%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP036-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n011.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 0.41s 0.59s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_identity_equals_another_identity,negated_conjecture,
    identity != another_identity,
    input ).

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

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

cnf(c11,plain,
    ( ~ product(identity,X28,X29)
    | X29 = X28 ),
    inference(resolution,status(thm),[total_function2,left_identity]) ).

cnf(another_right_identity,plain,
    ( ~ subgroup_member(X18)
    | product(X18,another_identity,X18) ),
    input ).

cnf(another_identity_in_subgroup,plain,
    subgroup_member(another_identity),
    input ).

cnf(another_inverse_in_subgroup,plain,
    ( ~ subgroup_member(X9)
    | subgroup_member(another_inverse(X9)) ),
    input ).

cnf(c5,plain,
    subgroup_member(another_inverse(another_identity)),
    inference(resolution,status(thm),[another_inverse_in_subgroup,another_identity_in_subgroup]) ).

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

cnf(closure_of_product_and_inverse,axiom,
    ( ~ subgroup_member(X39)
    | ~ subgroup_member(X40)
    | ~ product(X39,inverse(X40),X41)
    | subgroup_member(X41) ),
    input ).

cnf(c46,plain,
    ( ~ subgroup_member(X42)
    | subgroup_member(identity) ),
    inference(resolution,status(thm),[closure_of_product_and_inverse,right_inverse]) ).

cnf(c50,plain,
    subgroup_member(identity),
    inference(resolution,status(thm),[c46,c5]) ).

cnf(c55,plain,
    product(identity,another_identity,identity),
    inference(resolution,status(thm),[c50,another_right_identity]) ).

cnf(c67,plain,
    identity = another_identity,
    inference(resolution,status(thm),[c55,c11]) ).

cnf(c72,plain,
    $false,
    inference(resolution,status(thm),[c67,prove_identity_equals_another_identity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP036-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.34  % Computer : n011.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 17:59:34 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.41/0.59  # Version:  1.3
% 0.41/0.59  # SZS status Unsatisfiable
% 0.41/0.59  # SZS output start CNFRefutation
% See solution above
% 0.41/0.59  
% 0.41/0.59  # Initial clauses    : 24
% 0.41/0.59  # Processed clauses  : 33
% 0.41/0.59  # Factors computed   : 0
% 0.41/0.59  # Resolvents computed: 74
% 0.41/0.59  # Tautologies deleted: 1
% 0.41/0.59  # Forward subsumed   : 8
% 0.41/0.59  # Backward subsumed  : 1
% 0.41/0.59  # -------- CPU Time ---------
% 0.41/0.59  # User time          : 0.227 s
% 0.41/0.59  # System time        : 0.016 s
% 0.41/0.59  # Total time         : 0.243 s
%------------------------------------------------------------------------------