%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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 10:32:35 EDT 2022

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   17 (   9 unt;   0 nHn;  13 RR)
%            Number of literals    :   31 (   0 equ;  15 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   :   12 (   1 sgn)

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

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_a_inverse_is_in_subgroup,negated_conjecture,
    ~ subgroup_member(inverse(a)) ).

cnf(refute_0_0,plain,
    product(identity,inverse(X_74),inverse(X_74)),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_74)))]]) ).

cnf(refute_0_1,plain,
    ( ~ product(identity,inverse(X_74),inverse(X_74))
    | ~ subgroup_member(X_74)
    | ~ subgroup_member(identity)
    | subgroup_member(inverse(X_74)) ),
    inference(subst,[],[closure_of_product_and_inverse:[bind(A,$fot(identity)),bind(B,$fot(X_74)),bind(C,$fot(inverse(X_74)))]]) ).

cnf(refute_0_2,plain,
    ( ~ subgroup_member(X_74)
    | ~ subgroup_member(identity)
    | subgroup_member(inverse(X_74)) ),
    inference(resolve,[$cnf( product(identity,inverse(X_74),inverse(X_74)) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    product(X_74,inverse(X_74),identity),
    inference(subst,[],[right_inverse:[bind(X,$fot(X_74))]]) ).

cnf(refute_0_4,plain,
    ( ~ product(X_74,inverse(X_74),identity)
    | ~ subgroup_member(X_74)
    | subgroup_member(identity) ),
    inference(subst,[],[closure_of_product_and_inverse:[bind(A,$fot(X_74)),bind(B,$fot(X_74)),bind(C,$fot(identity))]]) ).

cnf(refute_0_5,plain,
    ( ~ subgroup_member(X_74)
    | subgroup_member(identity) ),
    inference(resolve,[$cnf( product(X_74,inverse(X_74),identity) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ subgroup_member(a)
    | subgroup_member(identity) ),
    inference(subst,[],[refute_0_5:[bind(X_74,$fot(a))]]) ).

cnf(refute_0_7,plain,
    subgroup_member(identity),
    inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ subgroup_member(X_74)
    | subgroup_member(inverse(X_74)) ),
    inference(resolve,[$cnf( subgroup_member(identity) )],[refute_0_7,refute_0_2]) ).

cnf(refute_0_9,plain,
    ( ~ subgroup_member(a)
    | subgroup_member(inverse(a)) ),
    inference(subst,[],[refute_0_8:[bind(X_74,$fot(a))]]) ).

cnf(refute_0_10,plain,
    subgroup_member(inverse(a)),
    inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_9]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( subgroup_member(inverse(a)) )],[refute_0_10,prove_a_inverse_is_in_subgroup]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n025.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 : Tue Jun 14 01:40:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.39  
% 0.20/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.40  
%------------------------------------------------------------------------------