TSTP Solution File: GRP143-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP143-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 10:37:01 EDT 2022

% Result   : Unsatisfiable 0.12s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   36 (  20 unt;   0 nHn;  27 RR)
%            Number of literals    :   60 (  59 equ;  27 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    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn)

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

cnf(associativity_of_glb,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).

cnf(idempotence_of_gld,axiom,
    greatest_lower_bound(X,X) = X ).

cnf(prove_ax_glb2b,negated_conjecture,
    greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
    | greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).

cnf(refute_0_4,plain,
    greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_3]) ).

cnf(refute_0_5,plain,
    greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
    inference(subst,[],[refute_0_4:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_6,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,a)) = greatest_lower_bound(a,greatest_lower_bound(b,a)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(b,a)))]]) ).

cnf(refute_0_7,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,a)) != greatest_lower_bound(a,greatest_lower_bound(b,a))
    | greatest_lower_bound(b,a) != greatest_lower_bound(a,b)
    | greatest_lower_bound(a,greatest_lower_bound(b,a)) = greatest_lower_bound(a,greatest_lower_bound(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,a)),greatest_lower_bound(a,greatest_lower_bound(b,a))) ),[1,1],$fot(greatest_lower_bound(a,b))]]) ).

cnf(refute_0_8,plain,
    ( greatest_lower_bound(b,a) != greatest_lower_bound(a,b)
    | greatest_lower_bound(a,greatest_lower_bound(b,a)) = greatest_lower_bound(a,greatest_lower_bound(a,b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,a)),greatest_lower_bound(a,greatest_lower_bound(b,a))) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,a)) = greatest_lower_bound(a,greatest_lower_bound(a,b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,a),greatest_lower_bound(a,b)) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
    | greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).

cnf(refute_0_11,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_10]) ).

cnf(refute_0_12,plain,
    greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(b,a)),
    inference(subst,[],[refute_0_11:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(a))]]) ).

cnf(refute_0_13,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_14,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,a)) != greatest_lower_bound(a,greatest_lower_bound(a,b))
    | greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,greatest_lower_bound(b,a))
    | greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(a,b)) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,b),a))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,a)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(a,b))))]]) ).

cnf(refute_0_16,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,a)) != greatest_lower_bound(a,greatest_lower_bound(a,b))
    | greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(a,b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),a),greatest_lower_bound(a,greatest_lower_bound(b,a))) )],[refute_0_12,refute_0_15]) ).

cnf(refute_0_17,plain,
    greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(a,b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,a)),greatest_lower_bound(a,greatest_lower_bound(a,b))) )],[refute_0_9,refute_0_16]) ).

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

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

cnf(refute_0_20,plain,
    greatest_lower_bound(a,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),a),greatest_lower_bound(a,b)) )],[refute_0_19,prove_ax_glb2b]) ).

cnf(refute_0_21,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)) = greatest_lower_bound(greatest_lower_bound(X_19,X_19),X_20),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_19)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).

cnf(refute_0_22,plain,
    greatest_lower_bound(X_19,X_19) = X_19,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_19))]]) ).

cnf(refute_0_23,plain,
    ( greatest_lower_bound(X_19,X_19) != X_19
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)) != greatest_lower_bound(greatest_lower_bound(X_19,X_19),X_20)
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)) = greatest_lower_bound(X_19,X_20) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)),greatest_lower_bound(greatest_lower_bound(X_19,X_19),X_20)) ),[1,0],$fot(X_19)]]) ).

cnf(refute_0_24,plain,
    ( greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)) != greatest_lower_bound(greatest_lower_bound(X_19,X_19),X_20)
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)) = greatest_lower_bound(X_19,X_20) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,X_19),X_19) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)) = greatest_lower_bound(X_19,X_20),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_20)),greatest_lower_bound(greatest_lower_bound(X_19,X_19),X_20)) )],[refute_0_21,refute_0_24]) ).

cnf(refute_0_26,plain,
    greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
    inference(subst,[],[refute_0_25:[bind(X_19,$fot(a)),bind(X_20,$fot(b))]]) ).

cnf(refute_0_27,plain,
    ( greatest_lower_bound(a,b) != greatest_lower_bound(a,b)
    | greatest_lower_bound(a,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
    | greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)) ),[0,1],$fot(greatest_lower_bound(a,b))]]) ).

cnf(refute_0_28,plain,
    ( greatest_lower_bound(a,b) != greatest_lower_bound(a,b)
    | greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    greatest_lower_bound(a,b) != greatest_lower_bound(a,b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)) )],[refute_0_28,refute_0_20]) ).

cnf(refute_0_30,plain,
    greatest_lower_bound(a,b) = greatest_lower_bound(a,b),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,b))]]) ).

cnf(refute_0_31,plain,
    $false,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,b)) )],[refute_0_30,refute_0_29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP143-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 13 04:35:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38  
% 0.12/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38  
%------------------------------------------------------------------------------