TSTP Solution File: GRP159-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 10:37:06 EDT 2022

% Result   : Unsatisfiable 0.19s 0.37s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   41 (  24 unt;   0 nHn;  30 RR)
%            Number of literals    :   65 (  64 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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (   3 sgn)

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

cnf(symmetry_of_lub,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X) ).

cnf(lub_absorbtion,axiom,
    least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).

cnf(ax_mono2c_1,hypothesis,
    greatest_lower_bound(a,b) = a ).

cnf(prove_ax_mono2c,negated_conjecture,
    least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,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,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
    | least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).

cnf(refute_0_4,plain,
    least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_3]) ).

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

cnf(refute_0_6,plain,
    ( multiply(c,least_upper_bound(a,b)) != multiply(c,b)
    | least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,least_upper_bound(a,b))
    | least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,least_upper_bound(a,b))) ),[1],$fot(multiply(c,b))]]) ).

cnf(refute_0_7,plain,
    ( multiply(c,least_upper_bound(a,b)) != multiply(c,b)
    | least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,least_upper_bound(a,b))) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    multiply(c,least_upper_bound(a,b)) != multiply(c,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)) )],[refute_0_7,prove_ax_mono2c]) ).

cnf(refute_0_9,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_10,plain,
    greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).

cnf(refute_0_11,plain,
    ( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
    | greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).

cnf(refute_0_12,plain,
    greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
    | least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).

cnf(refute_0_14,plain,
    ( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_9,refute_0_14]) ).

cnf(refute_0_16,plain,
    least_upper_bound(b,greatest_lower_bound(a,b)) = b,
    inference(subst,[],[refute_0_15:[bind(X_8,$fot(b)),bind(X_9,$fot(a))]]) ).

cnf(refute_0_17,plain,
    ( greatest_lower_bound(a,b) != a
    | least_upper_bound(b,greatest_lower_bound(a,b)) != b
    | least_upper_bound(b,a) = b ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) ),[0,1],$fot(a)]]) ).

cnf(refute_0_18,plain,
    ( least_upper_bound(b,greatest_lower_bound(a,b)) != b
    | least_upper_bound(b,a) = b ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_mono2c_1,refute_0_17]) ).

cnf(refute_0_19,plain,
    least_upper_bound(b,a) = b,
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) )],[refute_0_16,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( least_upper_bound(X,Y) != least_upper_bound(Y,X)
    | least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_21,plain,
    least_upper_bound(Y,X) = least_upper_bound(X,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_20]) ).

cnf(refute_0_22,plain,
    least_upper_bound(b,a) = least_upper_bound(a,b),
    inference(subst,[],[refute_0_21:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_23,plain,
    ( least_upper_bound(b,a) != b
    | least_upper_bound(b,a) != least_upper_bound(a,b)
    | least_upper_bound(a,b) = b ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,a),b) ),[0],$fot(least_upper_bound(a,b))]]) ).

cnf(refute_0_24,plain,
    ( least_upper_bound(b,a) != b
    | least_upper_bound(a,b) = b ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,a),least_upper_bound(a,b)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    least_upper_bound(a,b) = b,
    inference(resolve,[$cnf( $equal(least_upper_bound(b,a),b) )],[refute_0_19,refute_0_24]) ).

cnf(refute_0_26,plain,
    multiply(c,least_upper_bound(a,b)) = multiply(c,least_upper_bound(a,b)),
    introduced(tautology,[refl,[$fot(multiply(c,least_upper_bound(a,b)))]]) ).

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

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

cnf(refute_0_29,plain,
    multiply(c,least_upper_bound(a,b)) = multiply(c,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,b),b) )],[refute_0_25,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( multiply(c,b) != multiply(c,b)
    | multiply(c,least_upper_bound(a,b)) != multiply(c,b)
    | multiply(c,least_upper_bound(a,b)) = multiply(c,b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) ),[1],$fot(multiply(c,b))]]) ).

cnf(refute_0_31,plain,
    ( multiply(c,b) != multiply(c,b)
    | multiply(c,least_upper_bound(a,b)) = multiply(c,b) ),
    inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    multiply(c,b) != multiply(c,b),
    inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) )],[refute_0_31,refute_0_8]) ).

cnf(refute_0_33,plain,
    multiply(c,b) = multiply(c,b),
    introduced(tautology,[refl,[$fot(multiply(c,b))]]) ).

cnf(refute_0_34,plain,
    $false,
    inference(resolve,[$cnf( $equal(multiply(c,b),multiply(c,b)) )],[refute_0_33,refute_0_32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n017.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 21:37:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37  
% 0.19/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37  
%------------------------------------------------------------------------------