%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU124+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 20:41:05 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (  10 unt;   0 def)
%            Number of atoms       :   93 (  10 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  108 (  40   ~;  42   |;  21   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   77 (  71   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : set_union2(A,B) = set_union2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A,B,C] :
      ( C = set_union2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,conjecture,
    ! [A,B] : subset(A,set_union2(A,B)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ ! [A,B] : subset(A,set_union2(A,B)),
    inference(negated_conjecture,[status(cth)],[f30]) ).

fof(f35,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f47,plain,
    ! [A,B,C] :
      ( ( C != set_union2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | in(D,A)
              | in(D,B) )
            & ( in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) ) ) )
      & ( C = set_union2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) )
            & ( in(D,C)
              | in(D,A)
              | in(D,B) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f6]) ).

fof(f48,plain,
    ( ! [A,B,C] :
        ( C != set_union2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | in(D,A)
              | in(D,B) )
          & ! [D] :
              ( in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) ) ) )
    & ! [A,B,C] :
        ( C = set_union2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) )
            & ( in(D,C)
              | in(D,A)
              | in(D,B) ) ) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( ! [A,B,C] :
        ( C != set_union2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | in(D,A)
              | in(D,B) )
          & ! [D] :
              ( in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) ) ) )
    & ! [A,B,C] :
        ( C = set_union2(A,B)
        | ( ( ~ in(sk0_1(C,B,A),C)
            | ( ~ in(sk0_1(C,B,A),A)
              & ~ in(sk0_1(C,B,A),B) ) )
          & ( in(sk0_1(C,B,A),C)
            | in(sk0_1(C,B,A),A)
            | in(sk0_1(C,B,A),B) ) ) ) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_union2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f56,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f57,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f57]) ).

fof(f59,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_2(B,A),A)
          & ~ in(sk0_2(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_2(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_2(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f118,plain,
    ? [A,B] : ~ subset(A,set_union2(A,B)),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f119,plain,
    ~ subset(sk0_8,set_union2(sk0_8,sk0_9)),
    inference(skolemization,[status(esa)],[f118]) ).

fof(f120,plain,
    ~ subset(sk0_8,set_union2(sk0_8,sk0_9)),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_union2(X1,X2))
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f52]) ).

fof(f551,plain,
    ! [X0,X1,X2] :
      ( subset(X0,set_union2(X1,X2))
      | ~ in(sk0_2(set_union2(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f62,f129]) ).

fof(f621,plain,
    ! [X0,X1] :
      ( subset(X0,set_union2(X1,X0))
      | subset(X0,set_union2(X1,X0)) ),
    inference(resolution,[status(thm)],[f551,f61]) ).

fof(f622,plain,
    ! [X0,X1] : subset(X0,set_union2(X1,X0)),
    inference(duplicate_literals_removal,[status(esa)],[f621]) ).

fof(f640,plain,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    inference(paramodulation,[status(thm)],[f35,f622]) ).

fof(f643,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f120,f640]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU124+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n025.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 : Mon Apr 29 20:06:56 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.38  % Refutation found
% 0.13/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.033016 seconds
% 0.13/0.38  % CPU time: 0.125340 seconds
% 0.13/0.38  % Total memory used: 23.276 MB
% 0.13/0.38  % Net memory used: 23.163 MB
%------------------------------------------------------------------------------