TSTP Solution File: GRP176-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP176-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 10:37:20 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   26 (  14 unt;   0 nHn;  21 RR)
%            Number of literals    :   44 (  43 equ;  20 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   29 (   0 sgn)

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

cnf(monotony_lub2,axiom,
    multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).

cnf(prove_p07,negated_conjecture,
    multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ).

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

cnf(refute_0_4,plain,
    least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_3]) ).

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

cnf(refute_0_6,plain,
    multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) = multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),
    introduced(tautology,[refl,[$fot(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))))]]) ).

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

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

cnf(refute_0_9,plain,
    multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,d),multiply(b,d)),multiply(least_upper_bound(a,b),d)) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,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_11,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_10]) ).

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

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,
    ( multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) != multiply(c,multiply(least_upper_bound(a,b),d))
    | least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) != multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))
    | least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))))),bind(Y0,$fot(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))))),bind(Z0,$fot(multiply(c,multiply(least_upper_bound(a,b),d))))]]) ).

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

cnf(refute_0_17,plain,
    least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)),
    inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d))) )],[refute_0_9,refute_0_16]) ).

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

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

cnf(refute_0_20,plain,
    multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,multiply(least_upper_bound(a,b),d)),
    inference(resolve,[$cnf( $equal(multiply(c,multiply(least_upper_bound(a,b),d)),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))) )],[refute_0_19,prove_p07]) ).

cnf(refute_0_21,plain,
    multiply(c,multiply(least_upper_bound(a,b),d)) = multiply(c,multiply(least_upper_bound(a,b),d)),
    introduced(tautology,[refl,[$fot(multiply(c,multiply(least_upper_bound(a,b),d)))]]) ).

cnf(refute_0_22,plain,
    $false,
    inference(resolve,[$cnf( $equal(multiply(c,multiply(least_upper_bound(a,b),d)),multiply(c,multiply(least_upper_bound(a,b),d))) )],[refute_0_21,refute_0_20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : GRP176-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 21:34:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------