%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n022.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 11:21:20 EDT 2022

% Result   : Unsatisfiable 0.56s 0.75s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_inverse_of_inverse_is_original,negated_conjecture,
    inverse(inverse(a)) != a,
    input ).

cnf(symmetry,axiom,
    ( X9 != X10
    | X10 = X9 ),
    eq_axiom ).

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

cnf(total_function2,axiom,
    ( ~ product(X17,X18,X19)
    | ~ product(X17,X18,X20)
    | X19 = X20 ),
    input ).

cnf(c7,plain,
    ( ~ product(identity,X21,X22)
    | X22 = X21 ),
    inference(resolution,status(thm),[total_function2,left_identity]) ).

cnf(right_inverse,axiom,
    product(X6,inverse(X6),identity),
    input ).

cnf(right_identity,axiom,
    product(X4,identity,X4),
    input ).

cnf(associativity2,axiom,
    ( ~ product(X39,X36,X38)
    | ~ product(X36,X37,X40)
    | ~ product(X39,X40,X35)
    | product(X38,X37,X35) ),
    input ).

cnf(c34,plain,
    ( ~ product(X145,X143,X146)
    | ~ product(X143,X144,identity)
    | product(X146,X144,X145) ),
    inference(resolution,status(thm),[associativity2,right_identity]) ).

cnf(c267,plain,
    ( ~ product(X239,X240,X241)
    | product(X241,inverse(X240),X239) ),
    inference(resolution,status(thm),[c34,right_inverse]) ).

cnf(c879,plain,
    product(identity,inverse(inverse(X249)),X249),
    inference(resolution,status(thm),[c267,right_inverse]) ).

cnf(c942,plain,
    X250 = inverse(inverse(X250)),
    inference(resolution,status(thm),[c879,c7]) ).

cnf(c949,plain,
    inverse(inverse(X255)) = X255,
    inference(resolution,status(thm),[c942,symmetry]) ).

cnf(c1006,plain,
    $false,
    inference(resolution,status(thm),[c949,prove_inverse_of_inverse_is_original]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.33  % Computer : n022.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 21:43:03 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.56/0.75  # Version:  1.3
% 0.56/0.75  # SZS status Unsatisfiable
% 0.56/0.75  # SZS output start CNFRefutation
% See solution above
% 0.56/0.75  
% 0.56/0.75  # Initial clauses    : 15
% 0.56/0.75  # Processed clauses  : 102
% 0.56/0.75  # Factors computed   : 2
% 0.56/0.75  # Resolvents computed: 1022
% 0.56/0.75  # Tautologies deleted: 4
% 0.56/0.75  # Forward subsumed   : 105
% 0.56/0.75  # Backward subsumed  : 2
% 0.56/0.75  # -------- CPU Time ---------
% 0.56/0.75  # User time          : 0.390 s
% 0.56/0.75  # System time        : 0.023 s
% 0.56/0.75  # Total time         : 0.413 s
%------------------------------------------------------------------------------