TSTP Solution File: GRP146-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP146-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.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 10:37:02 EDT 2022

% Result   : Unsatisfiable 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   27 (  14 unt;   0 nHn;  24 RR)
%            Number of literals    :   47 (  46 equ;  22 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   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity_of_lub,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).

cnf(ax_lub1a_1,hypothesis,
    least_upper_bound(a,c) = c ).

cnf(ax_lub1a_2,hypothesis,
    least_upper_bound(b,c) = c ).

cnf(prove_ax_lub1a,negated_conjecture,
    least_upper_bound(least_upper_bound(a,b),c) != c ).

cnf(refute_0_0,plain,
    least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,least_upper_bound(b,c)),
    introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(b,c)))]]) ).

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

cnf(refute_0_2,plain,
    ( least_upper_bound(b,c) != c
    | least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,least_upper_bound(b,c))) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),c) )],[ax_lub1a_2,refute_0_2]) ).

cnf(refute_0_4,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_8,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( least_upper_bound(a,c) != c
    | least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(b,c)) = c ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(b,c)))),bind(Y0,$fot(least_upper_bound(a,c))),bind(Z0,$fot(c))]]) ).

cnf(refute_0_10,plain,
    ( least_upper_bound(a,c) != c
    | least_upper_bound(a,least_upper_bound(b,c)) = c ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,c)) )],[refute_0_3,refute_0_9]) ).

cnf(refute_0_11,plain,
    least_upper_bound(a,least_upper_bound(b,c)) = c,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,c),c) )],[ax_lub1a_1,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
    | least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).

cnf(refute_0_13,plain,
    least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_12]) ).

cnf(refute_0_14,plain,
    least_upper_bound(least_upper_bound(a,b),c) = least_upper_bound(a,least_upper_bound(b,c)),
    inference(subst,[],[refute_0_13:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).

cnf(refute_0_15,plain,
    ( least_upper_bound(a,least_upper_bound(b,c)) != c
    | least_upper_bound(least_upper_bound(a,b),c) != least_upper_bound(a,least_upper_bound(b,c))
    | least_upper_bound(least_upper_bound(a,b),c) = c ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(least_upper_bound(least_upper_bound(a,b),c))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(b,c)))),bind(Z0,$fot(c))]]) ).

cnf(refute_0_16,plain,
    ( least_upper_bound(a,least_upper_bound(b,c)) != c
    | least_upper_bound(least_upper_bound(a,b),c) = c ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,b),c),least_upper_bound(a,least_upper_bound(b,c))) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    least_upper_bound(least_upper_bound(a,b),c) = c,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),c) )],[refute_0_11,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( c != c
    | least_upper_bound(least_upper_bound(a,b),c) != c
    | least_upper_bound(least_upper_bound(a,b),c) = c ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(a,b),c),c) ),[0,1],$fot(c)]]) ).

cnf(refute_0_19,plain,
    ( c != c
    | least_upper_bound(least_upper_bound(a,b),c) = c ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,b),c),c) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    c != c,
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,b),c),c) )],[refute_0_19,prove_ax_lub1a]) ).

cnf(refute_0_21,plain,
    c = c,
    introduced(tautology,[refl,[$fot(c)]]) ).

cnf(refute_0_22,plain,
    $false,
    inference(resolve,[$cnf( $equal(c,c) )],[refute_0_21,refute_0_20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP146-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n006.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 : Mon Jun 13 20:49:41 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37  % SZS status Unsatisfiable 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
% 0.13/0.37  
%------------------------------------------------------------------------------