%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 20:40:36 EDT 2024

% Result   : Theorem 0.11s 0.28s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   16 (   8 unt;   0 def)
%            Number of atoms       :   63 (  43 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :   77 (  30   ~;  29   |;  15   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-3 aty)
%            Number of variables   :   44 (  40   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A,B,C] :
      ( C = unordered_pair(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( D = A
            | D = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B] :
      ( in(A,B)
     => set_union2(singleton(A),B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f17,plain,
    ! [A,B,C] :
      ( ( C != unordered_pair(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | D = A
              | D = B )
            & ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
      & ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f18,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f19,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ( ( ~ in(sk0_0(C,B,A),C)
            | ( sk0_0(C,B,A) != A
              & sk0_0(C,B,A) != B ) )
          & ( in(sk0_0(C,B,A),C)
            | sk0_0(C,B,A) = A
            | sk0_0(C,B,A) = B ) ) ) ),
    inference(skolemization,[status(esa)],[f18]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X1 ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f34,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | set_union2(singleton(A),B) = B ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | set_union2(singleton(X0),X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f40,plain,
    ? [A,B] : set_union2(singleton(A),unordered_pair(A,B)) != unordered_pair(A,B),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f41,plain,
    set_union2(singleton(sk0_3),unordered_pair(sk0_3,sk0_4)) != unordered_pair(sk0_3,sk0_4),
    inference(skolemization,[status(esa)],[f40]) ).

fof(f42,plain,
    set_union2(singleton(sk0_3),unordered_pair(sk0_3,sk0_4)) != unordered_pair(sk0_3,sk0_4),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f44,plain,
    ! [X0,X1] : in(X0,unordered_pair(X0,X1)),
    inference(destructive_equality_resolution,[status(esa)],[f21]) ).

fof(f46,plain,
    ~ in(sk0_3,unordered_pair(sk0_3,sk0_4)),
    inference(resolution,[status(thm)],[f35,f42]) ).

fof(f51,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f46,f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27  % Computer : n014.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Mon Apr 29 21:41:04 EDT 2024
% 0.07/0.27  % CPUTime  : 
% 0.11/0.27  % Drodi V3.6.0
% 0.11/0.28  % Refutation found
% 0.11/0.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.28  % Elapsed time: 0.013030 seconds
% 0.11/0.28  % CPU time: 0.017636 seconds
% 0.11/0.28  % Total memory used: 10.893 MB
% 0.11/0.28  % Net memory used: 10.774 MB
%------------------------------------------------------------------------------