%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:35:28 EDT 2023

% Result   : Theorem 0.15s 0.55s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   22 (  13 unt;   0 def)
%            Number of atoms       :   31 (  19 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   20 (  11   ~;   4   |;   2   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (;  27   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B,C] :
      ( subset(unordered_pair(A,B),singleton(C))
     => A = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,conjecture,
    ! [A,B,C] :
      ( subset(unordered_pair(A,B),singleton(C))
     => unordered_pair(A,B) = singleton(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ~ ! [A,B,C] :
        ( subset(unordered_pair(A,B),singleton(C))
       => unordered_pair(A,B) = singleton(C) ),
    inference(negated_conjecture,[status(cth)],[f6]) ).

fof(f8,axiom,
    ! [A] : unordered_pair(A,A) = singleton(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f16,plain,
    ! [A,B,C] :
      ( ~ subset(unordered_pair(A,B),singleton(C))
      | A = C ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f17,plain,
    ! [A,C] :
      ( ! [B] : ~ subset(unordered_pair(A,B),singleton(C))
      | A = C ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ~ subset(unordered_pair(X0,X1),singleton(X2))
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ? [A,B,C] :
      ( subset(unordered_pair(A,B),singleton(C))
      & unordered_pair(A,B) != singleton(C) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f20,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),singleton(sk0_4))
    & unordered_pair(sk0_2,sk0_3) != singleton(sk0_4) ),
    inference(skolemization,[status(esa)],[f19]) ).

fof(f21,plain,
    subset(unordered_pair(sk0_2,sk0_3),singleton(sk0_4)),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    unordered_pair(sk0_2,sk0_3) != singleton(sk0_4),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f23,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f24,plain,
    sk0_2 = sk0_4,
    inference(resolution,[status(thm)],[f18,f21]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ subset(unordered_pair(X0,X1),singleton(X2))
      | X1 = X2 ),
    inference(paramodulation,[status(thm)],[f9,f18]) ).

fof(f28,plain,
    subset(unordered_pair(sk0_2,sk0_3),singleton(sk0_2)),
    inference(backward_demodulation,[status(thm)],[f24,f21]) ).

fof(f29,plain,
    unordered_pair(sk0_2,sk0_3) != singleton(sk0_2),
    inference(backward_demodulation,[status(thm)],[f24,f22]) ).

fof(f33,plain,
    sk0_3 = sk0_2,
    inference(resolution,[status(thm)],[f28,f25]) ).

fof(f36,plain,
    unordered_pair(sk0_2,sk0_2) != singleton(sk0_2),
    inference(backward_demodulation,[status(thm)],[f33,f29]) ).

fof(f37,plain,
    singleton(sk0_2) != singleton(sk0_2),
    inference(forward_demodulation,[status(thm)],[f23,f36]) ).

fof(f38,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem  : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n028.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 10:34:32 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.5.1
% 0.15/0.55  % Refutation found
% 0.15/0.55  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55  % Elapsed time: 0.010059 seconds
% 0.15/0.55  % CPU time: 0.010885 seconds
% 0.15/0.55  % Memory used: 2.262 MB
%------------------------------------------------------------------------------