%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU129+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 20:41:06 EDT 2024

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (  11 unt;   0 def)
%            Number of atoms       :   60 (   2 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   50 (  22   ~;  17   |;   5   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   45 (  39   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,lemma,
    ! [A,B] : subset(set_intersection2(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,lemma,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(A,C) )
     => subset(A,set_intersection2(B,C)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,lemma,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(B,C) )
     => subset(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f27,conjecture,
    ! [A,B,C] :
      ( subset(A,B)
     => subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,negated_conjecture,
    ~ ! [A,B,C] :
        ( subset(A,B)
       => subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(negated_conjecture,[status(cth)],[f27]) ).

fof(f42,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f103,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f104,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(A,C)
      | subset(A,set_intersection2(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ subset(X0,X2)
      | subset(X0,set_intersection2(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f107,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(B,C)
      | subset(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f108,plain,
    ! [A,C] :
      ( ! [B] :
          ( ~ subset(A,B)
          | ~ subset(B,C) )
      | subset(A,C) ),
    inference(miniscoping,[status(esa)],[f107]) ).

fof(f109,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X2)
      | subset(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f110,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & ~ subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f111,plain,
    ? [A,B] :
      ( subset(A,B)
      & ? [C] : ~ subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(miniscoping,[status(esa)],[f110]) ).

fof(f112,plain,
    ( subset(sk0_6,sk0_7)
    & ~ subset(set_intersection2(sk0_6,sk0_8),set_intersection2(sk0_7,sk0_8)) ),
    inference(skolemization,[status(esa)],[f111]) ).

fof(f113,plain,
    subset(sk0_6,sk0_7),
    inference(cnf_transformation,[status(esa)],[f112]) ).

fof(f114,plain,
    ~ subset(set_intersection2(sk0_6,sk0_8),set_intersection2(sk0_7,sk0_8)),
    inference(cnf_transformation,[status(esa)],[f112]) ).

fof(f151,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f42,f103]) ).

fof(f175,plain,
    ( spl0_2
  <=> subset(set_intersection2(sk0_6,sk0_8),sk0_7) ),
    introduced(split_symbol_definition) ).

fof(f177,plain,
    ( ~ subset(set_intersection2(sk0_6,sk0_8),sk0_7)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f175]) ).

fof(f178,plain,
    ( spl0_3
  <=> subset(set_intersection2(sk0_6,sk0_8),sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f180,plain,
    ( ~ subset(set_intersection2(sk0_6,sk0_8),sk0_8)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f178]) ).

fof(f181,plain,
    ( ~ subset(set_intersection2(sk0_6,sk0_8),sk0_7)
    | ~ subset(set_intersection2(sk0_6,sk0_8),sk0_8) ),
    inference(resolution,[status(thm)],[f105,f114]) ).

fof(f182,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f181,f175,f178]) ).

fof(f274,plain,
    ! [X0] :
      ( ~ subset(X0,sk0_6)
      | subset(X0,sk0_7) ),
    inference(resolution,[status(thm)],[f109,f113]) ).

fof(f279,plain,
    ! [X0] : subset(set_intersection2(sk0_6,X0),sk0_7),
    inference(resolution,[status(thm)],[f274,f103]) ).

fof(f288,plain,
    ( $false
    | spl0_2 ),
    inference(backward_subsumption_resolution,[status(thm)],[f177,f279]) ).

fof(f289,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f288]) ).

fof(f297,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f180,f151]) ).

fof(f298,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f297]) ).

fof(f299,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f182,f289,f298]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU129+2 : 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 : n023.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 : Mon Apr 29 20:02:25 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37  % Elapsed time: 0.022897 seconds
% 0.12/0.37  % CPU time: 0.055392 seconds
% 0.12/0.37  % Total memory used: 15.270 MB
% 0.12/0.37  % Net memory used: 15.195 MB
%------------------------------------------------------------------------------