TSTP Solution File: SEU094+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU094+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 12:38:24 EDT 2022

% Result   : Theorem 80.42s 80.66s
% Output   : CNFRefutation 80.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   64 (  23 unt;   0 def)
%            Number of atoms       :  138 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  125 (  51   ~;  33   |;  22   &)
%                                         (   4 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   60 (   0 sgn  41   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(l22_finset_1,axiom,
    ! [A] :
      ( ( finite(A)
        & ! [B] :
            ( in(B,A)
           => finite(B) ) )
     => finite(union(A)) ) ).

fof(t100_zfmisc_1,axiom,
    ! [A] : subset(A,powerset(union(A))) ).

fof(t13_finset_1,axiom,
    ! [A,B] :
      ( ( subset(A,B)
        & finite(B) )
     => finite(A) ) ).

fof(t24_finset_1,axiom,
    ! [A] :
      ( finite(A)
    <=> finite(powerset(A)) ) ).

fof(t25_finset_1,conjecture,
    ! [A] :
      ( ( finite(A)
        & ! [B] :
            ( in(B,A)
           => finite(B) ) )
    <=> finite(union(A)) ) ).

fof(t92_zfmisc_1,axiom,
    ! [A,B] :
      ( in(A,B)
     => subset(A,union(B)) ) ).

fof(subgoal_0,plain,
    ! [A] :
      ( ( finite(A)
        & ! [B] :
            ( in(B,A)
           => finite(B) ) )
     => finite(union(A)) ),
    inference(strip,[],[t25_finset_1]) ).

fof(subgoal_1,plain,
    ! [A] :
      ( finite(union(A))
     => finite(A) ),
    inference(strip,[],[t25_finset_1]) ).

fof(subgoal_2,plain,
    ! [A] :
      ( ( finite(union(A))
        & finite(A) )
     => ! [B] :
          ( in(B,A)
         => finite(B) ) ),
    inference(strip,[],[t25_finset_1]) ).

fof(negate_0_0,plain,
    ~ ! [A] :
        ( ( finite(A)
          & ! [B] :
              ( in(B,A)
             => finite(B) ) )
       => finite(union(A)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A] :
      ( ~ finite(union(A))
      & finite(A)
      & ! [B] :
          ( ~ in(B,A)
          | finite(B) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [A] :
      ( ~ finite(A)
      | finite(union(A))
      | ? [B] :
          ( ~ finite(B)
          & in(B,A) ) ),
    inference(canonicalize,[],[l22_finset_1]) ).

fof(normalize_0_2,plain,
    ! [A] :
      ( ~ finite(A)
      | finite(union(A))
      | ? [B] :
          ( ~ finite(B)
          & in(B,A) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_3]) ).

fof(negate_1_0,plain,
    ~ ! [A] :
        ( finite(union(A))
       => finite(A) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ? [A] :
      ( ~ finite(A)
      & finite(union(A)) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ( ~ finite(skolemFOFtoCNF_A_21)
    & finite(union(skolemFOFtoCNF_A_21)) ),
    inference(skolemize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    finite(union(skolemFOFtoCNF_A_21)),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [A] :
      ( ~ finite(A)
    <=> ~ finite(powerset(A)) ),
    inference(canonicalize,[],[t24_finset_1]) ).

fof(normalize_1_4,plain,
    ! [A] :
      ( ~ finite(A)
    <=> ~ finite(powerset(A)) ),
    inference(specialize,[],[normalize_1_3]) ).

fof(normalize_1_5,plain,
    ! [A] :
      ( ( ~ finite(A)
        | finite(powerset(A)) )
      & ( ~ finite(powerset(A))
        | finite(A) ) ),
    inference(clausify,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    ! [A] :
      ( ~ finite(A)
      | finite(powerset(A)) ),
    inference(conjunct,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    ! [A] : subset(A,powerset(union(A))),
    inference(canonicalize,[],[t100_zfmisc_1]) ).

fof(normalize_1_8,plain,
    ! [A] : subset(A,powerset(union(A))),
    inference(specialize,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ! [A,B] :
      ( ~ finite(B)
      | ~ subset(A,B)
      | finite(A) ),
    inference(canonicalize,[],[t13_finset_1]) ).

fof(normalize_1_10,plain,
    ! [A,B] :
      ( ~ finite(B)
      | ~ subset(A,B)
      | finite(A) ),
    inference(specialize,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    ~ finite(skolemFOFtoCNF_A_21),
    inference(conjunct,[],[normalize_1_1]) ).

cnf(refute_1_0,plain,
    finite(union(skolemFOFtoCNF_A_21)),
    inference(canonicalize,[],[normalize_1_2]) ).

cnf(refute_1_1,plain,
    ( ~ finite(A)
    | finite(powerset(A)) ),
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_2,plain,
    ( ~ finite(union(skolemFOFtoCNF_A_21))
    | finite(powerset(union(skolemFOFtoCNF_A_21))) ),
    inference(subst,[],[refute_1_1:[bind(A,$fot(union(skolemFOFtoCNF_A_21)))]]) ).

cnf(refute_1_3,plain,
    finite(powerset(union(skolemFOFtoCNF_A_21))),
    inference(resolve,[$cnf( finite(union(skolemFOFtoCNF_A_21)) )],[refute_1_0,refute_1_2]) ).

cnf(refute_1_4,plain,
    subset(A,powerset(union(A))),
    inference(canonicalize,[],[normalize_1_8]) ).

cnf(refute_1_5,plain,
    subset(X_108,powerset(union(X_108))),
    inference(subst,[],[refute_1_4:[bind(A,$fot(X_108))]]) ).

cnf(refute_1_6,plain,
    ( ~ finite(B)
    | ~ subset(A,B)
    | finite(A) ),
    inference(canonicalize,[],[normalize_1_10]) ).

cnf(refute_1_7,plain,
    ( ~ finite(powerset(union(X_108)))
    | ~ subset(X_108,powerset(union(X_108)))
    | finite(X_108) ),
    inference(subst,[],[refute_1_6:[bind(A,$fot(X_108)),bind(B,$fot(powerset(union(X_108))))]]) ).

cnf(refute_1_8,plain,
    ( ~ finite(powerset(union(X_108)))
    | finite(X_108) ),
    inference(resolve,[$cnf( subset(X_108,powerset(union(X_108))) )],[refute_1_5,refute_1_7]) ).

cnf(refute_1_9,plain,
    ( ~ finite(powerset(union(skolemFOFtoCNF_A_21)))
    | finite(skolemFOFtoCNF_A_21) ),
    inference(subst,[],[refute_1_8:[bind(X_108,$fot(skolemFOFtoCNF_A_21))]]) ).

cnf(refute_1_10,plain,
    finite(skolemFOFtoCNF_A_21),
    inference(resolve,[$cnf( finite(powerset(union(skolemFOFtoCNF_A_21))) )],[refute_1_3,refute_1_9]) ).

cnf(refute_1_11,plain,
    ~ finite(skolemFOFtoCNF_A_21),
    inference(canonicalize,[],[normalize_1_11]) ).

cnf(refute_1_12,plain,
    $false,
    inference(resolve,[$cnf( finite(skolemFOFtoCNF_A_21) )],[refute_1_10,refute_1_11]) ).

fof(negate_2_0,plain,
    ~ ! [A] :
        ( ( finite(union(A))
          & finite(A) )
       => ! [B] :
            ( in(B,A)
           => finite(B) ) ),
    inference(negate,[],[subgoal_2]) ).

fof(normalize_2_0,plain,
    ? [A] :
      ( finite(A)
      & finite(union(A))
      & ? [B] :
          ( ~ finite(B)
          & in(B,A) ) ),
    inference(canonicalize,[],[negate_2_0]) ).

fof(normalize_2_1,plain,
    ( finite(skolemFOFtoCNF_A_22)
    & finite(union(skolemFOFtoCNF_A_22))
    & ? [B] :
        ( ~ finite(B)
        & in(B,skolemFOFtoCNF_A_22) ) ),
    inference(skolemize,[],[normalize_2_0]) ).

fof(normalize_2_2,plain,
    ? [B] :
      ( ~ finite(B)
      & in(B,skolemFOFtoCNF_A_22) ),
    inference(conjunct,[],[normalize_2_1]) ).

fof(normalize_2_3,plain,
    ( ~ finite(skolemFOFtoCNF_B_6)
    & in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22) ),
    inference(skolemize,[],[normalize_2_2]) ).

fof(normalize_2_4,plain,
    in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22),
    inference(conjunct,[],[normalize_2_3]) ).

fof(normalize_2_5,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | subset(A,union(B)) ),
    inference(canonicalize,[],[t92_zfmisc_1]) ).

fof(normalize_2_6,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | subset(A,union(B)) ),
    inference(specialize,[],[normalize_2_5]) ).

fof(normalize_2_7,plain,
    ! [A,B] :
      ( ~ finite(B)
      | ~ subset(A,B)
      | finite(A) ),
    inference(canonicalize,[],[t13_finset_1]) ).

fof(normalize_2_8,plain,
    ! [A,B] :
      ( ~ finite(B)
      | ~ subset(A,B)
      | finite(A) ),
    inference(specialize,[],[normalize_2_7]) ).

fof(normalize_2_9,plain,
    finite(union(skolemFOFtoCNF_A_22)),
    inference(conjunct,[],[normalize_2_1]) ).

fof(normalize_2_10,plain,
    ~ finite(skolemFOFtoCNF_B_6),
    inference(conjunct,[],[normalize_2_3]) ).

cnf(refute_2_0,plain,
    in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22),
    inference(canonicalize,[],[normalize_2_4]) ).

cnf(refute_2_1,plain,
    ( ~ in(A,B)
    | subset(A,union(B)) ),
    inference(canonicalize,[],[normalize_2_6]) ).

cnf(refute_2_2,plain,
    ( ~ in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22)
    | subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22)) ),
    inference(subst,[],[refute_2_1:[bind(A,$fot(skolemFOFtoCNF_B_6)),bind(B,$fot(skolemFOFtoCNF_A_22))]]) ).

cnf(refute_2_3,plain,
    subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22)),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22) )],[refute_2_0,refute_2_2]) ).

cnf(refute_2_4,plain,
    ( ~ finite(B)
    | ~ subset(A,B)
    | finite(A) ),
    inference(canonicalize,[],[normalize_2_8]) ).

cnf(refute_2_5,plain,
    ( ~ finite(union(skolemFOFtoCNF_A_22))
    | ~ subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22))
    | finite(skolemFOFtoCNF_B_6) ),
    inference(subst,[],[refute_2_4:[bind(A,$fot(skolemFOFtoCNF_B_6)),bind(B,$fot(union(skolemFOFtoCNF_A_22)))]]) ).

cnf(refute_2_6,plain,
    ( ~ finite(union(skolemFOFtoCNF_A_22))
    | finite(skolemFOFtoCNF_B_6) ),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22)) )],[refute_2_3,refute_2_5]) ).

cnf(refute_2_7,plain,
    finite(union(skolemFOFtoCNF_A_22)),
    inference(canonicalize,[],[normalize_2_9]) ).

cnf(refute_2_8,plain,
    finite(skolemFOFtoCNF_B_6),
    inference(resolve,[$cnf( finite(union(skolemFOFtoCNF_A_22)) )],[refute_2_7,refute_2_6]) ).

cnf(refute_2_9,plain,
    ~ finite(skolemFOFtoCNF_B_6),
    inference(canonicalize,[],[normalize_2_10]) ).

cnf(refute_2_10,plain,
    $false,
    inference(resolve,[$cnf( finite(skolemFOFtoCNF_B_6) )],[refute_2_8,refute_2_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU094+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n020.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 : Sun Jun 19 22:50:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 80.42/80.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.42/80.66  
% 80.42/80.66  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 80.42/80.66  
%------------------------------------------------------------------------------