%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP035-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n020.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 11:21:26 EDT 2022

% Result   : Unsatisfiable 84.23s 84.40s
% Output   : Refutation 84.23s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_c_is_in_subgroup,negated_conjecture,
    ~ subgroup_member(c),
    input ).

cnf(c3,plain,
    ( X17 != X16
    | ~ subgroup_member(X17)
    | subgroup_member(X16) ),
    eq_axiom ).

cnf(total_function1,axiom,
    product(X7,X8,multiply(X7,X8)),
    input ).

cnf(a_times_b_is_c,plain,
    product(a,b,c),
    input ).

cnf(total_function2,axiom,
    ( ~ product(X12,X13,X11)
    | ~ product(X12,X13,X14)
    | X11 = X14 ),
    input ).

cnf(c9,plain,
    ( ~ product(a,b,X81)
    | X81 = c ),
    inference(resolution,status(thm),[total_function2,a_times_b_is_c]) ).

cnf(c125,plain,
    multiply(a,b) = c,
    inference(resolution,status(thm),[c9,total_function1]) ).

cnf(c151,plain,
    ( ~ subgroup_member(multiply(a,b))
    | subgroup_member(c) ),
    inference(resolution,status(thm),[c125,c3]) ).

cnf(a_is_in_subgroup,plain,
    subgroup_member(a),
    input ).

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

cnf(closure_of_product_and_inverse,axiom,
    ( ~ subgroup_member(X41)
    | ~ subgroup_member(X40)
    | ~ product(X41,inverse(X40),X42)
    | subgroup_member(X42) ),
    input ).

cnf(c42,plain,
    ( ~ subgroup_member(X43)
    | subgroup_member(identity) ),
    inference(resolution,status(thm),[closure_of_product_and_inverse,right_inverse]) ).

cnf(c44,plain,
    subgroup_member(identity),
    inference(resolution,status(thm),[c42,a_is_in_subgroup]) ).

cnf(b_is_in_subgroup,plain,
    subgroup_member(b),
    input ).

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

cnf(c43,plain,
    ( ~ subgroup_member(identity)
    | ~ subgroup_member(X101)
    | subgroup_member(inverse(X101)) ),
    inference(resolution,status(thm),[closure_of_product_and_inverse,left_identity]) ).

cnf(c169,plain,
    ( ~ subgroup_member(identity)
    | subgroup_member(inverse(b)) ),
    inference(resolution,status(thm),[c43,b_is_in_subgroup]) ).

cnf(c180,plain,
    subgroup_member(inverse(b)),
    inference(resolution,status(thm),[c169,c44]) ).

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

cnf(associativity2,axiom,
    ( ~ product(X33,X34,X35)
    | ~ product(X34,X32,X30)
    | ~ product(X33,X30,X31)
    | product(X35,X32,X31) ),
    input ).

cnf(c30,plain,
    ( ~ product(X126,X125,X127)
    | ~ product(X125,X124,identity)
    | product(X127,X124,X126) ),
    inference(resolution,status(thm),[associativity2,right_identity]) ).

cnf(c228,plain,
    ( ~ product(X262,X260,X261)
    | product(X261,inverse(X260),X262) ),
    inference(resolution,status(thm),[c30,right_inverse]) ).

cnf(c1129,plain,
    product(multiply(X271,X272),inverse(X272),X271),
    inference(resolution,status(thm),[c228,total_function1]) ).

cnf(c1203,plain,
    ( ~ subgroup_member(multiply(X582,X583))
    | ~ subgroup_member(X583)
    | subgroup_member(X582) ),
    inference(resolution,status(thm),[c1129,closure_of_product_and_inverse]) ).

cnf(c6,plain,
    ( ~ product(X69,X71,X70)
    | X70 = multiply(X69,X71) ),
    inference(resolution,status(thm),[total_function2,total_function1]) ).

cnf(c1205,plain,
    X614 = multiply(multiply(X614,X615),inverse(X615)),
    inference(resolution,status(thm),[c1129,c6]) ).

cnf(c4777,plain,
    ( ~ subgroup_member(X4998)
    | subgroup_member(multiply(multiply(X4998,X4997),inverse(X4997))) ),
    inference(resolution,status(thm),[c1205,c3]) ).

cnf(c90228,plain,
    subgroup_member(multiply(multiply(a,X4999),inverse(X4999))),
    inference(resolution,status(thm),[c4777,a_is_in_subgroup]) ).

cnf(c90450,plain,
    ( ~ subgroup_member(inverse(X5005))
    | subgroup_member(multiply(a,X5005)) ),
    inference(resolution,status(thm),[c90228,c1203]) ).

cnf(c91263,plain,
    subgroup_member(multiply(a,b)),
    inference(resolution,status(thm),[c90450,c180]) ).

cnf(c91375,plain,
    subgroup_member(c),
    inference(resolution,status(thm),[c91263,c151]) ).

cnf(c91422,plain,
    $false,
    inference(resolution,status(thm),[c91375,prove_c_is_in_subgroup]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GRP035-3 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33  % Computer : n020.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 01:03:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 84.23/84.40  # Version:  1.3
% 84.23/84.40  # SZS status Unsatisfiable
% 84.23/84.40  # SZS output start CNFRefutation
% See solution above
% 84.23/84.40  
% 84.23/84.40  # Initial clauses    : 20
% 84.23/84.40  # Processed clauses  : 1660
% 84.23/84.40  # Factors computed   : 21
% 84.23/84.40  # Resolvents computed: 91511
% 84.23/84.40  # Tautologies deleted: 30
% 84.23/84.40  # Forward subsumed   : 4232
% 84.23/84.40  # Backward subsumed  : 95
% 84.23/84.40  # -------- CPU Time ---------
% 84.23/84.40  # User time          : 83.866 s
% 84.23/84.40  # System time        : 0.206 s
% 84.23/84.40  # Total time         : 84.072 s
%------------------------------------------------------------------------------