%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP041-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 10:32:38 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   5 RR)
%            Number of literals    :   11 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    8 (   0 sgn)

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

cnf(total_function2,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,Y,W)
    | equalish(Z,W) ) ).

cnf(prove_reflexivity,negated_conjecture,
    ~ equalish(a,a) ).

cnf(refute_0_0,plain,
    product(identity,X_6,X_6),
    inference(subst,[],[left_identity:[bind(X,$fot(X_6))]]) ).

cnf(refute_0_1,plain,
    ( ~ product(identity,X_6,X_6)
    | equalish(X_6,X_6) ),
    inference(subst,[],[total_function2:[bind(W,$fot(X_6)),bind(X,$fot(identity)),bind(Y,$fot(X_6)),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_2,plain,
    equalish(X_6,X_6),
    inference(resolve,[$cnf( product(identity,X_6,X_6) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    equalish(a,a),
    inference(subst,[],[refute_0_2:[bind(X_6,$fot(a))]]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( equalish(a,a) )],[refute_0_3,prove_reflexivity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP041-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n009.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 : Tue Jun 14 12:20:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------