%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET025-9 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 05:22:48 EDT 2022

% Result   : Unsatisfiable 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ordered_pair_predicate(a),
    file('SET025-9.p',unknown),
    [] ).

cnf(2,axiom,
    ~ little_set(a),
    file('SET025-9.p',unknown),
    [] ).

cnf(10,axiom,
    little_set(non_ordered_pair(u,v)),
    file('SET025-9.p',unknown),
    [] ).

cnf(12,axiom,
    equal(non_ordered_pair(singleton_set(u),non_ordered_pair(u,v)),ordered_pair(u,v)),
    file('SET025-9.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ ordered_pair_predicate(u)
    | equal(ordered_pair(f2(u),f3(u)),u) ),
    file('SET025-9.p',unknown),
    [] ).

cnf(427,plain,
    little_set(ordered_pair(u,v)),
    inference(spr,[status(thm),theory(equality)],[12,10]),
    [iquote('0:SpR:12.0,10.0')] ).

cnf(432,plain,
    ( ~ ordered_pair_predicate(u)
    | little_set(u) ),
    inference(spr,[status(thm),theory(equality)],[15,427]),
    [iquote('0:SpR:15.1,427.0')] ).

cnf(438,plain,
    ~ ordered_pair_predicate(a),
    inference(res,[status(thm),theory(equality)],[432,2]),
    [iquote('0:Res:432.1,2.0')] ).

cnf(440,plain,
    $false,
    inference(ssi,[status(thm)],[438,1]),
    [iquote('0:SSi:438.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET025-9 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 17:17:57 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.47  
% 0.18/0.47  SPASS V 3.9 
% 0.18/0.47  SPASS beiseite: Proof found.
% 0.18/0.47  % SZS status Theorem
% 0.18/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.47  SPASS derived 279 clauses, backtracked 8 clauses, performed 3 splits and kept 389 clauses.
% 0.18/0.47  SPASS allocated 76177 KBytes.
% 0.18/0.47  SPASS spent	0:00:00.13 on the problem.
% 0.18/0.47  		0:00:00.04 for the input.
% 0.18/0.47  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47  		0:00:00.01 for inferences.
% 0.18/0.47  		0:00:00.00 for the backtracking.
% 0.18/0.47  		0:00:00.06 for the reduction.
% 0.18/0.47  
% 0.18/0.47  
% 0.18/0.47  Here is a proof with depth 3, length 9 :
% 0.18/0.47  % SZS output start Refutation
% See solution above
% 0.18/0.47  Formulae used in the proof : an_ordered_pair_predicate prove_predicate_is_small non_ordered_pair4 ordered_pair ordered_pair_predicate3
% 0.18/0.47  
%------------------------------------------------------------------------------