%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET386-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 05:26:02 EDT 2022

% Result   : Unsatisfiable 0.99s 1.16s
% Output   : Refutation 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   7 unt;   3 nHn;  12 RR)
%            Number of literals    :   17 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(restrict(x__dfg,universal_class,universal_class),x__dfg),
    file('SET386-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ subclass(x__dfg,cross_product(universal_class,universal_class)),
    file('SET386-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET386-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET386-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET386-6.p',unknown),
    [] ).

cnf(30,axiom,
    equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
    file('SET386-6.p',unknown),
    [] ).

cnf(173,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),v) ),
    inference(res,[status(thm),theory(equality)],[4,24]),
    [iquote('0:Res:4.1,24.0')] ).

cnf(4089,plain,
    ( subclass(intersection(u,v),v)
    | subclass(intersection(u,v),v) ),
    inference(res,[status(thm),theory(equality)],[173,5]),
    [iquote('0:Res:173.1,5.0')] ).

cnf(4091,plain,
    subclass(intersection(u,v),v),
    inference(obv,[status(thm),theory(equality)],[4089]),
    [iquote('0:Obv:4089.0')] ).

cnf(4109,plain,
    subclass(restrict(u,v,w),cross_product(v,w)),
    inference(spr,[status(thm),theory(equality)],[30,4091]),
    [iquote('0:SpR:30.0,4091.0')] ).

cnf(5128,plain,
    subclass(x__dfg,cross_product(universal_class,universal_class)),
    inference(spr,[status(thm),theory(equality)],[1,4109]),
    [iquote('0:SpR:1.0,4109.0')] ).

cnf(5135,plain,
    $false,
    inference(mrr,[status(thm)],[5128,2]),
    [iquote('0:MRR:5128.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET386-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n008.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jul 11 10:51:53 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.99/1.16  
% 0.99/1.16  SPASS V 3.9 
% 0.99/1.16  SPASS beiseite: Proof found.
% 0.99/1.16  % SZS status Theorem
% 0.99/1.16  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.99/1.16  SPASS derived 4508 clauses, backtracked 207 clauses, performed 4 splits and kept 2279 clauses.
% 0.99/1.16  SPASS allocated 80301 KBytes.
% 0.99/1.16  SPASS spent	0:00:00.76 on the problem.
% 0.99/1.16  		0:00:00.04 for the input.
% 0.99/1.16  		0:00:00.00 for the FLOTTER CNF translation.
% 0.99/1.16  		0:00:00.05 for inferences.
% 0.99/1.16  		0:00:00.03 for the backtracking.
% 0.99/1.16  		0:00:00.60 for the reduction.
% 0.99/1.16  
% 0.99/1.16  
% 0.99/1.16  Here is a proof with depth 4, length 12 :
% 0.99/1.16  % SZS output start Refutation
% See solution above
% 0.99/1.16  Formulae used in the proof : prove_relation_property4_1 prove_relation_property4_2 not_subclass_members1 not_subclass_members2 intersection2 restriction1
% 0.99/1.16  
%------------------------------------------------------------------------------