%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU162+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 12:36:04 EDT 2023

% Result   : Theorem 0.15s 0.32s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (   2 unt;   0 def)
%            Number of atoms       :   86 (  23 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   84 (  38   ~;  32   |;   5   &)
%                                         (   6 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (;  38   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A,B] :
      ~ ( disjoint(singleton(A),B)
        & in(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B] :
      ( ~ in(A,B)
     => disjoint(singleton(A),B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,conjecture,
    ! [A,B] :
      ( set_difference(A,singleton(B)) = A
    <=> ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    ~ ! [A,B] :
        ( set_difference(A,singleton(B)) = A
      <=> ~ in(B,A) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

fof(f9,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> set_difference(A,B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,plain,
    ! [A,B] :
      ( ~ disjoint(singleton(A),B)
      | ~ in(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ disjoint(singleton(X0),X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f14,plain,
    ! [A,B] :
      ( in(A,B)
      | disjoint(singleton(A),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | disjoint(singleton(X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [A,B] :
      ( ~ disjoint(A,B)
      | disjoint(B,A) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f18,plain,
    ? [A,B] :
      ( set_difference(A,singleton(B)) = A
    <~> ~ in(B,A) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f19,plain,
    ? [A,B] :
      ( ( set_difference(A,singleton(B)) = A
        | ~ in(B,A) )
      & ( set_difference(A,singleton(B)) != A
        | in(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    ( ( set_difference(sk0_0,singleton(sk0_1)) = sk0_0
      | ~ in(sk0_1,sk0_0) )
    & ( set_difference(sk0_0,singleton(sk0_1)) != sk0_0
      | in(sk0_1,sk0_0) ) ),
    inference(skolemization,[status(esa)],[f19]) ).

fof(f21,plain,
    ( set_difference(sk0_0,singleton(sk0_1)) = sk0_0
    | ~ in(sk0_1,sk0_0) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    ( set_difference(sk0_0,singleton(sk0_1)) != sk0_0
    | in(sk0_1,sk0_0) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f23,plain,
    ! [A,B] :
      ( ( ~ disjoint(A,B)
        | set_difference(A,B) = A )
      & ( disjoint(A,B)
        | set_difference(A,B) != A ) ),
    inference(NNF_transformation,[status(esa)],[f9]) ).

fof(f24,plain,
    ( ! [A,B] :
        ( ~ disjoint(A,B)
        | set_difference(A,B) = A )
    & ! [A,B] :
        ( disjoint(A,B)
        | set_difference(A,B) != A ) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_difference(X0,X1) = X0 ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | set_difference(X0,X1) != X0 ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f27,plain,
    ( spl0_0
  <=> set_difference(sk0_0,singleton(sk0_1)) = sk0_0 ),
    introduced(split_symbol_definition) ).

fof(f30,plain,
    ( spl0_1
  <=> in(sk0_1,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f31,plain,
    ( in(sk0_1,sk0_0)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f30]) ).

fof(f32,plain,
    ( ~ in(sk0_1,sk0_0)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f30]) ).

fof(f33,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f21,f27,f30]) ).

fof(f34,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f22,f27,f30]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_difference(X1,X0) = X1 ),
    inference(resolution,[status(thm)],[f17,f25]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( set_difference(X0,singleton(X1)) = X0
      | in(X1,X0) ),
    inference(resolution,[status(thm)],[f44,f15]) ).

fof(f58,plain,
    ( set_difference(sk0_0,singleton(sk0_1)) = sk0_0
    | spl0_1 ),
    inference(resolution,[status(thm)],[f32,f45]) ).

fof(f64,plain,
    ( spl0_2
  <=> sk0_0 = sk0_0 ),
    introduced(split_symbol_definition) ).

fof(f66,plain,
    ( sk0_0 != sk0_0
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f64]) ).

fof(f81,plain,
    ( ~ disjoint(singleton(sk0_1),sk0_0)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f31,f13]) ).

fof(f86,plain,
    ( ~ disjoint(sk0_0,singleton(sk0_1))
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f81,f17]) ).

fof(f89,plain,
    ( set_difference(sk0_0,singleton(sk0_1)) != sk0_0
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f86,f26]) ).

fof(f90,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f89,f27,f30]) ).

fof(f91,plain,
    ( $false
    | spl0_2 ),
    inference(trivial_equality_resolution,[status(esa)],[f66]) ).

fof(f92,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f91]) ).

fof(f93,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f58,f27,f30]) ).

fof(f94,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f33,f34,f90,f92,f93]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SEU162+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n017.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 08:36:55 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.15/0.31  % Drodi V3.5.1
% 0.15/0.32  % Refutation found
% 0.15/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54  % Elapsed time: 0.012540 seconds
% 0.15/0.54  % CPU time: 0.012070 seconds
% 0.15/0.54  % Memory used: 2.886 MB
%------------------------------------------------------------------------------