%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 : Fri Jul 15 00:07:32 EDT 2022

% Result   : Unsatisfiable 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :    8 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    there_exists(a),
    file('CAT016-4.p',unknown),
    [] ).

cnf(2,axiom,
    ~ there_exists(domain__dfg(a)),
    file('CAT016-4.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ there_exists(compose(u,v))
    | there_exists(domain__dfg(u)) ),
    file('CAT016-4.p',unknown),
    [] ).

cnf(12,axiom,
    equal(compose(u,domain__dfg(u)),u),
    file('CAT016-4.p',unknown),
    [] ).

cnf(14,plain,
    ~ there_exists(compose(a,u)),
    inference(res,[status(thm),theory(equality)],[8,2]),
    [iquote('0:Res:8.1,2.0')] ).

cnf(20,plain,
    ~ there_exists(a),
    inference(spl,[status(thm),theory(equality)],[12,14]),
    [iquote('0:SpL:12.0,14.0')] ).

cnf(21,plain,
    $false,
    inference(mrr,[status(thm)],[20,1]),
    [iquote('0:MRR:20.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n029.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 May 29 23:31:28 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses.
% 0.18/0.41  SPASS allocated 75589 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.04 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.00 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 2, length 7 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : assume_a_exists prove_domain_of_a_exists composition_implies_domain compose_domain
% 0.18/0.41  
%------------------------------------------------------------------------------