%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 12:36:31 EDT 2023

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   34 (   5 unt;   0 def)
%            Number of atoms       :  105 (  90 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  122 (  51   ~;  47   |;  14   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  106 (;  88   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f26,axiom,
    ! [A] :
      ( ? [B,C] : A = ordered_pair(B,C)
     => ! [B] :
          ( B = pair_first(A)
        <=> ! [C,D] :
              ( A = ordered_pair(C,D)
             => B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    ! [A] :
      ( ? [B,C] : A = ordered_pair(B,C)
     => ! [B] :
          ( B = pair_second(A)
        <=> ! [C,D] :
              ( A = ordered_pair(C,D)
             => B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f325,conjecture,
    ! [A,B] :
      ( pair_first(ordered_pair(A,B)) = A
      & pair_second(ordered_pair(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f326,negated_conjecture,
    ~ ! [A,B] :
        ( pair_first(ordered_pair(A,B)) = A
        & pair_second(ordered_pair(A,B)) = B ),
    inference(negated_conjecture,[status(cth)],[f325]) ).

fof(f470,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ! [B] :
          ( B = pair_first(A)
        <=> ! [C,D] :
              ( A != ordered_pair(C,D)
              | B = C ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f471,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ! [B] :
          ( ( B != pair_first(A)
            | ! [C,D] :
                ( A != ordered_pair(C,D)
                | B = C ) )
          & ( B = pair_first(A)
            | ? [C,D] :
                ( A = ordered_pair(C,D)
                & B != C ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f470]) ).

fof(f472,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ( ! [B] :
            ( B != pair_first(A)
            | ! [C] :
                ( ! [D] : A != ordered_pair(C,D)
                | B = C ) )
        & ! [B] :
            ( B = pair_first(A)
            | ? [C] :
                ( ? [D] : A = ordered_pair(C,D)
                & B != C ) ) ) ),
    inference(miniscoping,[status(esa)],[f471]) ).

fof(f473,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ( ! [B] :
            ( B != pair_first(A)
            | ! [C] :
                ( ! [D] : A != ordered_pair(C,D)
                | B = C ) )
        & ! [B] :
            ( B = pair_first(A)
            | ( A = ordered_pair(sk0_17(B,A),sk0_18(B,A))
              & B != sk0_17(B,A) ) ) ) ),
    inference(skolemization,[status(esa)],[f472]) ).

fof(f474,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( X0 != ordered_pair(X1,X2)
      | X3 != pair_first(X0)
      | X0 != ordered_pair(X4,X5)
      | X3 = X4 ),
    inference(cnf_transformation,[status(esa)],[f473]) ).

fof(f537,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ! [B] :
          ( B = pair_second(A)
        <=> ! [C,D] :
              ( A != ordered_pair(C,D)
              | B = D ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f538,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ! [B] :
          ( ( B != pair_second(A)
            | ! [C,D] :
                ( A != ordered_pair(C,D)
                | B = D ) )
          & ( B = pair_second(A)
            | ? [C,D] :
                ( A = ordered_pair(C,D)
                & B != D ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f537]) ).

fof(f539,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ( ! [B] :
            ( B != pair_second(A)
            | ! [D] :
                ( ! [C] : A != ordered_pair(C,D)
                | B = D ) )
        & ! [B] :
            ( B = pair_second(A)
            | ? [D] :
                ( ? [C] : A = ordered_pair(C,D)
                & B != D ) ) ) ),
    inference(miniscoping,[status(esa)],[f538]) ).

fof(f540,plain,
    ! [A] :
      ( ! [B,C] : A != ordered_pair(B,C)
      | ( ! [B] :
            ( B != pair_second(A)
            | ! [D] :
                ( ! [C] : A != ordered_pair(C,D)
                | B = D ) )
        & ! [B] :
            ( B = pair_second(A)
            | ( A = ordered_pair(sk0_31(B,A),sk0_30(B,A))
              & B != sk0_30(B,A) ) ) ) ),
    inference(skolemization,[status(esa)],[f539]) ).

fof(f541,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( X0 != ordered_pair(X1,X2)
      | X3 != pair_second(X0)
      | X0 != ordered_pair(X4,X5)
      | X3 = X5 ),
    inference(cnf_transformation,[status(esa)],[f540]) ).

fof(f1526,plain,
    ? [A,B] :
      ( pair_first(ordered_pair(A,B)) != A
      | pair_second(ordered_pair(A,B)) != B ),
    inference(pre_NNF_transformation,[status(esa)],[f326]) ).

fof(f1527,plain,
    ( ? [A,B] : pair_first(ordered_pair(A,B)) != A
    | ? [A,B] : pair_second(ordered_pair(A,B)) != B ),
    inference(miniscoping,[status(esa)],[f1526]) ).

fof(f1528,plain,
    ( pair_first(ordered_pair(sk0_131,sk0_132)) != sk0_131
    | pair_second(ordered_pair(sk0_133,sk0_134)) != sk0_134 ),
    inference(skolemization,[status(esa)],[f1527]) ).

fof(f1529,plain,
    ( pair_first(ordered_pair(sk0_131,sk0_132)) != sk0_131
    | pair_second(ordered_pair(sk0_133,sk0_134)) != sk0_134 ),
    inference(cnf_transformation,[status(esa)],[f1528]) ).

fof(f1628,plain,
    ( spl0_2
  <=> pair_first(ordered_pair(sk0_131,sk0_132)) = sk0_131 ),
    introduced(split_symbol_definition) ).

fof(f1630,plain,
    ( pair_first(ordered_pair(sk0_131,sk0_132)) != sk0_131
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f1628]) ).

fof(f1631,plain,
    ( spl0_3
  <=> pair_second(ordered_pair(sk0_133,sk0_134)) = sk0_134 ),
    introduced(split_symbol_definition) ).

fof(f1633,plain,
    ( pair_second(ordered_pair(sk0_133,sk0_134)) != sk0_134
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f1631]) ).

fof(f1634,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f1529,f1628,f1631]) ).

fof(f1659,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | pair_first(ordered_pair(X0,X1)) = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f474]) ).

fof(f1675,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | pair_second(ordered_pair(X0,X1)) = X3 ),
    inference(destructive_equality_resolution,[status(esa)],[f541]) ).

fof(f1737,plain,
    ! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
    inference(equality_resolution,[status(esa)],[f1659]) ).

fof(f1739,plain,
    ! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
    inference(equality_resolution,[status(esa)],[f1675]) ).

fof(f1747,plain,
    ( sk0_131 != sk0_131
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f1737,f1630]) ).

fof(f1748,plain,
    ( $false
    | spl0_2 ),
    inference(trivial_equality_resolution,[status(esa)],[f1747]) ).

fof(f1749,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f1748]) ).

fof(f1750,plain,
    ( sk0_134 != sk0_134
    | spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f1739,f1633]) ).

fof(f1751,plain,
    ( $false
    | spl0_3 ),
    inference(trivial_equality_resolution,[status(esa)],[f1750]) ).

fof(f1752,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f1751]) ).

fof(f1753,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1634,f1749,f1752]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n031.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 09:38:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.38  % Drodi V3.5.1
% 0.13/0.39  % Refutation found
% 0.13/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.41  % Elapsed time: 0.057526 seconds
% 0.19/0.41  % CPU time: 0.095517 seconds
% 0.19/0.41  % Memory used: 21.547 MB
%------------------------------------------------------------------------------