%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 : Mon Jul 18 20:35:45 EDT 2022

% Result   : Unsatisfiable 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :   11 (  10 equ;   5 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    :    5 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :    2 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(middle_associator,axiom,
    multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ).

cnf(prove_equality,negated_conjecture,
    multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity ).

cnf(refute_0_0,plain,
    multiply(multiply(associator(a,a,b),a),associator(a,a,b)) = additive_identity,
    inference(subst,[],[middle_associator:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_1,plain,
    ( multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity
    | additive_identity != additive_identity
    | multiply(multiply(associator(a,a,b),a),associator(a,a,b)) = additive_identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(associator(a,a,b),a),associator(a,a,b)),additive_identity) ),[0],$fot(additive_identity)]]) ).

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

cnf(refute_0_3,plain,
    additive_identity != additive_identity,
    inference(resolve,[$cnf( $equal(multiply(multiply(associator(a,a,b),a),associator(a,a,b)),additive_identity) )],[refute_0_2,prove_equality]) ).

cnf(refute_0_4,plain,
    additive_identity = additive_identity,
    introduced(tautology,[refl,[$fot(additive_identity)]]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_4,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon May 30 20:01:59 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  
% 0.14/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36  
%------------------------------------------------------------------------------