%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP029-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n025.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 1.38s 1.56s
% Output   : Refutation 1.38s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_there_is_a_right_identity,negated_conjecture,
    ~ product(not_right_identity(X15),X15,not_right_identity(X15)),
    input ).

cnf(left_inverse,axiom,
    product(inverse(X12),X12,identity),
    input ).

cnf(associativity1,axiom,
    ( ~ product(X75,X73,X70)
    | ~ product(X73,X71,X74)
    | ~ product(X70,X71,X72)
    | product(X75,X74,X72) ),
    input ).

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

cnf(product_substitution1,axiom,
    ( ~ equalish(X32,X31)
    | ~ product(X32,X29,X30)
    | product(X31,X29,X30) ),
    input ).

cnf(c7,plain,
    ( ~ equalish(identity,X33)
    | product(X33,X34,X34) ),
    inference(resolution,status(thm),[product_substitution1,left_identity]) ).

cnf(symmetry,axiom,
    ( ~ equalish(X5,X4)
    | equalish(X4,X5) ),
    input ).

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

cnf(total_function2,axiom,
    ( ~ product(X63,X62,X61)
    | ~ product(X63,X62,X60)
    | equalish(X61,X60) ),
    input ).

cnf(c22,plain,
    ( ~ product(identity,X65,X66)
    | equalish(X66,X65) ),
    inference(resolution,status(thm),[total_function2,left_identity]) ).

cnf(c23,plain,
    equalish(multiply(identity,X68),X68),
    inference(resolution,status(thm),[c22,total_function1]) ).

cnf(c33,plain,
    equalish(X69,multiply(identity,X69)),
    inference(resolution,status(thm),[c23,symmetry]) ).

cnf(c44,plain,
    product(multiply(identity,identity),X88,X88),
    inference(resolution,status(thm),[c33,c7]) ).

cnf(c62,plain,
    ( ~ product(X301,X298,multiply(identity,identity))
    | ~ product(X298,X300,X299)
    | product(X301,X299,X300) ),
    inference(resolution,status(thm),[c44,associativity1]) ).

cnf(product_substitution3,axiom,
    ( ~ equalish(X49,X48)
    | ~ product(X46,X47,X49)
    | product(X46,X47,X48) ),
    input ).

cnf(c15,plain,
    ( ~ equalish(multiply(X98,X96),X97)
    | product(X98,X96,X97) ),
    inference(resolution,status(thm),[product_substitution3,total_function1]) ).

cnf(c20,plain,
    ( ~ product(inverse(X103),X103,X104)
    | equalish(X104,identity) ),
    inference(resolution,status(thm),[total_function2,left_inverse]) ).

cnf(c14,plain,
    ( ~ equalish(identity,X94)
    | product(inverse(X95),X95,X94) ),
    inference(resolution,status(thm),[product_substitution3,left_inverse]) ).

cnf(c68,plain,
    product(inverse(X144),X144,multiply(identity,identity)),
    inference(resolution,status(thm),[c14,c33]) ).

cnf(c730,plain,
    ( ~ product(X353,X354,X352)
    | product(inverse(X353),X352,X354) ),
    inference(resolution,status(thm),[c62,c68]) ).

cnf(c1057,plain,
    product(inverse(X360),multiply(X360,X359),X359),
    inference(resolution,status(thm),[c730,total_function1]) ).

cnf(c1136,plain,
    product(inverse(inverse(X444)),X445,multiply(X444,X445)),
    inference(resolution,status(thm),[c1057,c730]) ).

cnf(c1768,plain,
    equalish(multiply(X446,inverse(X446)),identity),
    inference(resolution,status(thm),[c1136,c20]) ).

cnf(c1774,plain,
    product(X447,inverse(X447),identity),
    inference(resolution,status(thm),[c1768,c15]) ).

cnf(c1790,plain,
    ( ~ equalish(identity,X554)
    | product(X555,inverse(X555),X554) ),
    inference(resolution,status(thm),[c1774,product_substitution3]) ).

cnf(c2588,plain,
    product(X662,inverse(X662),multiply(identity,identity)),
    inference(resolution,status(thm),[c1790,c33]) ).

cnf(c3331,plain,
    ( ~ product(inverse(X743),X742,X741)
    | product(X743,X741,X742) ),
    inference(resolution,status(thm),[c2588,c62]) ).

cnf(c3992,plain,
    product(X748,identity,X748),
    inference(resolution,status(thm),[c3331,left_inverse]) ).

cnf(c4095,plain,
    $false,
    inference(resolution,status(thm),[c3992,prove_there_is_a_right_identity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP029-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 03:02:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.38/1.56  # Version:  1.3
% 1.38/1.56  # SZS status Unsatisfiable
% 1.38/1.56  # SZS output start CNFRefutation
% See solution above
% 1.38/1.56  
% 1.38/1.56  # Initial clauses    : 16
% 1.38/1.56  # Processed clauses  : 238
% 1.38/1.56  # Factors computed   : 10
% 1.38/1.56  # Resolvents computed: 4088
% 1.38/1.56  # Tautologies deleted: 5
% 1.38/1.56  # Forward subsumed   : 377
% 1.38/1.56  # Backward subsumed  : 6
% 1.38/1.56  # -------- CPU Time ---------
% 1.38/1.56  # User time          : 1.194 s
% 1.38/1.56  # System time        : 0.018 s
% 1.38/1.56  # Total time         : 1.212 s
%------------------------------------------------------------------------------