TSTP Solution File: NUM387+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 : Mon Jul 18 12:26:21 EDT 2022

% Result   : Theorem 0.17s 0.34s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   25 (  16 unt;   0 def)
%            Number of atoms       :   36 (  16 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   30 (  19   ~;  10   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   21 (   0 sgn  12   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ) ).

fof(t10_ordinal1,axiom,
    ! [A] : in(A,succ(A)) ).

fof(t14_ordinal1,conjecture,
    ! [A] : A != succ(A) ).

fof(subgoal_0,plain,
    ! [A] : A != succ(A),
    inference(strip,[],[t14_ordinal1]) ).

fof(negate_0_0,plain,
    ~ ! [A] : A != succ(A),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A] : in(A,succ(A)),
    inference(canonicalize,[],[t10_ordinal1]) ).

fof(normalize_0_1,plain,
    ! [A] : in(A,succ(A)),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [A] : A = succ(A),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_3,plain,
    skolemFOFtoCNF_A_10 = succ(skolemFOFtoCNF_A_10),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | ~ in(B,A) ),
    inference(canonicalize,[],[antisymmetry_r2_hidden]) ).

fof(normalize_0_5,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | ~ in(B,A) ),
    inference(specialize,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    in(A,succ(A)),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    in(skolemFOFtoCNF_A_10,succ(skolemFOFtoCNF_A_10)),
    inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_10))]]) ).

cnf(refute_0_2,plain,
    skolemFOFtoCNF_A_10 = succ(skolemFOFtoCNF_A_10),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_4,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_5,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( skolemFOFtoCNF_A_10 != succ(skolemFOFtoCNF_A_10)
    | succ(skolemFOFtoCNF_A_10) = skolemFOFtoCNF_A_10 ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_A_10)),bind(Y,$fot(succ(skolemFOFtoCNF_A_10)))]]) ).

cnf(refute_0_7,plain,
    succ(skolemFOFtoCNF_A_10) = skolemFOFtoCNF_A_10,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_10,succ(skolemFOFtoCNF_A_10)) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( succ(skolemFOFtoCNF_A_10) != skolemFOFtoCNF_A_10
    | ~ in(skolemFOFtoCNF_A_10,succ(skolemFOFtoCNF_A_10))
    | in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) ),
    introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_A_10,succ(skolemFOFtoCNF_A_10)) ),[1],$fot(skolemFOFtoCNF_A_10)]]) ).

cnf(refute_0_9,plain,
    ( ~ in(skolemFOFtoCNF_A_10,succ(skolemFOFtoCNF_A_10))
    | in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) ),
    inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_A_10),skolemFOFtoCNF_A_10) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_A_10,succ(skolemFOFtoCNF_A_10)) )],[refute_0_1,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ in(A,B)
    | ~ in(B,A) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_12,plain,
    ~ in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10),
    inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_10)),bind(B,$fot(skolemFOFtoCNF_A_10))]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) )],[refute_0_10,refute_0_12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.32  % Computer : n004.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Tue Jul  5 11:50:53 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.17/0.32  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.34  
% 0.17/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.17/0.34  
%------------------------------------------------------------------------------