%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU151+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 12:36:00 EDT 2023

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   31 (  10 unt;   0 def)
%            Number of atoms       :  100 (  69 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  117 (  48   ~;  40   |;  25   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   60 (;  50   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B,C] :
      ( C = unordered_pair(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( D = A
            | D = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,conjecture,
    ! [A,B,C,D] :
      ~ ( unordered_pair(A,B) = unordered_pair(C,D)
        & A != C
        & A != D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ~ ! [A,B,C,D] :
        ~ ( unordered_pair(A,B) = unordered_pair(C,D)
          & A != C
          & A != D ),
    inference(negated_conjecture,[status(cth)],[f5]) ).

fof(f9,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f10,plain,
    ! [A,B,C] :
      ( ( C != unordered_pair(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | D = A
              | D = B )
            & ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
      & ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f11,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f12,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ( ( ~ in(sk0_0(C,B,A),C)
            | ( sk0_0(C,B,A) != A
              & sk0_0(C,B,A) != B ) )
          & ( in(sk0_0(C,B,A),C)
            | sk0_0(C,B,A) = A
            | sk0_0(C,B,A) = B ) ) ) ),
    inference(skolemization,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | ~ in(X3,X0)
      | X3 = X1
      | X3 = X2 ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X1 ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f19,plain,
    ? [A,B,C,D] :
      ( unordered_pair(A,B) = unordered_pair(C,D)
      & A != C
      & A != D ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f20,plain,
    ? [A,D] :
      ( ? [C] :
          ( ? [B] : unordered_pair(A,B) = unordered_pair(C,D)
          & A != C )
      & A != D ),
    inference(miniscoping,[status(esa)],[f19]) ).

fof(f21,plain,
    ( unordered_pair(sk0_1,sk0_4) = unordered_pair(sk0_3,sk0_2)
    & sk0_1 != sk0_3
    & sk0_1 != sk0_2 ),
    inference(skolemization,[status(esa)],[f20]) ).

fof(f22,plain,
    unordered_pair(sk0_1,sk0_4) = unordered_pair(sk0_3,sk0_2),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    sk0_1 != sk0_3,
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f24,plain,
    sk0_1 != sk0_2,
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f13]) ).

fof(f26,plain,
    ! [X0,X1] : in(X0,unordered_pair(X0,X1)),
    inference(destructive_equality_resolution,[status(esa)],[f14]) ).

fof(f28,plain,
    unordered_pair(sk0_1,sk0_4) = unordered_pair(sk0_2,sk0_3),
    inference(paramodulation,[status(thm)],[f22,f9]) ).

fof(f52,plain,
    ( spl0_0
  <=> sk0_3 = sk0_1 ),
    introduced(split_symbol_definition) ).

fof(f53,plain,
    ( sk0_3 = sk0_1
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f52]) ).

fof(f60,plain,
    ( spl0_2
  <=> sk0_2 = sk0_1 ),
    introduced(split_symbol_definition) ).

fof(f61,plain,
    ( sk0_2 = sk0_1
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f60]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sk0_1,sk0_4))
      | X0 = sk0_2
      | X0 = sk0_3 ),
    inference(paramodulation,[status(thm)],[f28,f25]) ).

fof(f72,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f61,f24]) ).

fof(f73,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f72]) ).

fof(f74,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f53,f23]) ).

fof(f75,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f74]) ).

fof(f91,plain,
    ( sk0_1 = sk0_2
    | sk0_1 = sk0_3 ),
    inference(resolution,[status(thm)],[f68,f26]) ).

fof(f92,plain,
    ( spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f91,f60,f52]) ).

fof(f93,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f73,f75,f92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU151+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 09:04:16 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.61  % Elapsed time: 0.054940 seconds
% 0.20/0.61  % CPU time: 0.020409 seconds
% 0.20/0.61  % Memory used: 3.607 MB
%------------------------------------------------------------------------------