%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET242-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 05:25:14 EDT 2022

% Result   : Unsatisfiable 1.92s 2.11s
% Output   : Refutation 1.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   13 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(z__dfg,xr),
    file('SET242-6.p',unknown),
    [] ).

cnf(2,axiom,
    member(z__dfg,cross_product(x__dfg,y__dfg)),
    file('SET242-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ member(z__dfg,restrict(xr,x__dfg,y__dfg)),
    file('SET242-6.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('SET242-6.p',unknown),
    [] ).

cnf(31,axiom,
    equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
    file('SET242-6.p',unknown),
    [] ).

cnf(1268,plain,
    ( ~ member(u,cross_product(v,w))
    | ~ member(u,x)
    | member(u,restrict(x,v,w)) ),
    inference(spr,[status(thm),theory(equality)],[31,26]),
    [iquote('0:SpR:31.0,26.2')] ).

cnf(8237,plain,
    ( ~ member(z__dfg,cross_product(x__dfg,y__dfg))
    | ~ member(z__dfg,xr) ),
    inference(res,[status(thm),theory(equality)],[1268,3]),
    [iquote('0:Res:1268.2,3.0')] ).

cnf(8255,plain,
    $false,
    inference(mrr,[status(thm)],[8237,2,1]),
    [iquote('0:MRR:8237.0,8237.1,2.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET242-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jul  9 18:04:10 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 1.92/2.11  
% 1.92/2.11  SPASS V 3.9 
% 1.92/2.11  SPASS beiseite: Proof found.
% 1.92/2.11  % SZS status Theorem
% 1.92/2.11  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.92/2.11  SPASS derived 7119 clauses, backtracked 0 clauses, performed 3 splits and kept 3648 clauses.
% 1.92/2.11  SPASS allocated 83297 KBytes.
% 1.92/2.11  SPASS spent	0:00:01.71 on the problem.
% 1.92/2.11  		0:00:00.04 for the input.
% 1.92/2.11  		0:00:00.00 for the FLOTTER CNF translation.
% 1.92/2.11  		0:00:00.08 for inferences.
% 1.92/2.11  		0:00:00.07 for the backtracking.
% 1.92/2.11  		0:00:01.44 for the reduction.
% 1.92/2.11  
% 1.92/2.11  
% 1.92/2.11  Here is a proof with depth 2, length 8 :
% 1.92/2.11  % SZS output start Refutation
% See solution above
% 1.92/2.11  Formulae used in the proof : prove_restriction_alternate_defn5_1 prove_restriction_alternate_defn5_2 prove_restriction_alternate_defn5_3 intersection3 restriction1
% 1.92/2.11  
%------------------------------------------------------------------------------