%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 20:41:45 EDT 2024

% Result   : Theorem 0.15s 0.33s
% Output   : CNFRefutation 0.15s
% 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(f17,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(f18,negated_conjecture,
    ~ ! [A,B] :
        ( pair_first(ordered_pair(A,B)) = A
        & pair_second(ordered_pair(A,B)) = B ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f19,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(f20,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(f43,plain,
    ? [A,B] :
      ( pair_first(ordered_pair(A,B)) != A
      | pair_second(ordered_pair(A,B)) != B ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f44,plain,
    ( ? [A,B] : pair_first(ordered_pair(A,B)) != A
    | ? [A,B] : pair_second(ordered_pair(A,B)) != B ),
    inference(miniscoping,[status(esa)],[f43]) ).

fof(f45,plain,
    ( pair_first(ordered_pair(sk0_3,sk0_4)) != sk0_3
    | pair_second(ordered_pair(sk0_5,sk0_6)) != sk0_6 ),
    inference(skolemization,[status(esa)],[f44]) ).

fof(f46,plain,
    ( pair_first(ordered_pair(sk0_3,sk0_4)) != sk0_3
    | pair_second(ordered_pair(sk0_5,sk0_6)) != sk0_6 ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f47,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)],[f19]) ).

fof(f48,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)],[f47]) ).

fof(f49,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)],[f48]) ).

fof(f50,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_7(B,A),sk0_8(B,A))
              & B != sk0_7(B,A) ) ) ) ),
    inference(skolemization,[status(esa)],[f49]) ).

fof(f51,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)],[f50]) ).

fof(f54,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)],[f20]) ).

fof(f55,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)],[f54]) ).

fof(f56,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)],[f55]) ).

fof(f57,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_10(B,A),sk0_9(B,A))
              & B != sk0_9(B,A) ) ) ) ),
    inference(skolemization,[status(esa)],[f56]) ).

fof(f58,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)],[f57]) ).

fof(f61,plain,
    ( spl0_0
  <=> pair_first(ordered_pair(sk0_3,sk0_4)) = sk0_3 ),
    introduced(split_symbol_definition) ).

fof(f63,plain,
    ( pair_first(ordered_pair(sk0_3,sk0_4)) != sk0_3
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f61]) ).

fof(f64,plain,
    ( spl0_1
  <=> pair_second(ordered_pair(sk0_5,sk0_6)) = sk0_6 ),
    introduced(split_symbol_definition) ).

fof(f66,plain,
    ( pair_second(ordered_pair(sk0_5,sk0_6)) != sk0_6
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f64]) ).

fof(f67,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f46,f61,f64]) ).

fof(f68,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)],[f51]) ).

fof(f71,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)],[f58]) ).

fof(f74,plain,
    ! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
    inference(equality_resolution,[status(esa)],[f68]) ).

fof(f75,plain,
    ( sk0_3 != sk0_3
    | spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f74,f63]) ).

fof(f76,plain,
    ( $false
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f75]) ).

fof(f77,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f76]) ).

fof(f79,plain,
    ! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
    inference(equality_resolution,[status(esa)],[f71]) ).

fof(f80,plain,
    ( sk0_6 != sk0_6
    | spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f79,f66]) ).

fof(f81,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f80]) ).

fof(f82,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f81]) ).

fof(f83,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f67,f77,f82]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n003.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Mon Apr 29 19:50:48 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.6.0
% 0.15/0.33  % Refutation found
% 0.15/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.34  % Elapsed time: 0.022414 seconds
% 0.15/0.34  % CPU time: 0.028518 seconds
% 0.15/0.34  % Total memory used: 11.148 MB
% 0.15/0.34  % Net memory used: 11.064 MB
%------------------------------------------------------------------------------