%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET103-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 05:24:05 EDT 2022

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   1 nHn;   7 RR)
%            Number of literals    :    8 (   0 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(35,axiom,
    ( member(u,universal_class)
    | equal(singleton(u),null_class) ),
    file('SET103-7.p',unknown),
    [] ).

cnf(57,axiom,
    ~ equal(unordered_pair(singleton(x__dfg),unordered_pair(x__dfg,null_class)),ordered_pair(x__dfg,y__dfg)),
    file('SET103-7.p',unknown),
    [] ).

cnf(58,axiom,
    ~ member(y__dfg,universal_class),
    file('SET103-7.p',unknown),
    [] ).

cnf(71,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET103-7.p',unknown),
    [] ).

cnf(159,plain,
    equal(singleton(y__dfg),null_class),
    inference(res,[status(thm),theory(equality)],[35,58]),
    [iquote('0:Res:35.0,58.0')] ).

cnf(1198,plain,
    equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,y__dfg)),
    inference(spr,[status(thm),theory(equality)],[159,71]),
    [iquote('0:SpR:159.0,71.0')] ).

cnf(1214,plain,
    $false,
    inference(unc,[status(thm)],[1198,57]),
    [iquote('0:UnC:1198.0,57.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET103-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n012.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 09:20:58 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.55  
% 0.20/0.55  SPASS V 3.9 
% 0.20/0.55  SPASS beiseite: Proof found.
% 0.20/0.55  % SZS status Theorem
% 0.20/0.55  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.55  SPASS derived 876 clauses, backtracked 0 clauses, performed 2 splits and kept 478 clauses.
% 0.20/0.55  SPASS allocated 76725 KBytes.
% 0.20/0.55  SPASS spent	0:00:00.18 on the problem.
% 0.20/0.55  		0:00:00.04 for the input.
% 0.20/0.55  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55  		0:00:00.01 for inferences.
% 0.20/0.55  		0:00:00.00 for the backtracking.
% 0.20/0.55  		0:00:00.09 for the reduction.
% 0.20/0.55  
% 0.20/0.55  
% 0.20/0.55  Here is a proof with depth 2, length 7 :
% 0.20/0.55  % SZS output start Refutation
% See solution above
% 0.20/0.55  Formulae used in the proof : singleton_is_null_class prove_property_1_of_ordered_pair_1 prove_property_1_of_ordered_pair_2 ordered_pair
% 0.20/0.55  
%------------------------------------------------------------------------------