TSTP Solution File: SET238-6 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 05:25:12 EDT 2022

% Result   : Unsatisfiable 1.01s 1.19s
% Output   : Refutation 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (   9 unt;   3 nHn;  17 RR)
%            Number of literals    :   26 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(z__dfg,restrict(xr,x__dfg,y__dfg)),
    file('SET238-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(ordered_pair(first(z__dfg),second(z__dfg)),restrict(xr,x__dfg,y__dfg)),
    file('SET238-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET238-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET238-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET238-6.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ member(u,cross_product(v,w))
    | equal(ordered_pair(first(u),second(u)),u) ),
    file('SET238-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET238-6.p',unknown),
    [] ).

cnf(30,axiom,
    equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
    file('SET238-6.p',unknown),
    [] ).

cnf(117,plain,
    ( ~ subclass(restrict(xr,x__dfg,y__dfg),u)
    | member(z__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[1,3]),
    [iquote('0:Res:1.0,3.1')] ).

cnf(172,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(4451,plain,
    ( subclass(intersection(u,v),v)
    | subclass(intersection(u,v),v) ),
    inference(res,[status(thm),theory(equality)],[172,5]),
    [iquote('0:Res:172.1,5.0')] ).

cnf(4453,plain,
    subclass(intersection(u,v),v),
    inference(obv,[status(thm),theory(equality)],[4451]),
    [iquote('0:Obv:4451.0')] ).

cnf(4471,plain,
    subclass(restrict(u,v,w),cross_product(v,w)),
    inference(spr,[status(thm),theory(equality)],[30,4453]),
    [iquote('0:SpR:30.0,4453.0')] ).

cnf(5534,plain,
    member(z__dfg,cross_product(x__dfg,y__dfg)),
    inference(res,[status(thm),theory(equality)],[4471,117]),
    [iquote('0:Res:4471.0,117.0')] ).

cnf(5567,plain,
    equal(ordered_pair(first(z__dfg),second(z__dfg)),z__dfg),
    inference(res,[status(thm),theory(equality)],[5534,19]),
    [iquote('0:Res:5534.0,19.0')] ).

cnf(5568,plain,
    ~ member(z__dfg,restrict(xr,x__dfg,y__dfg)),
    inference(rew,[status(thm),theory(equality)],[5567,2]),
    [iquote('0:Rew:5567.0,2.0')] ).

cnf(5574,plain,
    $false,
    inference(mrr,[status(thm)],[5568,1]),
    [iquote('0:MRR:5568.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 : Mon Jul 11 01:22:31 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.01/1.19  
% 1.01/1.19  SPASS V 3.9 
% 1.01/1.19  SPASS beiseite: Proof found.
% 1.01/1.19  % SZS status Theorem
% 1.01/1.19  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.01/1.19  SPASS derived 4894 clauses, backtracked 174 clauses, performed 4 splits and kept 2347 clauses.
% 1.01/1.19  SPASS allocated 80513 KBytes.
% 1.01/1.19  SPASS spent	0:00:00.82 on the problem.
% 1.01/1.19  		0:00:00.04 for the input.
% 1.01/1.19  		0:00:00.00 for the FLOTTER CNF translation.
% 1.01/1.19  		0:00:00.06 for inferences.
% 1.01/1.19  		0:00:00.02 for the backtracking.
% 1.01/1.19  		0:00:00.66 for the reduction.
% 1.01/1.19  
% 1.01/1.19  
% 1.01/1.19  Here is a proof with depth 5, length 17 :
% 1.01/1.19  % SZS output start Refutation
% See solution above
% 1.01/1.19  Formulae used in the proof : prove_corollary_to_restriction_alternate_defn1_1 prove_corollary_to_restriction_alternate_defn1_2 subclass_members not_subclass_members1 not_subclass_members2 cartesian_product4 intersection2 restriction1
% 1.01/1.19  
%------------------------------------------------------------------------------