%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:35:33 EDT 2023

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (   2 unt;   0 def)
%            Number of atoms       :  134 (  48 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  148 (  56   ~;  67   |;  16   &)
%                                         (   8 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (;  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,conjecture,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = singleton(A)
    <=> ( ~ in(A,C)
        & ( in(B,C)
          | A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ~ ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = singleton(A)
      <=> ( ~ in(A,C)
          & ( in(B,C)
            | A = B ) ) ),
    inference(negated_conjecture,[status(cth)],[f5]) ).

fof(f7,axiom,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = singleton(A)
    <=> ( ~ in(A,C)
        & ( in(B,C)
          | A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,plain,
    ? [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = singleton(A)
    <~> ( ~ in(A,C)
        & ( in(B,C)
          | A = B ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f16,plain,
    ? [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) = singleton(A)
        | ( ~ in(A,C)
          & ( in(B,C)
            | A = B ) ) )
      & ( set_difference(unordered_pair(A,B),C) != singleton(A)
        | in(A,C)
        | ( ~ in(B,C)
          & A != B ) ) ),
    inference(NNF_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ( ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = singleton(sk0_2)
      | ( ~ in(sk0_2,sk0_4)
        & ( in(sk0_3,sk0_4)
          | sk0_2 = sk0_3 ) ) )
    & ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2)
      | in(sk0_2,sk0_4)
      | ( ~ in(sk0_3,sk0_4)
        & sk0_2 != sk0_3 ) ) ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f18,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = singleton(sk0_2)
    | ~ in(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = singleton(sk0_2)
    | in(sk0_3,sk0_4)
    | sk0_2 = sk0_3 ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2)
    | in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2)
    | in(sk0_2,sk0_4)
    | sk0_2 != sk0_3 ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f22,plain,
    ! [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) != singleton(A)
        | ( ~ in(A,C)
          & ( in(B,C)
            | A = B ) ) )
      & ( set_difference(unordered_pair(A,B),C) = singleton(A)
        | in(A,C)
        | ( ~ in(B,C)
          & A != B ) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
    ( ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) != singleton(A)
        | ( ~ in(A,C)
          & ( in(B,C)
            | A = B ) ) )
    & ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = singleton(A)
        | in(A,C)
        | ( ~ in(B,C)
          & A != B ) ) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
      | in(X1,X2)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      | in(X0,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      | in(X0,X2)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f28,plain,
    ( spl0_0
  <=> set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = singleton(sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f29,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = singleton(sk0_2)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f28]) ).

fof(f30,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f28]) ).

fof(f31,plain,
    ( spl0_1
  <=> in(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f34,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f18,f28,f31]) ).

fof(f35,plain,
    ( spl0_2
  <=> in(sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f38,plain,
    ( spl0_3
  <=> sk0_2 = sk0_3 ),
    introduced(split_symbol_definition) ).

fof(f39,plain,
    ( sk0_2 = sk0_3
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f38]) ).

fof(f41,plain,
    ( spl0_0
    | spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f19,f28,f35,f38]) ).

fof(f42,plain,
    ( ~ spl0_0
    | spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f20,f28,f31,f35]) ).

fof(f43,plain,
    ( ~ spl0_0
    | spl0_1
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f21,f28,f31,f38]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( set_difference(unordered_pair(X0,X0),X1) = singleton(X0)
      | in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f27]) ).

fof(f58,plain,
    ( in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f30,f26]) ).

fof(f59,plain,
    ( spl0_1
    | ~ spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f58,f31,f35,f28]) ).

fof(f60,plain,
    ( in(sk0_3,sk0_4)
    | sk0_2 = sk0_3
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f29,f25]) ).

fof(f61,plain,
    ( spl0_2
    | spl0_3
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f60,f35,f38,f28]) ).

fof(f67,plain,
    ( spl0_5
  <=> singleton(sk0_2) = singleton(sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f69,plain,
    ( singleton(sk0_2) != singleton(sk0_2)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f67]) ).

fof(f78,plain,
    ( singleton(sk0_2) != singleton(sk0_2)
    | ~ in(sk0_2,sk0_4)
    | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f29,f24]) ).

fof(f79,plain,
    ( ~ spl0_5
    | ~ spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f78,f67,f31,f28]) ).

fof(f80,plain,
    ( $false
    | spl0_5 ),
    inference(trivial_equality_resolution,[status(esa)],[f69]) ).

fof(f81,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f80]) ).

fof(f83,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_2),sk0_4) != singleton(sk0_2)
    | ~ spl0_3
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f39,f30]) ).

fof(f90,plain,
    ( singleton(sk0_2) != singleton(sk0_2)
    | in(sk0_2,sk0_4)
    | ~ spl0_3
    | spl0_0 ),
    inference(paramodulation,[status(thm)],[f44,f83]) ).

fof(f91,plain,
    ( ~ spl0_5
    | spl0_1
    | ~ spl0_3
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f90,f67,f31,f38,f28]) ).

fof(f92,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f34,f41,f42,f43,f59,f61,f79,f81,f91]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n010.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 10:10:07 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
% 0.20/0.62  % Elapsed time: 0.043017 seconds
% 0.20/0.62  % CPU time: 0.020939 seconds
% 0.20/0.62  % Memory used: 3.609 MB
%------------------------------------------------------------------------------