TSTP Solution File: GRP163-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Sat Jul 16 10:37:07 EDT 2022

% Result   : Unsatisfiable 0.21s 0.47s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   21 (  12 unt;   0 nHn;  17 RR)
%            Number of literals    :   34 (  33 equ;  15 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   12 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity_of_glb,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).

cnf(ax_transb_1,hypothesis,
    greatest_lower_bound(a,b) = a ).

cnf(ax_transb_2,hypothesis,
    greatest_lower_bound(b,c) = b ).

cnf(prove_ax_transb,negated_conjecture,
    greatest_lower_bound(a,c) != a ).

cnf(refute_0_0,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(greatest_lower_bound(a,b),X_30),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_30))]]) ).

cnf(refute_0_1,plain,
    ( greatest_lower_bound(a,b) != a
    | greatest_lower_bound(a,greatest_lower_bound(b,X_30)) != greatest_lower_bound(greatest_lower_bound(a,b),X_30)
    | greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(a,X_30) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_30)),greatest_lower_bound(greatest_lower_bound(a,b),X_30)) ),[1,0],$fot(a)]]) ).

cnf(refute_0_2,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,X_30)) != greatest_lower_bound(greatest_lower_bound(a,b),X_30)
    | greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(a,X_30) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_transb_1,refute_0_1]) ).

cnf(refute_0_3,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(a,X_30),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_30)),greatest_lower_bound(greatest_lower_bound(a,b),X_30)) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c),
    inference(subst,[],[refute_0_3:[bind(X_30,$fot(c))]]) ).

cnf(refute_0_5,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
    | greatest_lower_bound(b,c) != b
    | greatest_lower_bound(a,b) = greatest_lower_bound(a,c) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) ),[0,1],$fot(b)]]) ).

cnf(refute_0_6,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
    | greatest_lower_bound(a,b) = greatest_lower_bound(a,c) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),b) )],[ax_transb_2,refute_0_5]) ).

cnf(refute_0_7,plain,
    greatest_lower_bound(a,b) = greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( greatest_lower_bound(a,b) != a
    | greatest_lower_bound(a,b) != greatest_lower_bound(a,c)
    | a = greatest_lower_bound(a,c) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ),[0],$fot(a)]]) ).

cnf(refute_0_9,plain,
    ( greatest_lower_bound(a,b) != greatest_lower_bound(a,c)
    | a = greatest_lower_bound(a,c) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_transb_1,refute_0_8]) ).

cnf(refute_0_10,plain,
    a = greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) )],[refute_0_7,refute_0_9]) ).

cnf(refute_0_11,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_13,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( a != greatest_lower_bound(a,c)
    | greatest_lower_bound(a,c) = a ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(a)),bind(Y0,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_15,plain,
    a != greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),a) )],[refute_0_14,prove_ax_transb]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,greatest_lower_bound(a,c)) )],[refute_0_10,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.14/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jun 14 10:13:03 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.47  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47  
% 0.21/0.47  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.47  
%------------------------------------------------------------------------------