%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT014-1 : 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 00:07:31 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     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   21 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(codomain(codomain(a)),codomain(a)),
    file('CAT014-1.p',unknown),
    [] ).

cnf(12,axiom,
    identity_map(codomain(u)),
    file('CAT014-1.p',unknown),
    [] ).

cnf(14,axiom,
    defined(codomain(u),u),
    file('CAT014-1.p',unknown),
    [] ).

cnf(16,axiom,
    product(codomain(u),u,u),
    file('CAT014-1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ identity_map(u)
    | ~ defined(v,u)
    | product(v,u,v) ),
    file('CAT014-1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equal(x,w) ),
    file('CAT014-1.p',unknown),
    [] ).

cnf(37,plain,
    ( ~ product(codomain(u),u,v)
    | equal(v,u) ),
    inference(res,[status(thm),theory(equality)],[16,19]),
    [iquote('0:Res:16.0,19.0')] ).

cnf(48,plain,
    ( ~ identity_map(u)
    | ~ defined(codomain(u),u)
    | equal(codomain(u),u) ),
    inference(res,[status(thm),theory(equality)],[18,37]),
    [iquote('0:Res:18.2,37.0')] ).

cnf(50,plain,
    ( ~ identity_map(u)
    | equal(codomain(u),u) ),
    inference(mrr,[status(thm)],[48,14]),
    [iquote('0:MRR:48.1,14.0')] ).

cnf(61,plain,
    ( ~ identity_map(codomain(a))
    | ~ equal(codomain(a),codomain(a)) ),
    inference(spl,[status(thm),theory(equality)],[50,1]),
    [iquote('0:SpL:50.1,1.0')] ).

cnf(64,plain,
    ~ identity_map(codomain(a)),
    inference(obv,[status(thm),theory(equality)],[61]),
    [iquote('0:Obv:61.1')] ).

cnf(65,plain,
    $false,
    inference(ssi,[status(thm)],[64,12]),
    [iquote('0:SSi:64.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : CAT014-1 : 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 15:55:43 EDT 2022
% 0.12/0.33  % 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/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 37 clauses, backtracked 0 clauses, performed 0 splits and kept 38 clauses.
% 0.18/0.40  SPASS allocated 75639 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 12 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : prove_codomain_is_idempotent codomain_is_an_identity_map mapping_from_codomain_of_x_to_x product_on_codomain identity2 composition_is_well_defined
% 0.18/0.40  
%------------------------------------------------------------------------------