%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT011-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 00:07:30 EDT 2022

% Result   : Unsatisfiable 0.18s 0.40s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   6 unt;   0 nHn;  13 RR)
%            Number of literals    :   21 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   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('CAT011-4.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(domain__dfg(domain__dfg(a)),domain__dfg(a)),
    file('CAT011-4.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ there_exists(domain__dfg(u))
    | there_exists(u) ),
    file('CAT011-4.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ there_exists(compose(u,v))
    | equal(domain__dfg(u),codomain(v)) ),
    file('CAT011-4.p',unknown),
    [] ).

cnf(12,axiom,
    equal(compose(u,domain__dfg(u)),u),
    file('CAT011-4.p',unknown),
    [] ).

cnf(13,axiom,
    equal(compose(codomain(u),u),u),
    file('CAT011-4.p',unknown),
    [] ).

cnf(23,plain,
    ( ~ there_exists(u)
    | equal(domain__dfg(codomain(u)),codomain(u)) ),
    inference(spl,[status(thm),theory(equality)],[13,9]),
    [iquote('0:SpL:13.0,9.0')] ).

cnf(24,plain,
    ( ~ there_exists(u)
    | equal(codomain(domain__dfg(u)),domain__dfg(u)) ),
    inference(spl,[status(thm),theory(equality)],[12,9]),
    [iquote('0:SpL:12.0,9.0')] ).

cnf(33,plain,
    ( ~ there_exists(u)
    | ~ there_exists(domain__dfg(u))
    | equal(domain__dfg(domain__dfg(u)),domain__dfg(u)) ),
    inference(spr,[status(thm),theory(equality)],[24,23]),
    [iquote('0:SpR:24.1,23.1')] ).

cnf(37,plain,
    ( ~ there_exists(domain__dfg(u))
    | equal(domain__dfg(domain__dfg(u)),domain__dfg(u)) ),
    inference(mrr,[status(thm)],[33,6]),
    [iquote('0:MRR:33.0,6.1')] ).

cnf(46,plain,
    ( ~ there_exists(domain__dfg(a))
    | ~ equal(domain__dfg(a),domain__dfg(a)) ),
    inference(spl,[status(thm),theory(equality)],[37,2]),
    [iquote('0:SpL:37.1,2.0')] ).

cnf(49,plain,
    ~ there_exists(domain__dfg(a)),
    inference(obv,[status(thm),theory(equality)],[46]),
    [iquote('0:Obv:46.1')] ).

cnf(50,plain,
    $false,
    inference(mrr,[status(thm)],[49,1]),
    [iquote('0:MRR:49.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : CAT011-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 17:17:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.18/0.40  
% 0.18/0.40  SPASS V 3.9 
% 0.18/0.40  SPASS beiseite: Proof found.
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 33 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.18/0.40  SPASS allocated 75624 KBytes.
% 0.18/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.40  		0:00:00.03 for the input.
% 0.18/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40  		0:00:00.00 for inferences.
% 0.18/0.40  		0:00:00.00 for the backtracking.
% 0.18/0.40  		0:00:00.00 for the reduction.
% 0.18/0.40  
% 0.18/0.40  
% 0.18/0.40  Here is a proof with depth 3, length 13 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : assume_domain_exists prove_domain_is_idempotent domain_has_elements domain_codomain_composition1 compose_domain compose_codomain
% 0.18/0.40  
%------------------------------------------------------------------------------