%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT007-1 : 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 00:07:29 EDT 2022

% Result   : Unsatisfiable 0.12s 0.39s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   8 unt;   0 nHn;  11 RR)
%            Number of literals    :   17 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(codomain(b),domain__dfg(a)),
    file('CAT007-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ defined(a,b),
    file('CAT007-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ identity_map(u)
    | ~ defined(v,u)
    | ~ defined(u,w)
    | defined(v,w) ),
    file('CAT007-1.p',unknown),
    [] ).

cnf(12,axiom,
    identity_map(domain__dfg(u)),
    file('CAT007-1.p',unknown),
    [] ).

cnf(14,axiom,
    defined(u,domain__dfg(u)),
    file('CAT007-1.p',unknown),
    [] ).

cnf(15,axiom,
    defined(codomain(u),u),
    file('CAT007-1.p',unknown),
    [] ).

cnf(25,plain,
    ( ~ identity_map(u)
    | ~ defined(u,b)
    | ~ defined(a,u) ),
    inference(res,[status(thm),theory(equality)],[11,2]),
    [iquote('0:Res:11.3,2.0')] ).

cnf(28,plain,
    defined(domain__dfg(a),b),
    inference(spr,[status(thm),theory(equality)],[1,15]),
    [iquote('0:SpR:1.0,15.0')] ).

cnf(40,plain,
    ( ~ identity_map(domain__dfg(a))
    | ~ defined(a,domain__dfg(a)) ),
    inference(res,[status(thm),theory(equality)],[28,25]),
    [iquote('0:Res:28.0,25.1')] ).

cnf(42,plain,
    ~ defined(a,domain__dfg(a)),
    inference(ssi,[status(thm)],[40,12]),
    [iquote('0:SSi:40.0,12.0')] ).

cnf(43,plain,
    $false,
    inference(mrr,[status(thm)],[42,14]),
    [iquote('0:MRR:42.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : CAT007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % 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 23:13:28 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.39  
% 0.12/0.39  SPASS V 3.9 
% 0.12/0.39  SPASS beiseite: Proof found.
% 0.12/0.39  % SZS status Theorem
% 0.12/0.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.12/0.39  SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.12/0.39  SPASS allocated 75618 KBytes.
% 0.12/0.39  SPASS spent	0:00:00.05 on the problem.
% 0.12/0.39  		0:00:00.03 for the input.
% 0.12/0.39  		0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.39  		0:00:00.00 for inferences.
% 0.12/0.39  		0:00:00.00 for the backtracking.
% 0.12/0.39  		0:00:00.00 for the reduction.
% 0.12/0.39  
% 0.12/0.39  
% 0.12/0.39  Here is a proof with depth 2, length 11 :
% 0.12/0.39  % SZS output start Refutation
% See solution above
% 0.12/0.39  Formulae used in the proof : domain_of_a_equals_codomain_of_b prove_ab_is_defined category_theory_axiom6 domain_is_an_identity_map mapping_from_x_to_its_domain mapping_from_codomain_of_x_to_x
% 0.12/0.39  
%------------------------------------------------------------------------------