%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET081-6 : 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 05:23:43 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   6 unt;   1 nHn;   8 RR)
%            Number of literals    :   11 (   0 equ;   5 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;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(y__dfg,singleton(x__dfg)),
    file('SET081-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(x__dfg,y__dfg),
    file('SET081-6.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET081-6.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET081-6.p',unknown),
    [] ).

cnf(101,plain,
    ( ~ member(y__dfg,unordered_pair(u,x__dfg))
    | equal(y__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[10,2]),
    [iquote('0:Res:10.2,2.0')] ).

cnf(111,plain,
    ~ member(y__dfg,unordered_pair(x__dfg,x__dfg)),
    inference(res,[status(thm),theory(equality)],[101,2]),
    [iquote('0:Res:101.1,2.0')] ).

cnf(115,plain,
    ~ member(y__dfg,singleton(x__dfg)),
    inference(rew,[status(thm),theory(equality)],[14,111]),
    [iquote('0:Rew:14.0,111.0')] ).

cnf(116,plain,
    $false,
    inference(mrr,[status(thm)],[115,1]),
    [iquote('0:MRR:115.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET081-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.12  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 09:07:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 100 clauses.
% 0.19/0.42  SPASS allocated 75745 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 8 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : prove_only_member_in_singleton_1 prove_only_member_in_singleton_2 unordered_pair_member singleton_set
% 0.19/0.42  
%------------------------------------------------------------------------------