%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET822-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 12:35:16 EDT 2023

% Result   : Unsatisfiable 0.18s 0.55s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   19 (   9 unt;   0 def)
%            Number of atoms       :   33 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   29 (  15   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   38 (;  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [V_a,V_b,V_A,T_a] :
      ( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
      | c_in(V_a,V_A,T_a)
      | V_a = V_b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,negated_conjecture,
    v_P(v_f(v_b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,negated_conjecture,
    ! [V_U,V_V] :
      ( ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint)
      | c_in(v_x(V_U,V_V),V_V,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ! [V_U,V_V] :
      ( ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint)
      | ~ v_P(v_x(V_U,V_V)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,plain,
    ! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f8,plain,
    ! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f9,plain,
    ! [V_a,V_b] :
      ( ! [V_A,T_a] :
          ( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
          | c_in(V_a,V_A,T_a) )
      | V_a = V_b ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f10,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_insert(X1,X2,X3),X3)
      | c_in(X0,X2,X3)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f11,plain,
    v_P(v_f(v_b)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
      | c_in(v_x(X0,X1),X1,tc_IntDef_Oint) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
      | ~ v_P(v_x(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( c_in(v_x(X0,c_insert(X1,X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint)
      | v_x(X0,c_insert(X1,X2,tc_IntDef_Oint)) = X1
      | ~ c_in(v_f(X0),c_insert(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(resolution,[status(thm)],[f10,f12]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( c_in(v_x(X0,c_insert(v_f(X0),X1,tc_IntDef_Oint)),X1,tc_IntDef_Oint)
      | v_x(X0,c_insert(v_f(X0),X1,tc_IntDef_Oint)) = v_f(X0) ),
    inference(resolution,[status(thm)],[f15,f8]) ).

fof(f18,plain,
    ! [X0] : v_x(X0,c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint)) = v_f(X0),
    inference(resolution,[status(thm)],[f16,f7]) ).

fof(f20,plain,
    ! [X0] :
      ( ~ c_in(v_f(X0),c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ v_P(v_f(X0)) ),
    inference(paramodulation,[status(thm)],[f18,f13]) ).

fof(f21,plain,
    ! [X0] : ~ v_P(v_f(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f20,f8]) ).

fof(f22,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f11,f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET822-2 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.31  % Computer : n013.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.31  % DateTime : Tue May 30 10:17:35 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 0.12/0.32  % Drodi V3.5.1
% 0.18/0.55  % Refutation found
% 0.18/0.55  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.55  % Elapsed time: 0.011032 seconds
% 0.18/0.55  % CPU time: 0.011774 seconds
% 0.18/0.55  % Memory used: 2.858 MB
%------------------------------------------------------------------------------