%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n026.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 11:21:16 EDT 2022

% Result   : Unsatisfiable 2.13s 2.31s
% Output   : Refutation 2.13s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_a_equals_c,negated_conjecture,
    a != c,
    input ).

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

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

cnf(total_function2,axiom,
    ( ~ product(X13,X15,X14)
    | ~ product(X13,X15,X12)
    | X14 = X12 ),
    input ).

cnf(c7,plain,
    ( ~ product(identity,X16,X17)
    | X17 = X16 ),
    inference(resolution,status(thm),[total_function2,left_identity]) ).

cnf(c_is_an_inverse_of_b,plain,
    product(c,b,identity),
    input ).

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

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

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

cnf(c34,plain,
    ( ~ product(X159,X158,X160)
    | ~ product(X158,X157,identity)
    | product(X160,X157,X159) ),
    inference(resolution,status(thm),[associativity2,right_identity]) ).

cnf(c354,plain,
    ( ~ product(X326,X328,X327)
    | product(X327,inverse(X328),X326) ),
    inference(resolution,status(thm),[c34,right_inverse]) ).

cnf(c1818,plain,
    product(identity,inverse(b),c),
    inference(resolution,status(thm),[c354,c_is_an_inverse_of_b]) ).

cnf(c2109,plain,
    c = inverse(b),
    inference(resolution,status(thm),[c1818,c7]) ).

cnf(transitivity,axiom,
    ( X39 != X41
    | X41 != X40
    | X39 = X40 ),
    eq_axiom ).

cnf(a_is_an_inverse_of_b,plain,
    product(a,b,identity),
    input ).

cnf(c1814,plain,
    product(identity,inverse(b),a),
    inference(resolution,status(thm),[c354,a_is_an_inverse_of_b]) ).

cnf(c1966,plain,
    a = inverse(b),
    inference(resolution,status(thm),[c1814,c7]) ).

cnf(c1995,plain,
    inverse(b) = a,
    inference(resolution,status(thm),[c1966,symmetry]) ).

cnf(c2001,plain,
    ( X623 != inverse(b)
    | X623 = a ),
    inference(resolution,status(thm),[c1995,transitivity]) ).

cnf(c6603,plain,
    c = a,
    inference(resolution,status(thm),[c2001,c2109]) ).

cnf(c6666,plain,
    a = c,
    inference(resolution,status(thm),[c6603,symmetry]) ).

cnf(c6681,plain,
    $false,
    inference(resolution,status(thm),[c6666,prove_a_equals_c]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.34  % Computer : n026.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 21:40:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.13/2.31  # Version:  1.3
% 2.13/2.31  # SZS status Unsatisfiable
% 2.13/2.31  # SZS output start CNFRefutation
% See solution above
% 2.13/2.31  
% 2.13/2.31  # Initial clauses    : 17
% 2.13/2.31  # Processed clauses  : 321
% 2.13/2.31  # Factors computed   : 2
% 2.13/2.31  # Resolvents computed: 6696
% 2.13/2.31  # Tautologies deleted: 6
% 2.13/2.31  # Forward subsumed   : 461
% 2.13/2.31  # Backward subsumed  : 5
% 2.13/2.31  # -------- CPU Time ---------
% 2.13/2.31  # User time          : 1.937 s
% 2.13/2.31  # System time        : 0.026 s
% 2.13/2.31  # Total time         : 1.963 s
%------------------------------------------------------------------------------