%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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  : 300s
% DateTime : Wed May 31 12:33:42 EDT 2023

% Result   : Unsatisfiable 7.69s 1.38s
% Output   : CNFRefutation 8.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   38 (  11 unt;   0 def)
%            Number of atoms       :   75 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   73 (  36   ~;  34   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (;  34   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f86,axiom,
    ! [Xf] :
      ( ~ function(Xf)
      | relation(Xf) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f87,axiom,
    ! [Xf] :
      ( ~ function(Xf)
      | single_valued_set(Xf) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f88,axiom,
    ! [Xf] :
      ( function(Xf)
      | ~ relation(Xf)
      | ~ single_valued_set(Xf) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f145,axiom,
    ! [X,Y] :
      ( ~ subset(X,Y)
      | ~ subset(Y,X)
      | X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f165,axiom,
    ! [Xf,X,Xg] :
      ( ~ function(Xf)
      | ~ member(X,domain_of(Xf))
      | subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f166,axiom,
    ! [Xf,Xg,X] :
      ( ~ function(Xf)
      | subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f167,hypothesis,
    function(a_function),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f168,hypothesis,
    member(a,domain_of(a_function)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f169,negated_conjecture,
    apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f276,plain,
    ! [X0] :
      ( ~ function(X0)
      | relation(X0) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f277,plain,
    ! [X0] :
      ( ~ function(X0)
      | single_valued_set(X0) ),
    inference(cnf_transformation,[status(esa)],[f87]) ).

fof(f278,plain,
    ! [X0] :
      ( function(X0)
      | ~ relation(X0)
      | ~ single_valued_set(X0) ),
    inference(cnf_transformation,[status(esa)],[f88]) ).

fof(f353,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f377,plain,
    ! [Xf,X] :
      ( ~ function(Xf)
      | ~ member(X,domain_of(Xf))
      | ! [Xg] : subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
    inference(miniscoping,[status(esa)],[f165]) ).

fof(f378,plain,
    ! [X0,X1,X2] :
      ( ~ function(X0)
      | ~ member(X1,domain_of(X0))
      | subset(apply(X2,apply(X0,X1)),apply(compose(X2,X0),X1)) ),
    inference(cnf_transformation,[status(esa)],[f377]) ).

fof(f379,plain,
    ! [Xf] :
      ( ~ function(Xf)
      | ! [Xg,X] : subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ),
    inference(miniscoping,[status(esa)],[f166]) ).

fof(f380,plain,
    ! [X0,X1,X2] :
      ( ~ function(X0)
      | subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2))) ),
    inference(cnf_transformation,[status(esa)],[f379]) ).

fof(f381,plain,
    function(a_function),
    inference(cnf_transformation,[status(esa)],[f167]) ).

fof(f382,plain,
    member(a,domain_of(a_function)),
    inference(cnf_transformation,[status(esa)],[f168]) ).

fof(f383,plain,
    apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
    inference(cnf_transformation,[status(esa)],[f169]) ).

fof(f401,plain,
    relation(a_function),
    inference(resolution,[status(thm)],[f276,f381]) ).

fof(f406,plain,
    single_valued_set(a_function),
    inference(resolution,[status(thm)],[f277,f381]) ).

fof(f458,plain,
    ( spl0_4
  <=> function(a_function) ),
    introduced(split_symbol_definition) ).

fof(f461,plain,
    ( spl0_5
  <=> relation(a_function) ),
    introduced(split_symbol_definition) ).

fof(f463,plain,
    ( ~ relation(a_function)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f461]) ).

fof(f464,plain,
    ( function(a_function)
    | ~ relation(a_function) ),
    inference(resolution,[status(thm)],[f278,f406]) ).

fof(f465,plain,
    ( spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f464,f458,f461]) ).

fof(f476,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f463,f401]) ).

fof(f477,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f476]) ).

fof(f12381,plain,
    ! [X0,X1,X2] :
      ( ~ function(X0)
      | ~ member(X1,domain_of(X0))
      | ~ subset(apply(compose(X2,X0),X1),apply(X2,apply(X0,X1)))
      | apply(compose(X2,X0),X1) = apply(X2,apply(X0,X1)) ),
    inference(resolution,[status(thm)],[f378,f353]) ).

fof(f12382,plain,
    ! [X0,X1,X2] :
      ( ~ function(X0)
      | ~ member(X1,domain_of(X0))
      | apply(compose(X2,X0),X1) = apply(X2,apply(X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f12381,f380]) ).

fof(f14608,plain,
    ( spl0_556
  <=> member(a,domain_of(a_function)) ),
    introduced(split_symbol_definition) ).

fof(f14610,plain,
    ( ~ member(a,domain_of(a_function))
    | spl0_556 ),
    inference(component_clause,[status(thm)],[f14608]) ).

fof(f14611,plain,
    ( ~ function(a_function)
    | ~ member(a,domain_of(a_function)) ),
    inference(resolution,[status(thm)],[f12382,f383]) ).

fof(f14612,plain,
    ( ~ spl0_4
    | ~ spl0_556 ),
    inference(split_clause,[status(thm)],[f14611,f458,f14608]) ).

fof(f14620,plain,
    ( $false
    | spl0_556 ),
    inference(forward_subsumption_resolution,[status(thm)],[f14610,f382]) ).

fof(f14621,plain,
    spl0_556,
    inference(contradiction_clause,[status(thm)],[f14620]) ).

fof(f14622,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f465,f477,f14612,f14621]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n014.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  : 300
% 0.12/0.33  % DateTime : Tue May 30 10:13:33 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 7.69/1.38  % Refutation found
% 7.69/1.38  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.69/1.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.26/1.43  % Elapsed time: 1.084277 seconds
% 8.26/1.43  % CPU time: 8.324640 seconds
% 8.26/1.43  % Memory used: 131.610 MB
%------------------------------------------------------------------------------