%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n022.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 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% 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    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn)

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

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_X_times_id_is_X,negated_conjecture,
    multiply(a,identity) != a ).

cnf(refute_0_0,plain,
    product(X_60,identity,multiply(X_60,identity)),
    inference(subst,[],[total_function1:[bind(X,$fot(X_60)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_1,plain,
    product(X_50,identity,X_50),
    inference(subst,[],[right_identity:[bind(X,$fot(X_50))]]) ).

cnf(refute_0_2,plain,
    ( ~ product(X_50,identity,X_50)
    | ~ product(X_50,identity,X_53)
    | X_53 = X_50 ),
    inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(X_50)),bind(Y,$fot(identity)),bind(Z,$fot(X_53))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(X_50,identity,X_53)
    | X_53 = X_50 ),
    inference(resolve,[$cnf( product(X_50,identity,X_50) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ product(X_60,identity,multiply(X_60,identity))
    | multiply(X_60,identity) = X_60 ),
    inference(subst,[],[refute_0_3:[bind(X_50,$fot(X_60)),bind(X_53,$fot(multiply(X_60,identity)))]]) ).

cnf(refute_0_5,plain,
    multiply(X_60,identity) = X_60,
    inference(resolve,[$cnf( product(X_60,identity,multiply(X_60,identity)) )],[refute_0_0,refute_0_4]) ).

cnf(refute_0_6,plain,
    multiply(a,identity) = a,
    inference(subst,[],[refute_0_5:[bind(X_60,$fot(a))]]) ).

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

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

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

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n022.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 07:10:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39  
% 0.13/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39  
%------------------------------------------------------------------------------