TSTP Solution File: KLE053+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KLE053+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 : Sun Jul 17 02:14:56 EDT 2022

% Result   : Theorem 0.12s 0.40s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   38 (  27 unt;   0 def)
%            Number of atoms       :   54 (  53 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  21   ~;  16   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  12   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
    ! [A] : multiplication(one,A) = A ).

fof(domain2,axiom,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).

fof(goals,conjecture,
    ! [X0] : domain(domain(X0)) = domain(X0) ).

fof(subgoal_0,plain,
    ! [X0] : domain(domain(X0)) = domain(X0),
    inference(strip,[],[goals]) ).

fof(negate_0_0,plain,
    ~ ! [X0] : domain(domain(X0)) = domain(X0),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X0] : domain(domain(X0)) != domain(X0),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    domain(domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(canonicalize,[],[domain2]) ).

fof(normalize_0_3,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A] : multiplication(one,A) = A,
    inference(canonicalize,[],[multiplicative_left_identity]) ).

fof(normalize_0_5,plain,
    ! [A] : multiplication(one,A) = A,
    inference(specialize,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    domain(domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    domain(multiplication(one,X_31)) = domain(multiplication(one,domain(X_31))),
    inference(subst,[],[refute_0_1:[bind(X0,$fot(one)),bind(X1,$fot(X_31))]]) ).

cnf(refute_0_3,plain,
    multiplication(one,A) = A,
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_4,plain,
    multiplication(one,domain(X_31)) = domain(X_31),
    inference(subst,[],[refute_0_3:[bind(A,$fot(domain(X_31)))]]) ).

cnf(refute_0_5,plain,
    ( domain(multiplication(one,X_31)) != domain(multiplication(one,domain(X_31)))
    | multiplication(one,domain(X_31)) != domain(X_31)
    | domain(multiplication(one,X_31)) = domain(domain(X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,domain(X_31)))) ),[1,0],$fot(domain(X_31))]]) ).

cnf(refute_0_6,plain,
    ( domain(multiplication(one,X_31)) != domain(multiplication(one,domain(X_31)))
    | domain(multiplication(one,X_31)) = domain(domain(X_31)) ),
    inference(resolve,[$cnf( $equal(multiplication(one,domain(X_31)),domain(X_31)) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    domain(multiplication(one,X_31)) = domain(domain(X_31)),
    inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,domain(X_31)))) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    multiplication(one,X_31) = X_31,
    inference(subst,[],[refute_0_3:[bind(A,$fot(X_31))]]) ).

cnf(refute_0_9,plain,
    domain(multiplication(one,X_31)) = domain(multiplication(one,X_31)),
    introduced(tautology,[refl,[$fot(domain(multiplication(one,X_31)))]]) ).

cnf(refute_0_10,plain,
    ( domain(multiplication(one,X_31)) != domain(multiplication(one,X_31))
    | multiplication(one,X_31) != X_31
    | domain(multiplication(one,X_31)) = domain(X_31) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,X_31))) ),[1,0],$fot(X_31)]]) ).

cnf(refute_0_11,plain,
    ( multiplication(one,X_31) != X_31
    | domain(multiplication(one,X_31)) = domain(X_31) ),
    inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,X_31))) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    domain(multiplication(one,X_31)) = domain(X_31),
    inference(resolve,[$cnf( $equal(multiplication(one,X_31),X_31) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( domain(multiplication(one,X_31)) != domain(X_31)
    | domain(multiplication(one,X_31)) != domain(domain(X_31))
    | domain(X_31) = domain(domain(X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_31)),domain(domain(X_31))) ),[0],$fot(domain(X_31))]]) ).

cnf(refute_0_14,plain,
    ( domain(multiplication(one,X_31)) != domain(domain(X_31))
    | domain(X_31) = domain(domain(X_31)) ),
    inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(X_31)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    domain(X_31) = domain(domain(X_31)),
    inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(domain(X_31))) )],[refute_0_7,refute_0_14]) ).

cnf(refute_0_16,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_17,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_18,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( domain(X_31) != domain(domain(X_31))
    | domain(domain(X_31)) = domain(X_31) ),
    inference(subst,[],[refute_0_18:[bind(X,$fot(domain(X_31))),bind(Y,$fot(domain(domain(X_31))))]]) ).

cnf(refute_0_20,plain,
    domain(domain(X_31)) = domain(X_31),
    inference(resolve,[$cnf( $equal(domain(X_31),domain(domain(X_31))) )],[refute_0_15,refute_0_19]) ).

cnf(refute_0_21,plain,
    domain(domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0),
    inference(subst,[],[refute_0_20:[bind(X_31,$fot(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_22,plain,
    ( domain(domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
    | domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
    | domain(domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(domain(domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) ),[0],$fot(domain(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_23,plain,
    ( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
    | domain(domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
    inference(resolve,[$cnf( $equal(domain(domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0),
    inference(resolve,[$cnf( $equal(domain(domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_23,refute_0_0]) ).

cnf(refute_0_25,plain,
    domain(skolemFOFtoCNF_X0) = domain(skolemFOFtoCNF_X0),
    introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_26,plain,
    $false,
    inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) )],[refute_0_25,refute_0_24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : KLE053+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n011.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 : Thu Jun 16 12:05:51 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40  
% 0.12/0.40  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.41  
%------------------------------------------------------------------------------