TSTP Solution File: KLE076+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KLE076+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 02:15:04 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  28 unt;   0 def)
%            Number of atoms       :   61 (  60 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   45 (  25   ~;  20   |;   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   :   31 (   1 sgn  12   !;   1   ?)

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

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

fof(domain4,axiom,
    domain(zero) = zero ).

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

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

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

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

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

fof(normalize_0_2,plain,
    domain(zero) = zero,
    inference(canonicalize,[],[domain4]) ).

fof(normalize_0_3,plain,
    ! [A] : multiplication(A,zero) = zero,
    inference(canonicalize,[],[right_annihilation]) ).

fof(normalize_0_4,plain,
    ! [A] : multiplication(A,zero) = zero,
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(canonicalize,[],[domain2]) ).

fof(normalize_0_6,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(specialize,[],[normalize_0_5]) ).

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

cnf(refute_0_1,plain,
    domain(zero) = zero,
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    multiplication(A,zero) = zero,
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    multiplication(skolemFOFtoCNF_X0,zero) = zero,
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_4,plain,
    domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(multiplication(skolemFOFtoCNF_X0,zero)),
    introduced(tautology,[refl,[$fot(domain(multiplication(skolemFOFtoCNF_X0,zero)))]]) ).

cnf(refute_0_5,plain,
    ( domain(multiplication(skolemFOFtoCNF_X0,zero)) != domain(multiplication(skolemFOFtoCNF_X0,zero))
    | multiplication(skolemFOFtoCNF_X0,zero) != zero
    | domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(zero) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),domain(multiplication(skolemFOFtoCNF_X0,zero))) ),[1,0],$fot(zero)]]) ).

cnf(refute_0_6,plain,
    ( multiplication(skolemFOFtoCNF_X0,zero) != zero
    | domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(zero) ),
    inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),domain(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    domain(multiplication(skolemFOFtoCNF_X0,zero)) = domain(zero),
    inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,zero),zero) )],[refute_0_3,refute_0_6]) ).

cnf(refute_0_8,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_9,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_10,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_12,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( domain(multiplication(skolemFOFtoCNF_X0,zero)) != domain(zero)
    | domain(zero) != zero
    | domain(multiplication(skolemFOFtoCNF_X0,zero)) = zero ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(domain(multiplication(skolemFOFtoCNF_X0,zero)))),bind(Y,$fot(domain(zero))),bind(Z,$fot(zero))]]) ).

cnf(refute_0_14,plain,
    ( domain(zero) != zero
    | domain(multiplication(skolemFOFtoCNF_X0,zero)) = zero ),
    inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),domain(zero)) )],[refute_0_7,refute_0_13]) ).

cnf(refute_0_15,plain,
    domain(multiplication(skolemFOFtoCNF_X0,zero)) = zero,
    inference(resolve,[$cnf( $equal(domain(zero),zero) )],[refute_0_1,refute_0_14]) ).

cnf(refute_0_16,plain,
    domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_17,plain,
    ( domain(multiplication(X0,X1)) != domain(multiplication(X0,domain(X1)))
    | domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(domain(multiplication(X0,X1)))),bind(Y,$fot(domain(multiplication(X0,domain(X1)))))]]) ).

cnf(refute_0_18,plain,
    domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
    inference(resolve,[$cnf( $equal(domain(multiplication(X0,X1)),domain(multiplication(X0,domain(X1)))) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = domain(multiplication(skolemFOFtoCNF_X0,zero)),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(zero))]]) ).

cnf(refute_0_20,plain,
    ( domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) != domain(multiplication(skolemFOFtoCNF_X0,zero))
    | domain(multiplication(skolemFOFtoCNF_X0,zero)) != zero
    | domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))))),bind(Y,$fot(domain(multiplication(skolemFOFtoCNF_X0,zero)))),bind(Z,$fot(zero))]]) ).

cnf(refute_0_21,plain,
    ( domain(multiplication(skolemFOFtoCNF_X0,zero)) != zero
    | domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
    inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),domain(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero,
    inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,zero)),zero) )],[refute_0_15,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) != zero
    | zero != zero
    | domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_24,plain,
    ( zero != zero
    | domain(multiplication(skolemFOFtoCNF_X0,domain(zero))) = zero ),
    inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),zero) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    zero != zero,
    inference(resolve,[$cnf( $equal(domain(multiplication(skolemFOFtoCNF_X0,domain(zero))),zero) )],[refute_0_24,refute_0_0]) ).

cnf(refute_0_26,plain,
    zero = zero,
    introduced(tautology,[refl,[$fot(zero)]]) ).

cnf(refute_0_27,plain,
    $false,
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_26,refute_0_25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : KLE076+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n011.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 : Thu Jun 16 10:45:06 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37  
% 0.13/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38  
%------------------------------------------------------------------------------