TSTP Solution File: GRP157-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP157-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n012.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 10:37:05 EDT 2022

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   23 (  12 unt;   0 nHn;  20 RR)
%            Number of literals    :   40 (  39 equ;  19 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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).

cnf(ax_mono2a_1,hypothesis,
    least_upper_bound(a,b) = b ).

cnf(prove_ax_mono2a,negated_conjecture,
    least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b) ).

cnf(refute_0_0,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_1,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_2,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_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    multiply(c,least_upper_bound(a,b)) = multiply(c,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,b),b) )],[ax_mono2a_1,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,
    ( 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_6:[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_8,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_7]) ).

cnf(refute_0_9,plain,
    least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,least_upper_bound(a,b)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).

cnf(refute_0_10,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_11,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_10]) ).

cnf(refute_0_12,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) ),
    inference(subst,[],[refute_0_11:[bind(X0,$fot(least_upper_bound(multiply(c,a),multiply(c,b)))),bind(Y0,$fot(multiply(c,least_upper_bound(a,b)))),bind(Z0,$fot(multiply(c,b)))]]) ).

cnf(refute_0_13,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_9,refute_0_12]) ).

cnf(refute_0_14,plain,
    least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b),
    inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) )],[refute_0_3,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( multiply(c,b) != multiply(c,b)
    | least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b)
    | least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)) ),[0,1],$fot(multiply(c,b))]]) ).

cnf(refute_0_16,plain,
    ( multiply(c,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,b)) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    multiply(c,b) != multiply(c,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)) )],[refute_0_16,prove_ax_mono2a]) ).

cnf(refute_0_18,plain,
    multiply(c,b) = multiply(c,b),
    introduced(tautology,[refl,[$fot(multiply(c,b))]]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( $equal(multiply(c,b),multiply(c,b)) )],[refute_0_18,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP157-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n012.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 20:54:25 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36  
% 0.12/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36  
%------------------------------------------------------------------------------