TSTP Solution File: SEU089+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 12:38:23 EDT 2022

% Result   : Theorem 19.46s 19.65s
% Output   : CNFRefutation 19.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (  19 unt;   0 def)
%            Number of atoms       :   80 (  15 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   66 (  26   ~;  21   |;  14   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   49 (   0 sgn  26   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d3_zfmisc_1,axiom,
    ! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C) ).

fof(fc14_finset_1,axiom,
    ! [A,B] :
      ( ( finite(A)
        & finite(B) )
     => finite(cartesian_product2(A,B)) ) ).

fof(t19_finset_1,axiom,
    ! [A,B] :
      ( ( finite(A)
        & finite(B) )
     => finite(cartesian_product2(A,B)) ) ).

fof(t20_finset_1,conjecture,
    ! [A,B,C] :
      ( ( finite(A)
        & finite(B)
        & finite(C) )
     => finite(cartesian_product3(A,B,C)) ) ).

fof(subgoal_0,plain,
    ! [A,B,C] :
      ( ( finite(A)
        & finite(B)
        & finite(C) )
     => finite(cartesian_product3(A,B,C)) ),
    inference(strip,[],[t20_finset_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C] :
        ( ( finite(A)
          & finite(B)
          & finite(C) )
       => finite(cartesian_product3(A,B,C)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B,C] :
      ( ~ finite(cartesian_product3(A,B,C))
      & finite(A)
      & finite(B)
      & finite(C) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C))
    & finite(skolemFOFtoCNF_A_21)
    & finite(skolemFOFtoCNF_B_5)
    & finite(skolemFOFtoCNF_C) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    finite(skolemFOFtoCNF_C),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( ~ finite(A)
      | ~ finite(B)
      | finite(cartesian_product2(A,B)) ),
    inference(canonicalize,[],[t19_finset_1]) ).

fof(normalize_0_4,plain,
    ! [A,B] :
      ( ~ finite(A)
      | ~ finite(B)
      | finite(cartesian_product2(A,B)) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    finite(skolemFOFtoCNF_B_5),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_6,plain,
    finite(skolemFOFtoCNF_A_21),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_7,plain,
    ! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
    inference(canonicalize,[],[d3_zfmisc_1]) ).

fof(normalize_0_8,plain,
    ! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ~ finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)),
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    finite(skolemFOFtoCNF_C),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ finite(A)
    | ~ finite(B)
    | finite(cartesian_product2(A,B)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ finite(X_111)
    | ~ finite(skolemFOFtoCNF_C)
    | finite(cartesian_product2(X_111,skolemFOFtoCNF_C)) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(X_111)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_3,plain,
    ( ~ finite(X_111)
    | finite(cartesian_product2(X_111,skolemFOFtoCNF_C)) ),
    inference(resolve,[$cnf( finite(skolemFOFtoCNF_C) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5))
    | finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)) ),
    inference(subst,[],[refute_0_3:[bind(X_111,$fot(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)))]]) ).

cnf(refute_0_5,plain,
    finite(skolemFOFtoCNF_B_5),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_6,plain,
    finite(skolemFOFtoCNF_A_21),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_7,plain,
    ( ~ finite(X_112)
    | ~ finite(skolemFOFtoCNF_A_21)
    | finite(cartesian_product2(skolemFOFtoCNF_A_21,X_112)) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_21)),bind(B,$fot(X_112))]]) ).

cnf(refute_0_8,plain,
    ( ~ finite(X_112)
    | finite(cartesian_product2(skolemFOFtoCNF_A_21,X_112)) ),
    inference(resolve,[$cnf( finite(skolemFOFtoCNF_A_21) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ finite(skolemFOFtoCNF_B_5)
    | finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)) ),
    inference(subst,[],[refute_0_8:[bind(X_112,$fot(skolemFOFtoCNF_B_5))]]) ).

cnf(refute_0_10,plain,
    finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)),
    inference(resolve,[$cnf( finite(skolemFOFtoCNF_B_5) )],[refute_0_5,refute_0_9]) ).

cnf(refute_0_11,plain,
    finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)),
    inference(resolve,[$cnf( finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)) )],[refute_0_10,refute_0_4]) ).

cnf(refute_0_12,plain,
    cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_13,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_14,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_15,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( cartesian_product3(A,B,C) != cartesian_product2(cartesian_product2(A,B),C)
    | cartesian_product2(cartesian_product2(A,B),C) = cartesian_product3(A,B,C) ),
    inference(subst,[],[refute_0_15:[bind(X,$fot(cartesian_product3(A,B,C))),bind(Y,$fot(cartesian_product2(cartesian_product2(A,B),C)))]]) ).

cnf(refute_0_17,plain,
    cartesian_product2(cartesian_product2(A,B),C) = cartesian_product3(A,B,C),
    inference(resolve,[$cnf( $equal(cartesian_product3(A,B,C),cartesian_product2(cartesian_product2(A,B),C)) )],[refute_0_12,refute_0_16]) ).

cnf(refute_0_18,plain,
    cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C) = cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C),
    inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_21)),bind(B,$fot(skolemFOFtoCNF_B_5)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_19,plain,
    ( cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C) != cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)
    | ~ finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C))
    | finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) ),
    introduced(tautology,[equality,[$cnf( finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)) ),[0],$fot(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C))]]) ).

cnf(refute_0_20,plain,
    ( ~ finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C))
    | finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C),cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)),
    inference(resolve,[$cnf( finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)) )],[refute_0_11,refute_0_20]) ).

cnf(refute_0_22,plain,
    ~ finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) )],[refute_0_21,refute_0_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 04:18:47 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.46/19.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.46/19.65  
% 19.46/19.65  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.46/19.66  
%------------------------------------------------------------------------------