TSTP Solution File: GRP165-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP165-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 10:37:07 EDT 2022

% Result   : Unsatisfiable 0.42s 0.59s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   35 (  20 unt;   0 nHn;  24 RR)
%            Number of literals    :   58 (  57 equ;  25 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;   2 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X ).

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

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

cnf(lat1a_1,hypothesis,
    least_upper_bound(a,identity) = a ).

cnf(prove_lat1a,negated_conjecture,
    least_upper_bound(a,multiply(a,a)) != multiply(a,a) ).

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

cnf(refute_0_1,plain,
    ( multiply(least_upper_bound(a,identity),a) != multiply(least_upper_bound(a,identity),a)
    | least_upper_bound(a,identity) != a
    | multiply(least_upper_bound(a,identity),a) = multiply(a,a) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,identity),a),multiply(least_upper_bound(a,identity),a)) ),[1,0],$fot(a)]]) ).

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

cnf(refute_0_3,plain,
    multiply(least_upper_bound(a,identity),a) = multiply(a,a),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),a) )],[lat1a_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(multiply(X_58,X_57),multiply(identity,X_57)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_57)),bind(Y,$fot(X_58)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_5,plain,
    multiply(identity,X_57) = X_57,
    inference(subst,[],[left_identity:[bind(X,$fot(X_57))]]) ).

cnf(refute_0_6,plain,
    ( multiply(identity,X_57) != X_57
    | multiply(least_upper_bound(X_58,identity),X_57) != least_upper_bound(multiply(X_58,X_57),multiply(identity,X_57))
    | multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(multiply(X_58,X_57),X_57) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_58,identity),X_57),least_upper_bound(multiply(X_58,X_57),multiply(identity,X_57))) ),[1,1],$fot(X_57)]]) ).

cnf(refute_0_7,plain,
    ( multiply(least_upper_bound(X_58,identity),X_57) != least_upper_bound(multiply(X_58,X_57),multiply(identity,X_57))
    | multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(multiply(X_58,X_57),X_57) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_57),X_57) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(multiply(X_58,X_57),X_57),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_58,identity),X_57),least_upper_bound(multiply(X_58,X_57),multiply(identity,X_57))) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    least_upper_bound(X_18,X_17) = least_upper_bound(X_17,X_18),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_10,plain,
    least_upper_bound(multiply(X_58,X_57),X_57) = least_upper_bound(X_57,multiply(X_58,X_57)),
    inference(subst,[],[refute_0_9:[bind(X_17,$fot(X_57)),bind(X_18,$fot(multiply(X_58,X_57)))]]) ).

cnf(refute_0_11,plain,
    ( multiply(least_upper_bound(X_58,identity),X_57) != least_upper_bound(multiply(X_58,X_57),X_57)
    | least_upper_bound(multiply(X_58,X_57),X_57) != least_upper_bound(X_57,multiply(X_58,X_57))
    | multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(X_57,multiply(X_58,X_57)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_58,identity),X_57),least_upper_bound(X_57,multiply(X_58,X_57))) ),[0],$fot(least_upper_bound(multiply(X_58,X_57),X_57))]]) ).

cnf(refute_0_12,plain,
    ( multiply(least_upper_bound(X_58,identity),X_57) != least_upper_bound(multiply(X_58,X_57),X_57)
    | multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(X_57,multiply(X_58,X_57)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_58,X_57),X_57),least_upper_bound(X_57,multiply(X_58,X_57))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    multiply(least_upper_bound(X_58,identity),X_57) = least_upper_bound(X_57,multiply(X_58,X_57)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_58,identity),X_57),least_upper_bound(multiply(X_58,X_57),X_57)) )],[refute_0_8,refute_0_12]) ).

cnf(refute_0_14,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_15,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_16,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( multiply(least_upper_bound(X_58,identity),X_57) != least_upper_bound(X_57,multiply(X_58,X_57))
    | least_upper_bound(X_57,multiply(X_58,X_57)) = multiply(least_upper_bound(X_58,identity),X_57) ),
    inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_58,identity),X_57))),bind(Y0,$fot(least_upper_bound(X_57,multiply(X_58,X_57))))]]) ).

cnf(refute_0_18,plain,
    least_upper_bound(X_57,multiply(X_58,X_57)) = multiply(least_upper_bound(X_58,identity),X_57),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_58,identity),X_57),least_upper_bound(X_57,multiply(X_58,X_57))) )],[refute_0_13,refute_0_17]) ).

cnf(refute_0_19,plain,
    least_upper_bound(a,multiply(a,a)) = multiply(least_upper_bound(a,identity),a),
    inference(subst,[],[refute_0_18:[bind(X_57,$fot(a)),bind(X_58,$fot(a))]]) ).

cnf(refute_0_20,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_21,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_16,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( multiply(least_upper_bound(a,identity),a) != multiply(a,a)
    | least_upper_bound(a,multiply(a,a)) != multiply(least_upper_bound(a,identity),a)
    | least_upper_bound(a,multiply(a,a)) = multiply(a,a) ),
    inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(a,multiply(a,a)))),bind(Y0,$fot(multiply(least_upper_bound(a,identity),a))),bind(Z0,$fot(multiply(a,a)))]]) ).

cnf(refute_0_23,plain,
    ( multiply(least_upper_bound(a,identity),a) != multiply(a,a)
    | least_upper_bound(a,multiply(a,a)) = multiply(a,a) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(a,a)),multiply(least_upper_bound(a,identity),a)) )],[refute_0_19,refute_0_22]) ).

cnf(refute_0_24,plain,
    least_upper_bound(a,multiply(a,a)) = multiply(a,a),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),a),multiply(a,a)) )],[refute_0_3,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( multiply(a,a) != multiply(a,a)
    | least_upper_bound(a,multiply(a,a)) != multiply(a,a)
    | least_upper_bound(a,multiply(a,a)) = multiply(a,a) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,multiply(a,a)),multiply(a,a)) ),[0,1],$fot(multiply(a,a))]]) ).

cnf(refute_0_26,plain,
    ( multiply(a,a) != multiply(a,a)
    | least_upper_bound(a,multiply(a,a)) = multiply(a,a) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(a,a)),multiply(a,a)) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    multiply(a,a) != multiply(a,a),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(a,a)),multiply(a,a)) )],[refute_0_26,prove_lat1a]) ).

cnf(refute_0_28,plain,
    multiply(a,a) = multiply(a,a),
    introduced(tautology,[refl,[$fot(multiply(a,a))]]) ).

cnf(refute_0_29,plain,
    $false,
    inference(resolve,[$cnf( $equal(multiply(a,a),multiply(a,a)) )],[refute_0_28,refute_0_27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP165-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n005.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 : Tue Jun 14 02:36:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.59  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.59  
% 0.42/0.59  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.42/0.59  
%------------------------------------------------------------------------------