%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET025-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 05:22:47 EDT 2022

% Result   : Unsatisfiable 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   13 (   9 unt;   1 nHn;  13 RR)
%            Number of literals    :   18 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(32,axiom,
    ( ~ member(u,universal_class)
    | ~ equal(singleton(u),null_class) ),
    file('SET025-7.p',unknown),
    [] ).

cnf(35,axiom,
    ( member(u,universal_class)
    | equal(singleton(u),null_class) ),
    file('SET025-7.p',unknown),
    [] ).

cnf(54,axiom,
    ~ member(ordered_pair(x__dfg,y__dfg),universal_class),
    file('SET025-7.p',unknown),
    [] ).

cnf(55,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET025-7.p',unknown),
    [] ).

cnf(58,axiom,
    subclass(u,universal_class),
    file('SET025-7.p',unknown),
    [] ).

cnf(65,axiom,
    member(unordered_pair(u,v),universal_class),
    file('SET025-7.p',unknown),
    [] ).

cnf(67,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET025-7.p',unknown),
    [] ).

cnf(163,plain,
    ( ~ subclass(u,universal_class)
    | ~ member(ordered_pair(x__dfg,y__dfg),u) ),
    inference(res,[status(thm),theory(equality)],[55,54]),
    [iquote('0:Res:55.2,54.0')] ).

cnf(164,plain,
    ~ member(ordered_pair(x__dfg,y__dfg),u),
    inference(mrr,[status(thm)],[163,58]),
    [iquote('0:MRR:163.0,58.0')] ).

cnf(170,plain,
    equal(singleton(ordered_pair(x__dfg,y__dfg)),null_class),
    inference(res,[status(thm),theory(equality)],[35,164]),
    [iquote('0:Res:35.0,164.0')] ).

cnf(235,plain,
    ~ equal(singleton(unordered_pair(u,v)),null_class),
    inference(res,[status(thm),theory(equality)],[65,32]),
    [iquote('0:Res:65.0,32.0')] ).

cnf(986,plain,
    ~ equal(singleton(ordered_pair(u,v)),null_class),
    inference(spl,[status(thm),theory(equality)],[67,235]),
    [iquote('0:SpL:67.0,235.0')] ).

cnf(990,plain,
    $false,
    inference(unc,[status(thm)],[986,170]),
    [iquote('0:UnC:986.0,170.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET025-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n010.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 : Sun Jul 10 03:57:30 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.21/0.52  
% 0.21/0.52  SPASS V 3.9 
% 0.21/0.52  SPASS beiseite: Proof found.
% 0.21/0.52  % SZS status Theorem
% 0.21/0.52  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.52  SPASS derived 713 clauses, backtracked 1 clauses, performed 3 splits and kept 395 clauses.
% 0.21/0.52  SPASS allocated 76484 KBytes.
% 0.21/0.52  SPASS spent	0:00:00.16 on the problem.
% 0.21/0.52  		0:00:00.04 for the input.
% 0.21/0.52  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.52  		0:00:00.01 for inferences.
% 0.21/0.52  		0:00:00.00 for the backtracking.
% 0.21/0.52  		0:00:00.07 for the reduction.
% 0.21/0.52  
% 0.21/0.52  
% 0.21/0.52  Here is a proof with depth 2, length 13 :
% 0.21/0.52  % SZS output start Refutation
% See solution above
% 0.21/0.52  Formulae used in the proof : corollary_to_set_in_its_singleton singleton_is_null_class prove_ordered_pair_is_set_1 subclass_members class_elements_are_sets unordered_pairs_in_universal ordered_pair
% 0.21/0.52  
%------------------------------------------------------------------------------