%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU154+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 20:41:14 EDT 2024

% Result   : Theorem 0.21s 0.41s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   32 (   8 unt;   0 def)
%            Number of atoms       :   77 (  19 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   78 (  33   ~;  30   |;   9   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   60 (  58   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [A,B] :
      ( A = B
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,conjecture,
    ! [A,B] :
      ( ~ in(A,B)
     => disjoint(singleton(A),B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,negated_conjecture,
    ~ ! [A,B] :
        ( ~ in(A,B)
       => disjoint(singleton(A),B) ),
    inference(negated_conjecture,[status(cth)],[f33]) ).

fof(f37,lemma,
    ! [A,B,C] :
      ( subset(A,B)
     => ( in(C,A)
        | subset(A,set_difference(B,singleton(C))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f56,lemma,
    ! [A,B] : subset(set_difference(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f74,lemma,
    ! [A,B] :
      ( disjoint(A,B)
    <=> set_difference(A,B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f86,plain,
    ! [A,B] :
      ( ( A != B
        | ( subset(A,B)
          & subset(B,A) ) )
      & ( A = B
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f6]) ).

fof(f87,plain,
    ( ! [A,B] :
        ( A != B
        | ( subset(A,B)
          & subset(B,A) ) )
    & ! [A,B] :
        ( A = B
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(miniscoping,[status(esa)],[f86]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f87]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f87]) ).

fof(f180,plain,
    ? [A,B] :
      ( ~ in(A,B)
      & ~ disjoint(singleton(A),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f34]) ).

fof(f181,plain,
    ( ~ in(sk0_8,sk0_9)
    & ~ disjoint(singleton(sk0_8),sk0_9) ),
    inference(skolemization,[status(esa)],[f180]) ).

fof(f182,plain,
    ~ in(sk0_8,sk0_9),
    inference(cnf_transformation,[status(esa)],[f181]) ).

fof(f183,plain,
    ~ disjoint(singleton(sk0_8),sk0_9),
    inference(cnf_transformation,[status(esa)],[f181]) ).

fof(f192,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | in(C,A)
      | subset(A,set_difference(B,singleton(C))) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f193,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | ! [C] :
          ( in(C,A)
          | subset(A,set_difference(B,singleton(C))) ) ),
    inference(miniscoping,[status(esa)],[f192]) ).

fof(f194,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | in(X2,X0)
      | subset(X0,set_difference(X1,singleton(X2))) ),
    inference(cnf_transformation,[status(esa)],[f193]) ).

fof(f206,plain,
    ! [A,B] :
      ( ~ disjoint(A,B)
      | disjoint(B,A) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f206]) ).

fof(f236,plain,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f275,plain,
    ! [A,B] :
      ( ( ~ disjoint(A,B)
        | set_difference(A,B) = A )
      & ( disjoint(A,B)
        | set_difference(A,B) != A ) ),
    inference(NNF_transformation,[status(esa)],[f74]) ).

fof(f276,plain,
    ( ! [A,B] :
        ( ~ disjoint(A,B)
        | set_difference(A,B) = A )
    & ! [A,B] :
        ( disjoint(A,B)
        | set_difference(A,B) != A ) ),
    inference(miniscoping,[status(esa)],[f275]) ).

fof(f278,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | set_difference(X0,X1) != X0 ),
    inference(cnf_transformation,[status(esa)],[f276]) ).

fof(f290,plain,
    ! [X0] : subset(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f88]) ).

fof(f314,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) != X0
      | disjoint(X1,X0) ),
    inference(resolution,[status(thm)],[f278,f207]) ).

fof(f315,plain,
    set_difference(sk0_9,singleton(sk0_8)) != sk0_9,
    inference(resolution,[status(thm)],[f314,f183]) ).

fof(f584,plain,
    ! [X0,X1,X2] :
      ( set_difference(X0,singleton(X1)) = X2
      | ~ subset(set_difference(X0,singleton(X1)),X2)
      | ~ subset(X2,X0)
      | in(X1,X2) ),
    inference(resolution,[status(thm)],[f90,f194]) ).

fof(f871,plain,
    ! [X0,X1] :
      ( set_difference(X0,singleton(X1)) = X0
      | ~ subset(X0,X0)
      | in(X1,X0) ),
    inference(resolution,[status(thm)],[f584,f236]) ).

fof(f872,plain,
    ! [X0,X1] :
      ( set_difference(X0,singleton(X1)) = X0
      | in(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f871,f290]) ).

fof(f1018,plain,
    set_difference(sk0_9,singleton(sk0_8)) = sk0_9,
    inference(resolution,[status(thm)],[f872,f182]) ).

fof(f1019,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f1018,f315]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU154+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.34  % Computer : n003.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Mon Apr 29 19:55:33 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.15/0.36  % Drodi V3.6.0
% 0.21/0.41  % Refutation found
% 0.21/0.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42  % Elapsed time: 0.071143 seconds
% 0.21/0.42  % CPU time: 0.433502 seconds
% 0.21/0.42  % Total memory used: 65.403 MB
% 0.21/0.42  % Net memory used: 65.196 MB
%------------------------------------------------------------------------------