%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP020-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n032.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 10:32:17 EDT 2022

% Result   : Unsatisfiable 0.15s 0.34s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (  10 unt;   0 nHn;  11 RR)
%            Number of literals    :   25 (  14 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn)

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

cnf(total_function1,axiom,
    product(X,Y,multiply(X,Y)) ).

cnf(total_function2,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,Y,W)
    | Z = W ) ).

cnf(prove_inverse_X_times_X_is_id,negated_conjecture,
    multiply(inverse(a),a) != identity ).

cnf(refute_0_0,plain,
    product(inverse(X_62),X_62,multiply(inverse(X_62),X_62)),
    inference(subst,[],[total_function1:[bind(X,$fot(inverse(X_62))),bind(Y,$fot(X_62))]]) ).

cnf(refute_0_1,plain,
    product(inverse(X_53),X_53,identity),
    inference(subst,[],[left_inverse:[bind(X,$fot(X_53))]]) ).

cnf(refute_0_2,plain,
    ( ~ product(inverse(X_53),X_53,X_54)
    | ~ product(inverse(X_53),X_53,identity)
    | X_54 = identity ),
    inference(subst,[],[total_function2:[bind(W,$fot(identity)),bind(X,$fot(inverse(X_53))),bind(Y,$fot(X_53)),bind(Z,$fot(X_54))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(inverse(X_53),X_53,X_54)
    | X_54 = identity ),
    inference(resolve,[$cnf( product(inverse(X_53),X_53,identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ product(inverse(X_62),X_62,multiply(inverse(X_62),X_62))
    | multiply(inverse(X_62),X_62) = identity ),
    inference(subst,[],[refute_0_3:[bind(X_53,$fot(X_62)),bind(X_54,$fot(multiply(inverse(X_62),X_62)))]]) ).

cnf(refute_0_5,plain,
    multiply(inverse(X_62),X_62) = identity,
    inference(resolve,[$cnf( product(inverse(X_62),X_62,multiply(inverse(X_62),X_62)) )],[refute_0_0,refute_0_4]) ).

cnf(refute_0_6,plain,
    multiply(inverse(a),a) = identity,
    inference(subst,[],[refute_0_5:[bind(X_62,$fot(a))]]) ).

cnf(refute_0_7,plain,
    ( multiply(inverse(a),a) != identity
    | identity != identity
    | multiply(inverse(a),a) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),a),identity) ),[0],$fot(identity)]]) ).

cnf(refute_0_8,plain,
    ( identity != identity
    | multiply(inverse(a),a) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    identity != identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_8,prove_inverse_X_times_X_is_id]) ).

cnf(refute_0_10,plain,
    identity = identity,
    introduced(tautology,[refl,[$fot(identity)]]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_10,refute_0_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : GRP020-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.11  % Command  : metis --show proof --show saturation %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Mon Jun 13 21:58:42 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.15/0.30  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.34  
% 0.15/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.34  
%------------------------------------------------------------------------------