TSTP Solution File: SET103-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET103-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 05:24:05 EDT 2022

% Result   : Unsatisfiable 0.22s 0.52s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   18 (   9 unt;   6 nHn;  18 RR)
%            Number of literals    :   31 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(unordered_pair(singleton(x__dfg),unordered_pair(x__dfg,null_class)),ordered_pair(x__dfg,y__dfg)),
    file('SET103-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(y__dfg,universal_class),
    file('SET103-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET103-6.p',unknown),
    [] ).

cnf(6,axiom,
    subclass(u,universal_class),
    file('SET103-6.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET103-6.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET103-6.p',unknown),
    [] ).

cnf(15,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET103-6.p',unknown),
    [] ).

cnf(68,axiom,
    ( equal(u,null_class)
    | member(regular(u),u) ),
    file('SET103-6.p',unknown),
    [] ).

cnf(101,plain,
    ( ~ subclass(u,universal_class)
    | ~ member(y__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Res:3.2,2.0')] ).

cnf(109,plain,
    ~ member(y__dfg,u),
    inference(mrr,[status(thm)],[101,6]),
    [iquote('0:MRR:101.0,6.0')] ).

cnf(463,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v)
    | equal(u,v) ),
    inference(spl,[status(thm),theory(equality)],[14,10]),
    [iquote('0:SpL:14.0,10.0')] ).

cnf(474,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[463]),
    [iquote('0:Obv:463.1')] ).

cnf(477,plain,
    ( equal(singleton(u),null_class)
    | equal(regular(singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[68,474]),
    [iquote('0:Res:68.1,474.0')] ).

cnf(555,plain,
    ( equal(singleton(u),null_class)
    | equal(singleton(u),null_class)
    | member(u,singleton(u)) ),
    inference(spr,[status(thm),theory(equality)],[477,68]),
    [iquote('0:SpR:477.1,68.1')] ).

cnf(559,plain,
    ( equal(singleton(u),null_class)
    | member(u,singleton(u)) ),
    inference(obv,[status(thm),theory(equality)],[555]),
    [iquote('0:Obv:555.0')] ).

cnf(562,plain,
    equal(singleton(y__dfg),null_class),
    inference(res,[status(thm),theory(equality)],[559,109]),
    [iquote('0:Res:559.1,109.0')] ).

cnf(577,plain,
    equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,y__dfg)),
    inference(spr,[status(thm),theory(equality)],[562,15]),
    [iquote('0:SpR:562.0,15.0')] ).

cnf(589,plain,
    $false,
    inference(unc,[status(thm)],[577,1]),
    [iquote('0:UnC:577.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SET103-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.15  % Command  : run_spass %d %s
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Sun Jul 10 04:03:17 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.22/0.52  
% 0.22/0.52  SPASS V 3.9 
% 0.22/0.52  SPASS beiseite: Proof found.
% 0.22/0.52  % SZS status Theorem
% 0.22/0.52  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.22/0.52  SPASS derived 432 clauses, backtracked 0 clauses, performed 0 splits and kept 399 clauses.
% 0.22/0.52  SPASS allocated 76337 KBytes.
% 0.22/0.52  SPASS spent	0:00:00.14 on the problem.
% 0.22/0.52  		0:00:00.04 for the input.
% 0.22/0.52  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.52  		0:00:00.01 for inferences.
% 0.22/0.52  		0:00:00.00 for the backtracking.
% 0.22/0.52  		0:00:00.07 for the reduction.
% 0.22/0.52  
% 0.22/0.52  
% 0.22/0.52  Here is a proof with depth 5, length 18 :
% 0.22/0.52  % SZS output start Refutation
% See solution above
% 0.22/0.52  Formulae used in the proof : prove_property_1_of_ordered_pair_1 prove_property_1_of_ordered_pair_2 subclass_members class_elements_are_sets unordered_pair_member singleton_set ordered_pair regularity1
% 0.22/0.52  
%------------------------------------------------------------------------------