%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET239-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 : Tue Jul 19 03:33:45 EDT 2022

% Result   : Unsatisfiable 98.13s 98.37s
% Output   : CNFRefutation 98.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  10 RR)
%            Number of literals    :   19 (   3 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   25 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(intersection1,axiom,
    ( ~ member(Z,intersection(X,Y))
    | member(Z,X) ) ).

cnf(restriction1,axiom,
    intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ).

cnf(prove_restriction_alternate_defn2_1,negated_conjecture,
    member(z,restrict(xr,x,y)) ).

cnf(prove_restriction_alternate_defn2_2,negated_conjecture,
    ~ member(z,xr) ).

cnf(refute_0_0,plain,
    ( ~ member(X_829,intersection(X_827,cross_product(X,Y)))
    | member(X_829,X_827) ),
    inference(subst,[],[intersection1:[bind(X,$fot(X_827)),bind(Y,$fot(cross_product(X,Y))),bind(Z,$fot(X_829))]]) ).

cnf(refute_0_1,plain,
    intersection(X_827,cross_product(X,Y)) = restrict(X_827,X,Y),
    inference(subst,[],[restriction1:[bind(Xr,$fot(X_827))]]) ).

cnf(refute_0_2,plain,
    ( intersection(X_827,cross_product(X,Y)) != restrict(X_827,X,Y)
    | ~ member(X_829,restrict(X_827,X,Y))
    | member(X_829,intersection(X_827,cross_product(X,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_829,intersection(X_827,cross_product(X,Y))) ),[1],$fot(restrict(X_827,X,Y))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(X_829,restrict(X_827,X,Y))
    | member(X_829,intersection(X_827,cross_product(X,Y))) ),
    inference(resolve,[$cnf( $equal(intersection(X_827,cross_product(X,Y)),restrict(X_827,X,Y)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(X_829,restrict(X_827,X,Y))
    | member(X_829,X_827) ),
    inference(resolve,[$cnf( member(X_829,intersection(X_827,cross_product(X,Y))) )],[refute_0_3,refute_0_0]) ).

cnf(refute_0_5,plain,
    ( ~ member(z,restrict(xr,x,y))
    | member(z,xr) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(x)),bind(Y,$fot(y)),bind(X_827,$fot(xr)),bind(X_829,$fot(z))]]) ).

cnf(refute_0_6,plain,
    member(z,xr),
    inference(resolve,[$cnf( member(z,restrict(xr,x,y)) )],[prove_restriction_alternate_defn2_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( member(z,xr) )],[refute_0_6,prove_restriction_alternate_defn2_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET239-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jul 10 09:31:50 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 98.13/98.37  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 98.13/98.37  
% 98.13/98.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 98.13/98.37  
%------------------------------------------------------------------------------