%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n023.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 11:21:15 EDT 2022

% Result   : Unsatisfiable 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_identity_is_an_element,negated_conjecture,
    ~ an_element(identity),
    input ).

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

cnf(right_inverse,axiom,
    product(X4,inverse(X4),identity),
    input ).

cnf(condition,axiom,
    ( ~ an_element(X7)
    | ~ an_element(X6)
    | ~ product(X7,inverse(X6),X8)
    | an_element(X8) ),
    input ).

cnf(c2,plain,
    ( ~ an_element(X9)
    | an_element(identity) ),
    inference(resolution,status(thm),[condition,right_inverse]) ).

cnf(c3,plain,
    an_element(identity),
    inference(resolution,status(thm),[c2,element_of_set]) ).

cnf(c4,plain,
    $false,
    inference(resolution,status(thm),[c3,prove_identity_is_an_element]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 12:06:21 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.50  # Version:  1.3
% 0.19/0.50  # SZS status Unsatisfiable
% 0.19/0.50  # SZS output start CNFRefutation
% See solution above
% 0.19/0.50  
% 0.19/0.50  # Initial clauses    : 9
% 0.19/0.50  # Processed clauses  : 9
% 0.19/0.50  # Factors computed   : 0
% 0.19/0.50  # Resolvents computed: 5
% 0.19/0.50  # Tautologies deleted: 0
% 0.19/0.50  # Forward subsumed   : 0
% 0.19/0.50  # Backward subsumed  : 1
% 0.19/0.50  # -------- CPU Time ---------
% 0.19/0.50  # User time          : 0.152 s
% 0.19/0.50  # System time        : 0.016 s
% 0.19/0.50  # Total time         : 0.168 s
%------------------------------------------------------------------------------