TSTP Solution File: SET183-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET183-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 05:24:50 EDT 2022

% Result   : Unsatisfiable 117.83s 117.99s
% Output   : Refutation 117.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   21 (   6 unt;   6 nHn;  21 RR)
%            Number of literals    :   45 (   0 equ;  22 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subclass(x__dfg,y__dfg),
    file('SET183-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(intersection(x__dfg,y__dfg),x__dfg),
    file('SET183-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET183-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET183-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET183-6.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ subclass(u,v)
    | ~ subclass(v,u)
    | equal(v,u) ),
    file('SET183-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET183-6.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('SET183-6.p',unknown),
    [] ).

cnf(121,plain,
    ( ~ subclass(x__dfg,intersection(x__dfg,y__dfg))
    | ~ subclass(intersection(x__dfg,y__dfg),x__dfg) ),
    inference(res,[status(thm),theory(equality)],[9,2]),
    [iquote('0:Res:9.2,2.0')] ).

cnf(181,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),u) ),
    inference(res,[status(thm),theory(equality)],[4,23]),
    [iquote('0:Res:4.1,23.0')] ).

cnf(365,plain,
    ( ~ subclass(u,v)
    | subclass(u,w)
    | member(not_subclass_element(u,w),v) ),
    inference(res,[status(thm),theory(equality)],[4,3]),
    [iquote('0:Res:4.1,3.0')] ).

cnf(804,plain,
    ( ~ member(not_subclass_element(u,intersection(v,w)),w)
    | ~ member(not_subclass_element(u,intersection(v,w)),v)
    | subclass(u,intersection(v,w)) ),
    inference(res,[status(thm),theory(equality)],[25,5]),
    [iquote('0:Res:25.2,5.0')] ).

cnf(7109,plain,
    ( subclass(intersection(u,v),u)
    | subclass(intersection(u,v),u) ),
    inference(res,[status(thm),theory(equality)],[181,5]),
    [iquote('0:Res:181.1,5.0')] ).

cnf(7114,plain,
    subclass(intersection(u,v),u),
    inference(obv,[status(thm),theory(equality)],[7109]),
    [iquote('0:Obv:7109.0')] ).

cnf(7115,plain,
    ~ subclass(x__dfg,intersection(x__dfg,y__dfg)),
    inference(mrr,[status(thm)],[121,7114]),
    [iquote('0:MRR:121.1,7114.0')] ).

cnf(13287,plain,
    ( ~ subclass(u,v)
    | ~ member(not_subclass_element(u,intersection(w,v)),w)
    | subclass(u,intersection(w,v))
    | subclass(u,intersection(w,v)) ),
    inference(res,[status(thm),theory(equality)],[365,804]),
    [iquote('0:Res:365.2,804.0')] ).

cnf(13290,plain,
    ( ~ subclass(u,v)
    | ~ member(not_subclass_element(u,intersection(w,v)),w)
    | subclass(u,intersection(w,v)) ),
    inference(obv,[status(thm),theory(equality)],[13287]),
    [iquote('0:Obv:13287.2')] ).

cnf(63591,plain,
    ( ~ subclass(u,v)
    | subclass(u,intersection(u,v))
    | subclass(u,intersection(u,v)) ),
    inference(res,[status(thm),theory(equality)],[4,13290]),
    [iquote('0:Res:4.1,13290.1')] ).

cnf(63623,plain,
    ( ~ subclass(u,v)
    | subclass(u,intersection(u,v)) ),
    inference(obv,[status(thm),theory(equality)],[63591]),
    [iquote('0:Obv:63591.1')] ).

cnf(108175,plain,
    ~ subclass(x__dfg,y__dfg),
    inference(res,[status(thm),theory(equality)],[63623,7115]),
    [iquote('0:Res:63623.1,7115.0')] ).

cnf(108195,plain,
    $false,
    inference(mrr,[status(thm)],[108175,1]),
    [iquote('0:MRR:108175.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET183-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  9 20:32:11 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 117.83/117.99  
% 117.83/117.99  SPASS V 3.9 
% 117.83/117.99  SPASS beiseite: Proof found.
% 117.83/117.99  % SZS status Theorem
% 117.83/117.99  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 117.83/117.99  SPASS derived 78305 clauses, backtracked 715 clauses, performed 14 splits and kept 27411 clauses.
% 117.83/117.99  SPASS allocated 165053 KBytes.
% 117.83/117.99  SPASS spent	0:1:55.90 on the problem.
% 117.83/117.99  		0:00:00.04 for the input.
% 117.83/117.99  		0:00:00.00 for the FLOTTER CNF translation.
% 117.83/117.99  		0:00:00.93 for inferences.
% 117.83/117.99  		0:0:11.45 for the backtracking.
% 117.83/117.99  		0:1:42.55 for the reduction.
% 117.83/117.99  
% 117.83/117.99  
% 117.83/117.99  Here is a proof with depth 4, length 21 :
% 117.83/117.99  % SZS output start Refutation
% See solution above
% 117.83/117.99  Formulae used in the proof : prove_subclass_property1_1 prove_subclass_property1_2 subclass_members not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 intersection3
% 117.83/117.99  
%------------------------------------------------------------------------------