%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 10:32:12 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   10 (   7 unt;   0 nHn;   8 RR)
%            Number of literals    :   16 (   0 equ;   9 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    8 (   2 sgn)

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

cnf(element_of_set,axiom,
    an_element(a) ).

cnf(condition,axiom,
    ( ~ an_element(X)
    | ~ an_element(Y)
    | ~ product(X,inverse(Y),Z)
    | an_element(Z) ) ).

cnf(prove_identity_is_an_element,negated_conjecture,
    ~ an_element(identity) ).

cnf(refute_0_0,plain,
    product(X_22,inverse(X_22),identity),
    inference(subst,[],[right_inverse:[bind(X,$fot(X_22))]]) ).

cnf(refute_0_1,plain,
    ( ~ an_element(X_22)
    | ~ product(X_22,inverse(X_22),identity)
    | an_element(identity) ),
    inference(subst,[],[condition:[bind(X,$fot(X_22)),bind(Y,$fot(X_22)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_2,plain,
    ( ~ an_element(X_22)
    | an_element(identity) ),
    inference(resolve,[$cnf( product(X_22,inverse(X_22),identity) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ~ an_element(X_22),
    inference(resolve,[$cnf( an_element(identity) )],[refute_0_2,prove_identity_is_an_element]) ).

cnf(refute_0_4,plain,
    ~ an_element(a),
    inference(subst,[],[refute_0_3:[bind(X_22,$fot(a))]]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( an_element(a) )],[element_of_set,refute_0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 11:58:02 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------