%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET820-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 : Tue Apr 30 20:40:25 EDT 2024

% Result   : Unsatisfiable 0.09s 0.31s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   21 (   9 unt;   0 def)
%            Number of atoms       :   37 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   35 (  19   ~;  16   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   43 (  43   !;   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_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f6,negated_conjecture,
    ! [V_W,V_U] :
      ( ~ c_in(V_W,V_U,tc_IntDef_Oint)
      | ~ v_P(v_x(V_U)) ),
    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_a),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f12,plain,
    ! [V_U] :
      ( ! [V_V] : ~ c_in(V_V,V_U,tc_IntDef_Oint)
      | c_in(v_x(V_U),V_U,tc_IntDef_Oint) ),
    inference(miniscoping,[status(esa)],[f5]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ c_in(X0,X1,tc_IntDef_Oint)
      | c_in(v_x(X1),X1,tc_IntDef_Oint) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f14,plain,
    ! [V_U] :
      ( ! [V_W] : ~ c_in(V_W,V_U,tc_IntDef_Oint)
      | ~ v_P(v_x(V_U)) ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ c_in(X0,X1,tc_IntDef_Oint)
      | ~ v_P(v_x(X1)) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),X1,tc_IntDef_Oint)
      | v_x(c_insert(X0,X1,tc_IntDef_Oint)) = X0
      | ~ c_in(X2,c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(resolution,[status(thm)],[f10,f13]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0
      | ~ c_in(X1,c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(resolution,[status(thm)],[f17,f7]) ).

fof(f22,plain,
    ! [X0] : v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
    inference(resolution,[status(thm)],[f19,f8]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ c_in(X0,c_insert(X1,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ v_P(X1) ),
    inference(paramodulation,[status(thm)],[f22,f15]) ).

fof(f26,plain,
    ! [X0] : ~ c_in(X0,c_insert(v_a,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(resolution,[status(thm)],[f25,f11]) ).

fof(f27,plain,
    $false,
    inference(resolution,[status(thm)],[f26,f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SET820-2 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n008.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Mon Apr 29 21:28:27 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.6.0
% 0.09/0.31  % Refutation found
% 0.09/0.31  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.32  % Elapsed time: 0.014341 seconds
% 0.15/0.32  % CPU time: 0.020503 seconds
% 0.15/0.32  % Total memory used: 10.933 MB
% 0.15/0.32  % Net memory used: 10.759 MB
%------------------------------------------------------------------------------