%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET451-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 05:26:22 EDT 2022

% Result   : Unsatisfiable 1.02s 1.19s
% Output   : Refutation 1.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   9 unt;   3 nHn;  14 RR)
%            Number of literals    :   19 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ subclass(subset_relation,cross_product(universal_class,universal_class)),
    file('SET451-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET451-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET451-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET451-6.p',unknown),
    [] ).

cnf(29,axiom,
    equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
    file('SET451-6.p',unknown),
    [] ).

cnf(30,axiom,
    equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
    file('SET451-6.p',unknown),
    [] ).

cnf(75,axiom,
    equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),subset_relation),
    file('SET451-6.p',unknown),
    [] ).

cnf(115,plain,
    equal(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),subset_relation),
    inference(rew,[status(thm),theory(equality)],[30,75]),
    [iquote('0:Rew:30.0,75.0,30.0,75.0')] ).

cnf(165,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),v) ),
    inference(res,[status(thm),theory(equality)],[3,23]),
    [iquote('0:Res:3.1,23.0')] ).

cnf(3799,plain,
    ( subclass(intersection(u,v),v)
    | subclass(intersection(u,v),v) ),
    inference(res,[status(thm),theory(equality)],[165,4]),
    [iquote('0:Res:165.1,4.0')] ).

cnf(3801,plain,
    subclass(intersection(u,v),v),
    inference(obv,[status(thm),theory(equality)],[3799]),
    [iquote('0:Obv:3799.0')] ).

cnf(3814,plain,
    subclass(restrict(u,v,w),cross_product(v,w)),
    inference(spr,[status(thm),theory(equality)],[29,3801]),
    [iquote('0:SpR:29.0,3801.0')] ).

cnf(4872,plain,
    subclass(subset_relation,cross_product(universal_class,universal_class)),
    inference(spr,[status(thm),theory(equality)],[115,3814]),
    [iquote('0:SpR:115.0,3814.0')] ).

cnf(4877,plain,
    $false,
    inference(mrr,[status(thm)],[4872,1]),
    [iquote('0:MRR:4872.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET451-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.14  % Command  : run_spass %d %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Sun Jul 10 03:31:57 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 1.02/1.19  
% 1.02/1.19  SPASS V 3.9 
% 1.02/1.19  SPASS beiseite: Proof found.
% 1.02/1.19  % SZS status Theorem
% 1.02/1.19  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.02/1.19  SPASS derived 4227 clauses, backtracked 194 clauses, performed 3 splits and kept 2113 clauses.
% 1.02/1.19  SPASS allocated 80134 KBytes.
% 1.02/1.19  SPASS spent	0:00:00.81 on the problem.
% 1.02/1.19  		0:00:00.04 for the input.
% 1.02/1.19  		0:00:00.00 for the FLOTTER CNF translation.
% 1.02/1.19  		0:00:00.06 for inferences.
% 1.02/1.19  		0:00:00.02 for the backtracking.
% 1.02/1.19  		0:00:00.64 for the reduction.
% 1.02/1.19  
% 1.02/1.19  
% 1.02/1.19  Here is a proof with depth 4, length 14 :
% 1.02/1.19  % SZS output start Refutation
% See solution above
% 1.02/1.19  Formulae used in the proof : prove_subset_relation_alternate_defn1_1 not_subclass_members1 not_subclass_members2 intersection2 restriction1 restriction2 subset_relation
% 1.02/1.19  
%------------------------------------------------------------------------------