%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP032-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 10:32:34 EDT 2022

% Result   : Unsatisfiable 0.18s 0.38s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   10 (   7 unt;   0 nHn;   8 RR)
%            Number of literals    :   16 (   0 equ;   9 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    8 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(right_inverse,axiom,
    product(X,inverse(X),identity) ).

cnf(closure_of_product_and_inverse,axiom,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,inverse(B),C)
    | subgroup_member(C) ) ).

cnf(a_is_in_subgroup,hypothesis,
    subgroup_member(a) ).

cnf(prove_identity_is_in_subgroup,negated_conjecture,
    ~ subgroup_member(identity) ).

cnf(refute_0_0,plain,
    product(X_75,inverse(X_75),identity),
    inference(subst,[],[right_inverse:[bind(X,$fot(X_75))]]) ).

cnf(refute_0_1,plain,
    ( ~ product(X_75,inverse(X_75),identity)
    | ~ subgroup_member(X_75)
    | subgroup_member(identity) ),
    inference(subst,[],[closure_of_product_and_inverse:[bind(A,$fot(X_75)),bind(B,$fot(X_75)),bind(C,$fot(identity))]]) ).

cnf(refute_0_2,plain,
    ( ~ subgroup_member(X_75)
    | subgroup_member(identity) ),
    inference(resolve,[$cnf( product(X_75,inverse(X_75),identity) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ~ subgroup_member(X_75),
    inference(resolve,[$cnf( subgroup_member(identity) )],[refute_0_2,prove_identity_is_in_subgroup]) ).

cnf(refute_0_4,plain,
    ~ subgroup_member(a),
    inference(subst,[],[refute_0_3:[bind(X_75,$fot(a))]]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP032-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n009.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 01:04:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.38  
% 0.18/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.38  
%------------------------------------------------------------------------------