%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET101-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 0.52s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :    7 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(17,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET101-7.p',unknown),
    [] ).

cnf(30,axiom,
    member(singleton(u),unordered_pair(v,singleton(u))),
    file('SET101-7.p',unknown),
    [] ).

cnf(55,axiom,
    ~ member(singleton(x__dfg),ordered_pair(x__dfg,y__dfg)),
    file('SET101-7.p',unknown),
    [] ).

cnf(68,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET101-7.p',unknown),
    [] ).

cnf(173,plain,
    member(singleton(u),unordered_pair(singleton(u),v)),
    inference(spr,[status(thm),theory(equality)],[17,30]),
    [iquote('0:SpR:17.0,30.0')] ).

cnf(909,plain,
    member(singleton(u),ordered_pair(u,v)),
    inference(spr,[status(thm),theory(equality)],[68,173]),
    [iquote('0:SpR:68.0,173.0')] ).

cnf(912,plain,
    $false,
    inference(unc,[status(thm)],[909,55]),
    [iquote('0:UnC:909.0,55.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET101-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n008.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat Jul  9 16:57:38 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.18/0.52  
% 0.18/0.52  SPASS V 3.9 
% 0.18/0.52  SPASS beiseite: Proof found.
% 0.18/0.52  % SZS status Theorem
% 0.18/0.52  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.52  SPASS derived 625 clauses, backtracked 63 clauses, performed 1 splits and kept 471 clauses.
% 0.18/0.52  SPASS allocated 76487 KBytes.
% 0.18/0.52  SPASS spent	0:00:00.18 on the problem.
% 0.18/0.52  		0:00:00.04 for the input.
% 0.18/0.52  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.52  		0:00:00.01 for inferences.
% 0.18/0.52  		0:00:00.00 for the backtracking.
% 0.18/0.52  		0:00:00.09 for the reduction.
% 0.18/0.52  
% 0.18/0.52  
% 0.18/0.52  Here is a proof with depth 2, length 7 :
% 0.18/0.52  % SZS output start Refutation
% See solution above
% 0.18/0.52  Formulae used in the proof : commutativity_of_unordered_pair corollary_1_to_singletons_are_sets prove_singleton_member_of_ordered_pair_1 ordered_pair
% 0.18/0.52  
%------------------------------------------------------------------------------