%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU140+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 12:35:56 EDT 2023

% Result   : Theorem 0.10s 0.34s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (  11 unt;   0 def)
%            Number of atoms       :   58 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   47 (  19   ~;  13   |;  10   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   49 (;  43   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> set_intersection2(A,B) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B,C] :
      ( subset(A,B)
     => subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [A] :
      ( subset(A,empty_set)
     => A = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & disjoint(B,C) )
     => disjoint(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & disjoint(B,C) )
       => disjoint(A,C) ),
    inference(negated_conjecture,[status(cth)],[f15]) ).

fof(f22,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f23,plain,
    ! [A,B] :
      ( ( ~ disjoint(A,B)
        | set_intersection2(A,B) = empty_set )
      & ( disjoint(A,B)
        | set_intersection2(A,B) != empty_set ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f24,plain,
    ( ! [A,B] :
        ( ~ disjoint(A,B)
        | set_intersection2(A,B) = empty_set )
    & ! [A,B] :
        ( disjoint(A,B)
        | set_intersection2(A,B) != empty_set ) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_intersection2(X0,X1) = empty_set ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | set_intersection2(X0,X1) != empty_set ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f38,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f39,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(miniscoping,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f42,plain,
    ! [A] :
      ( ~ subset(A,empty_set)
      | A = empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f43,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | X0 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & disjoint(B,C)
      & ~ disjoint(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f45,plain,
    ? [A,C] :
      ( ? [B] :
          ( subset(A,B)
          & disjoint(B,C) )
      & ~ disjoint(A,C) ),
    inference(miniscoping,[status(esa)],[f44]) ).

fof(f46,plain,
    ( subset(sk0_2,sk0_4)
    & disjoint(sk0_4,sk0_3)
    & ~ disjoint(sk0_2,sk0_3) ),
    inference(skolemization,[status(esa)],[f45]) ).

fof(f47,plain,
    subset(sk0_2,sk0_4),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    disjoint(sk0_4,sk0_3),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f49,plain,
    ~ disjoint(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f61,plain,
    set_intersection2(sk0_2,sk0_3) != empty_set,
    inference(resolution,[status(thm)],[f26,f49]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | subset(set_intersection2(X0,X2),set_intersection2(X2,X1)) ),
    inference(paramodulation,[status(thm)],[f22,f40]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_intersection2(X1,X0) = empty_set ),
    inference(paramodulation,[status(thm)],[f22,f25]) ).

fof(f125,plain,
    set_intersection2(sk0_3,sk0_4) = empty_set,
    inference(resolution,[status(thm)],[f105,f48]) ).

fof(f153,plain,
    ! [X0] : subset(set_intersection2(sk0_2,X0),set_intersection2(X0,sk0_4)),
    inference(resolution,[status(thm)],[f103,f47]) ).

fof(f174,plain,
    subset(set_intersection2(sk0_2,sk0_3),empty_set),
    inference(paramodulation,[status(thm)],[f125,f153]) ).

fof(f196,plain,
    set_intersection2(sk0_2,sk0_3) = empty_set,
    inference(resolution,[status(thm)],[f174,f43]) ).

fof(f197,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f196,f61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem  : SEU140+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n002.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 09:24:28 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.5.1
% 0.10/0.34  % Refutation found
% 0.10/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55  % Elapsed time: 0.013331 seconds
% 0.15/0.55  % CPU time: 0.013371 seconds
% 0.15/0.55  % Memory used: 2.347 MB
%------------------------------------------------------------------------------