%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n004.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 11:21:24 EDT 2022

% Result   : Unsatisfiable 1.98s 2.26s
% Output   : Refutation 1.98s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_a_has_an_inverse,negated_conjecture,
    ~ product(a,X4,identity),
    input ).

cnf(left_identity,plain,
    product(identity,X3,X3),
    input ).

cnf(left_inverse,plain,
    product(inverse(X7),X7,identity),
    input ).

cnf(associativity2,axiom,
    ( ~ product(X38,X37,X34)
    | ~ product(X37,X35,X36)
    | ~ product(X38,X36,X39)
    | product(X34,X35,X39) ),
    input ).

cnf(c20,plain,
    ( ~ product(inverse(X98),X99,X100)
    | ~ product(X99,X101,X98)
    | product(X100,X101,identity) ),
    inference(resolution,status(thm),[associativity2,left_inverse]) ).

cnf(associativity1,axiom,
    ( ~ product(X23,X22,X19)
    | ~ product(X22,X20,X21)
    | ~ product(X19,X20,X24)
    | product(X23,X21,X24) ),
    input ).

cnf(c11,plain,
    ( ~ product(X79,X81,identity)
    | ~ product(X81,X80,X82)
    | product(X79,X82,X80) ),
    inference(resolution,status(thm),[associativity1,left_identity]) ).

cnf(c68,plain,
    ( ~ product(X189,inverse(X188),identity)
    | product(X189,identity,X188) ),
    inference(resolution,status(thm),[c11,left_inverse]) ).

cnf(c555,plain,
    product(inverse(inverse(X193)),identity,X193),
    inference(resolution,status(thm),[c68,left_inverse]) ).

cnf(c601,plain,
    ( ~ product(identity,X753,inverse(X752))
    | product(X752,X753,identity) ),
    inference(resolution,status(thm),[c555,c20]) ).

cnf(c6413,plain,
    product(X756,inverse(X756),identity),
    inference(resolution,status(thm),[c601,left_identity]) ).

cnf(c6576,plain,
    $false,
    inference(resolution,status(thm),[c6413,prove_a_has_an_inverse]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33  % Computer : n004.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 05:20:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.98/2.26  # Version:  1.3
% 1.98/2.26  # SZS status Unsatisfiable
% 1.98/2.26  # SZS output start CNFRefutation
% See solution above
% 1.98/2.26  
% 1.98/2.26  # Initial clauses    : 13
% 1.98/2.26  # Processed clauses  : 294
% 1.98/2.26  # Factors computed   : 10
% 1.98/2.26  # Resolvents computed: 6569
% 1.98/2.26  # Tautologies deleted: 5
% 1.98/2.26  # Forward subsumed   : 422
% 1.98/2.26  # Backward subsumed  : 15
% 1.98/2.26  # -------- CPU Time ---------
% 1.98/2.26  # User time          : 1.855 s
% 1.98/2.26  # System time        : 0.029 s
% 1.98/2.26  # Total time         : 1.884 s
%------------------------------------------------------------------------------