%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT012-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 00:07:31 EDT 2022

% Result   : Unsatisfiable 0.12s 0.40s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    there_exists(domain__dfg(a)),
    file('CAT012-4.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(codomain(domain__dfg(a)),domain__dfg(a)),
    file('CAT012-4.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ there_exists(domain__dfg(u))
    | there_exists(u) ),
    file('CAT012-4.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ there_exists(compose(u,v))
    | equal(domain__dfg(u),codomain(v)) ),
    file('CAT012-4.p',unknown),
    [] ).

cnf(12,axiom,
    equal(compose(u,domain__dfg(u)),u),
    file('CAT012-4.p',unknown),
    [] ).

cnf(16,plain,
    ~ there_exists(compose(a,domain__dfg(a))),
    inference(res,[status(thm),theory(equality)],[9,2]),
    [iquote('0:Res:9.1,2.0')] ).

cnf(17,plain,
    ~ there_exists(a),
    inference(rew,[status(thm),theory(equality)],[12,16]),
    [iquote('0:Rew:12.0,16.0')] ).

cnf(18,plain,
    there_exists(a),
    inference(res,[status(thm),theory(equality)],[1,6]),
    [iquote('0:Res:1.0,6.0')] ).

cnf(19,plain,
    $false,
    inference(mrr,[status(thm)],[18,17]),
    [iquote('0:MRR:18.0,17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : CAT012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n020.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 20:34:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.40  
% 0.12/0.40  SPASS V 3.9 
% 0.12/0.40  SPASS beiseite: Proof found.
% 0.12/0.40  % SZS status Theorem
% 0.12/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.12/0.40  SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.12/0.40  SPASS allocated 75592 KBytes.
% 0.12/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.12/0.40  		0:00:00.03 for the input.
% 0.12/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.40  		0:00:00.00 for inferences.
% 0.12/0.40  		0:00:00.00 for the backtracking.
% 0.12/0.40  		0:00:00.00 for the reduction.
% 0.12/0.40  
% 0.12/0.40  
% 0.12/0.40  Here is a proof with depth 1, length 9 :
% 0.12/0.40  % SZS output start Refutation
% See solution above
% 0.12/0.40  Formulae used in the proof : assume_domain_exists prove_codomain_of_domain_is_domain domain_has_elements domain_codomain_composition1 compose_domain
% 0.12/0.40  
%------------------------------------------------------------------------------