

cnf(refute_0_22,plain,
    big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) )],[refute_0_14,refute_0_21]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z2)) )],[refute_0_22,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN347+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n010.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 20:42:00 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% 0.12/0.34  
%------------------------------------------------------------------------------