TSTP Solution File: SET082+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 05:23:44 EDT 2022

% Result   : Theorem 0.57s 0.75s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   20 (   9 unt;   6 nHn;  20 RR)
%            Number of literals    :   35 (   0 equ;  13 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    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    subclass(u,universal_class),
    file('SET082+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ member(skc3,universal_class),
    file('SET082+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(singleton(skc3),null_class),
    file('SET082+1.p',unknown),
    [] ).

cnf(10,axiom,
    member(unordered_pair(u,v),universal_class),
    file('SET082+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET082+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( equal(u,null_class)
    | member(skf9(u),u) ),
    file('SET082+1.p',unknown),
    [] ).

cnf(55,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET082+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET082+1.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ member(u,v)
    | ~ member(w,u)
    | member(w,sum_class(v)) ),
    file('SET082+1.p',unknown),
    [] ).

cnf(107,plain,
    ( ~ subclass(u,universal_class)
    | ~ member(skc3,u) ),
    inference(res,[status(thm),theory(equality)],[55,5]),
    [iquote('0:Res:55.2,5.0')] ).

cnf(118,plain,
    ~ member(skc3,u),
    inference(mrr,[status(thm)],[107,3]),
    [iquote('0:MRR:107.0,3.0')] ).

cnf(125,plain,
    member(singleton(u),universal_class),
    inference(spr,[status(thm),theory(equality)],[14,10]),
    [iquote('0:SpR:14.0,10.0')] ).

cnf(761,plain,
    ( ~ member(u,singleton(v))
    | member(u,sum_class(universal_class)) ),
    inference(res,[status(thm),theory(equality)],[125,66]),
    [iquote('0:Res:125.0,66.0')] ).

cnf(868,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v)
    | equal(u,v) ),
    inference(spl,[status(thm),theory(equality)],[14,63]),
    [iquote('0:SpL:14.0,63.0')] ).

cnf(882,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[868]),
    [iquote('0:Obv:868.1')] ).

cnf(930,plain,
    ( equal(singleton(u),null_class)
    | equal(skf9(singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[22,882]),
    [iquote('0:Res:22.1,882.0')] ).

cnf(1778,plain,
    ( equal(singleton(u),null_class)
    | member(skf9(singleton(u)),sum_class(universal_class)) ),
    inference(res,[status(thm),theory(equality)],[22,761]),
    [iquote('0:Res:22.1,761.0')] ).

cnf(1788,plain,
    ( equal(singleton(u),null_class)
    | member(u,sum_class(universal_class)) ),
    inference(rew,[status(thm),theory(equality)],[930,1778]),
    [iquote('0:Rew:930.1,1778.1')] ).

cnf(1798,plain,
    equal(singleton(skc3),null_class),
    inference(res,[status(thm),theory(equality)],[1788,118]),
    [iquote('0:Res:1788.1,118.0')] ).

cnf(1818,plain,
    $false,
    inference(mrr,[status(thm)],[1798,9]),
    [iquote('0:MRR:1798.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n005.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 22:14:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.57/0.75  
% 0.57/0.75  SPASS V 3.9 
% 0.57/0.75  SPASS beiseite: Proof found.
% 0.57/0.75  % SZS status Theorem
% 0.57/0.75  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.57/0.75  SPASS derived 1515 clauses, backtracked 4 clauses, performed 1 splits and kept 1028 clauses.
% 0.57/0.75  SPASS allocated 99151 KBytes.
% 0.57/0.75  SPASS spent	0:00:00.40 on the problem.
% 0.57/0.75  		0:00:00.04 for the input.
% 0.57/0.75  		0:00:00.05 for the FLOTTER CNF translation.
% 0.57/0.75  		0:00:00.03 for inferences.
% 0.57/0.75  		0:00:00.00 for the backtracking.
% 0.57/0.75  		0:00:00.25 for the reduction.
% 0.57/0.75  
% 0.57/0.75  
% 0.57/0.75  Here is a proof with depth 4, length 20 :
% 0.57/0.75  % SZS output start Refutation
% See solution above
% 0.57/0.75  Formulae used in the proof : class_elements_are_sets singleton_is_null_class unordered_pair singleton_set_defn regularity infinity subclass_defn unordered_pair_defn sum_class_defn
% 0.57/0.75  
%------------------------------------------------------------------------------