TSTP Solution File: SET027-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET027-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 05:22:50 EDT 2022

% Result   : Unsatisfiable 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   8 unt;   1 nHn;  13 RR)
%            Number of literals    :   19 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subclass(x__dfg,y__dfg),
    file('SET027-6.p',unknown),
    [] ).

cnf(2,axiom,
    subclass(y__dfg,z__dfg),
    file('SET027-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ subclass(x__dfg,z__dfg),
    file('SET027-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET027-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET027-6.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET027-6.p',unknown),
    [] ).

cnf(97,plain,
    ( ~ member(u,y__dfg)
    | member(u,z__dfg) ),
    inference(res,[status(thm),theory(equality)],[2,4]),
    [iquote('0:Res:2.0,4.0')] ).

cnf(100,plain,
    ( ~ member(u,x__dfg)
    | member(u,y__dfg) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.0,4.0')] ).

cnf(103,plain,
    ~ member(not_subclass_element(x__dfg,z__dfg),z__dfg),
    inference(res,[status(thm),theory(equality)],[6,3]),
    [iquote('0:Res:6.1,3.0')] ).

cnf(104,plain,
    member(not_subclass_element(x__dfg,z__dfg),x__dfg),
    inference(res,[status(thm),theory(equality)],[5,3]),
    [iquote('0:Res:5.1,3.0')] ).

cnf(110,plain,
    ~ member(not_subclass_element(x__dfg,z__dfg),y__dfg),
    inference(res,[status(thm),theory(equality)],[97,103]),
    [iquote('0:Res:97.1,103.0')] ).

cnf(111,plain,
    ~ member(not_subclass_element(x__dfg,z__dfg),x__dfg),
    inference(res,[status(thm),theory(equality)],[100,110]),
    [iquote('0:Res:100.1,110.0')] ).

cnf(112,plain,
    $false,
    inference(mrr,[status(thm)],[111,104]),
    [iquote('0:MRR:111.0,104.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET027-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 02:24:08 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 103 clauses.
% 0.19/0.43  SPASS allocated 75749 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.04 for the input.
% 0.19/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.01 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 3, length 13 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : prove_transitivity_of_subclass_1 prove_transitivity_of_subclass_2 prove_transitivity_of_subclass_3 subclass_members not_subclass_members1 not_subclass_members2
% 0.19/0.43  
%------------------------------------------------------------------------------