%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 8.11s 8.32s
% Output   : Refutation 8.11s
% 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(9,axiom,
    little_set(a),
    file('SET024-3.p',unknown),
    [] ).

cnf(10,axiom,
    ~ member(a,singleton_set(a)),
    file('SET024-3.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ little_set(u)
    | ~ equal(u,v)
    | member(u,non_ordered_pair(w,v)) ),
    file('SET024-3.p',unknown),
    [] ).

cnf(19,axiom,
    equal(non_ordered_pair(u,u),singleton_set(u)),
    file('SET024-3.p',unknown),
    [] ).

cnf(3386,plain,
    ( ~ little_set(u)
    | ~ equal(u,v)
    | member(u,singleton_set(v)) ),
    inference(spr,[status(thm),theory(equality)],[19,17]),
    [iquote('0:SpR:19.0,17.2')] ).

cnf(19809,plain,
    ( ~ little_set(a)
    | ~ equal(a,a) ),
    inference(res,[status(thm),theory(equality)],[3386,10]),
    [iquote('0:Res:3386.2,10.0')] ).

cnf(19810,plain,
    ~ little_set(a),
    inference(obv,[status(thm),theory(equality)],[19809]),
    [iquote('0:Obv:19809.1')] ).

cnf(19811,plain,
    $false,
    inference(ssi,[status(thm)],[19810,9]),
    [iquote('0:SSi:19810.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 20:31:16 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 8.11/8.32  
% 8.11/8.32  SPASS V 3.9 
% 8.11/8.32  SPASS beiseite: Proof found.
% 8.11/8.32  % SZS status Theorem
% 8.11/8.32  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 8.11/8.32  SPASS derived 15921 clauses, backtracked 4815 clauses, performed 25 splits and kept 11792 clauses.
% 8.11/8.32  SPASS allocated 90888 KBytes.
% 8.11/8.32  SPASS spent	0:00:07.81 on the problem.
% 8.11/8.32  		0:00:00.04 for the input.
% 8.11/8.32  		0:00:00.00 for the FLOTTER CNF translation.
% 8.11/8.32  		0:00:00.20 for inferences.
% 8.11/8.32  		0:00:00.45 for the backtracking.
% 8.11/8.32  		0:00:06.90 for the reduction.
% 8.11/8.32  
% 8.11/8.32  
% 8.11/8.32  Here is a proof with depth 2, length 8 :
% 8.11/8.32  % SZS output start Refutation
% See solution above
% 8.11/8.32  Formulae used in the proof : a_little_set prove_membership_of_singleton_set non_ordered_pair3 singleton_set
% 8.11/8.32  
%------------------------------------------------------------------------------