%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET101-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 05:24:03 EDT 2022

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ member(singleton(x__dfg),ordered_pair(x__dfg,y__dfg)),
    file('SET101-6.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ member(u,universal_class)
    | member(u,unordered_pair(u,v)) ),
    file('SET101-6.p',unknown),
    [] ).

cnf(12,axiom,
    member(unordered_pair(u,v),universal_class),
    file('SET101-6.p',unknown),
    [] ).

cnf(13,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET101-6.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET101-6.p',unknown),
    [] ).

cnf(104,plain,
    member(singleton(u),universal_class),
    inference(spr,[status(thm),theory(equality)],[13,12]),
    [iquote('0:SpR:13.0,12.0')] ).

cnf(202,plain,
    ( ~ member(singleton(u),universal_class)
    | member(singleton(u),ordered_pair(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[14,10]),
    [iquote('0:SpR:14.0,10.1')] ).

cnf(206,plain,
    member(singleton(u),ordered_pair(u,v)),
    inference(mrr,[status(thm)],[202,104]),
    [iquote('0:MRR:202.0,104.0')] ).

cnf(207,plain,
    $false,
    inference(unc,[status(thm)],[206,1]),
    [iquote('0:UnC:206.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET101-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n028.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 18:48:41 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  
% 0.18/0.44  SPASS V 3.9 
% 0.18/0.44  SPASS beiseite: Proof found.
% 0.18/0.44  % SZS status Theorem
% 0.18/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.44  SPASS derived 99 clauses, backtracked 0 clauses, performed 0 splits and kept 167 clauses.
% 0.18/0.44  SPASS allocated 75906 KBytes.
% 0.18/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.44  		0:00:00.04 for the input.
% 0.18/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.44  		0:00:00.00 for inferences.
% 0.18/0.44  		0:00:00.00 for the backtracking.
% 0.18/0.44  		0:00:00.02 for the reduction.
% 0.18/0.44  
% 0.18/0.44  
% 0.18/0.44  Here is a proof with depth 1, length 9 :
% 0.18/0.44  % SZS output start Refutation
% See solution above
% 0.18/0.44  Formulae used in the proof : prove_singleton_member_of_ordered_pair_1 unordered_pair2 unordered_pairs_in_universal singleton_set ordered_pair
% 0.18/0.44  
%------------------------------------------------------------------------------