%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET081+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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   : Theorem 0.21s 0.47s
% Output   : Refutation 0.21s
% 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(5,axiom,
    member(skc5,singleton(skc4)),
    file('SET081+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(skc5,skc4),
    file('SET081+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET081+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET081+1.p',unknown),
    [] ).

cnf(94,plain,
    ( ~ member(skc5,unordered_pair(u,skc4))
    | equal(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[63,6]),
    [iquote('0:Res:63.2,6.0')] ).

cnf(113,plain,
    ~ member(skc5,unordered_pair(skc4,skc4)),
    inference(res,[status(thm),theory(equality)],[94,6]),
    [iquote('0:Res:94.1,6.0')] ).

cnf(117,plain,
    ~ member(skc5,singleton(skc4)),
    inference(rew,[status(thm),theory(equality)],[13,113]),
    [iquote('0:Rew:13.0,113.0')] ).

cnf(118,plain,
    $false,
    inference(mrr,[status(thm)],[117,5]),
    [iquote('0:MRR:117.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET081+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.13/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n006.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 06:02:20 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.21/0.47  
% 0.21/0.47  SPASS V 3.9 
% 0.21/0.47  SPASS beiseite: Proof found.
% 0.21/0.47  % SZS status Theorem
% 0.21/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.47  SPASS derived 16 clauses, backtracked 0 clauses, performed 0 splits and kept 101 clauses.
% 0.21/0.47  SPASS allocated 98329 KBytes.
% 0.21/0.47  SPASS spent	0:00:00.12 on the problem.
% 0.21/0.47  		0:00:00.04 for the input.
% 0.21/0.47  		0:00:00.05 for the FLOTTER CNF translation.
% 0.21/0.47  		0:00:00.00 for inferences.
% 0.21/0.47  		0:00:00.00 for the backtracking.
% 0.21/0.47  		0:00:00.00 for the reduction.
% 0.21/0.47  
% 0.21/0.47  
% 0.21/0.47  Here is a proof with depth 2, length 8 :
% 0.21/0.47  % SZS output start Refutation
% See solution above
% 0.21/0.47  Formulae used in the proof : only_member_in_singleton singleton_set_defn unordered_pair_defn
% 0.21/0.47  
%------------------------------------------------------------------------------