%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET024-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 05:22:45 EDT 2022

% Result   : Unsatisfiable 2.44s 2.65s
% Output   : Refutation 2.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   13 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    little_set(a),
    file('SET024-4.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(a,singleton_set(a)),
    file('SET024-4.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ little_set(u)
    | ~ equal(u,v)
    | member(u,non_ordered_pair(w,v)) ),
    file('SET024-4.p',unknown),
    [] ).

cnf(11,axiom,
    equal(non_ordered_pair(u,u),singleton_set(u)),
    file('SET024-4.p',unknown),
    [] ).

cnf(1430,plain,
    ( ~ little_set(u)
    | ~ equal(u,v)
    | member(u,singleton_set(v)) ),
    inference(spr,[status(thm),theory(equality)],[11,9]),
    [iquote('0:SpR:11.0,9.2')] ).

cnf(9110,plain,
    ( ~ little_set(a)
    | ~ equal(a,a) ),
    inference(res,[status(thm),theory(equality)],[1430,2]),
    [iquote('0:Res:1430.2,2.0')] ).

cnf(9111,plain,
    ~ little_set(a),
    inference(obv,[status(thm),theory(equality)],[9110]),
    [iquote('0:Obv:9110.1')] ).

cnf(9112,plain,
    $false,
    inference(ssi,[status(thm)],[9111,1]),
    [iquote('0:SSi:9111.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET024-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n015.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 : Sat Jul  9 20:28:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.44/2.65  
% 2.44/2.65  SPASS V 3.9 
% 2.44/2.65  SPASS beiseite: Proof found.
% 2.44/2.65  % SZS status Theorem
% 2.44/2.65  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.44/2.65  SPASS derived 7323 clauses, backtracked 1342 clauses, performed 15 splits and kept 4921 clauses.
% 2.44/2.65  SPASS allocated 83435 KBytes.
% 2.44/2.65  SPASS spent	0:00:02.25 on the problem.
% 2.44/2.65  		0:00:00.04 for the input.
% 2.44/2.65  		0:00:00.00 for the FLOTTER CNF translation.
% 2.44/2.65  		0:00:00.09 for inferences.
% 2.44/2.65  		0:00:00.11 for the backtracking.
% 2.44/2.65  		0:00:01.92 for the reduction.
% 2.44/2.65  
% 2.44/2.65  
% 2.44/2.65  Here is a proof with depth 2, length 8 :
% 2.44/2.65  % SZS output start Refutation
% See solution above
% 2.44/2.65  Formulae used in the proof : a_little_set prove_membership_of_singleton_set non_ordered_pair3 singleton_set
% 2.44/2.65  
%------------------------------------------------------------------------------