%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n016.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 10:32:36 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   25 (  12 unt;   0 nHn;  22 RR)
%            Number of literals    :   42 (  11 equ;  18 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   15 (   0 sgn)

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

cnf(left_inverse,axiom,
    product(inverse(X),X,identity) ).

cnf(another_left_identity,hypothesis,
    ( ~ subgroup_member(A)
    | product(another_identity,A,A) ) ).

cnf(another_left_inverse,hypothesis,
    ( ~ subgroup_member(A)
    | product(another_inverse(A),A,another_identity) ) ).

cnf(product_left_cancellation,hypothesis,
    ( ~ product(A,B,C)
    | ~ product(D,B,C)
    | D = A ) ).

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

cnf(prove_two_inverses_are_equal,negated_conjecture,
    inverse(a) != another_inverse(a) ).

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

cnf(refute_0_1,plain,
    ( ~ subgroup_member(a)
    | product(another_identity,a,a) ),
    inference(subst,[],[another_left_identity:[bind(A,$fot(a))]]) ).

cnf(refute_0_2,plain,
    product(another_identity,a,a),
    inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ product(X_14,a,a)
    | ~ product(another_identity,a,a)
    | X_14 = another_identity ),
    inference(subst,[],[product_left_cancellation:[bind(A,$fot(another_identity)),bind(B,$fot(a)),bind(C,$fot(a)),bind(D,$fot(X_14))]]) ).

cnf(refute_0_4,plain,
    ( ~ product(X_14,a,a)
    | X_14 = another_identity ),
    inference(resolve,[$cnf( product(another_identity,a,a) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ product(identity,a,a)
    | identity = another_identity ),
    inference(subst,[],[refute_0_4:[bind(X_14,$fot(identity))]]) ).

cnf(refute_0_6,plain,
    identity = another_identity,
    inference(resolve,[$cnf( product(identity,a,a) )],[refute_0_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( identity != another_identity
    | ~ product(inverse(X),X,identity)
    | product(inverse(X),X,another_identity) ),
    introduced(tautology,[equality,[$cnf( product(inverse(X),X,identity) ),[2],$fot(another_identity)]]) ).

cnf(refute_0_8,plain,
    ( ~ product(inverse(X),X,identity)
    | product(inverse(X),X,another_identity) ),
    inference(resolve,[$cnf( $equal(identity,another_identity) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    product(inverse(X),X,another_identity),
    inference(resolve,[$cnf( product(inverse(X),X,identity) )],[left_inverse,refute_0_8]) ).

cnf(refute_0_10,plain,
    product(inverse(a),a,another_identity),
    inference(subst,[],[refute_0_9:[bind(X,$fot(a))]]) ).

cnf(refute_0_11,plain,
    ( ~ subgroup_member(a)
    | product(another_inverse(a),a,another_identity) ),
    inference(subst,[],[another_left_inverse:[bind(A,$fot(a))]]) ).

cnf(refute_0_12,plain,
    product(another_inverse(a),a,another_identity),
    inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ product(X_14,a,another_identity)
    | ~ product(another_inverse(a),a,another_identity)
    | X_14 = another_inverse(a) ),
    inference(subst,[],[product_left_cancellation:[bind(A,$fot(another_inverse(a))),bind(B,$fot(a)),bind(C,$fot(another_identity)),bind(D,$fot(X_14))]]) ).

cnf(refute_0_14,plain,
    ( ~ product(X_14,a,another_identity)
    | X_14 = another_inverse(a) ),
    inference(resolve,[$cnf( product(another_inverse(a),a,another_identity) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ product(inverse(a),a,another_identity)
    | inverse(a) = another_inverse(a) ),
    inference(subst,[],[refute_0_14:[bind(X_14,$fot(inverse(a)))]]) ).

cnf(refute_0_16,plain,
    inverse(a) = another_inverse(a),
    inference(resolve,[$cnf( product(inverse(a),a,another_identity) )],[refute_0_10,refute_0_15]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( $equal(inverse(a),another_inverse(a)) )],[refute_0_16,prove_two_inverses_are_equal]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n016.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 14:30:31 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48  
% 0.19/0.48  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48  
%------------------------------------------------------------------------------