TSTP Solution File: SET603+4 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:39:56 EDT 2024

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   33 (  11 unt;   0 def)
%            Number of atoms       :   91 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   93 (  35   ~;  37   |;  16   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   75 (  72   !;   3   ?)

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

fof(f2,axiom,
    ! [A,B] :
      ( equal_set(A,B)
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : ~ member(X,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [B,A,E] :
      ( member(B,difference(E,A))
    <=> ( member(B,E)
        & ~ member(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [E] : equal_set(difference(E,empty_set),E),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [E] : equal_set(difference(E,empty_set),E),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( ~ member(X,A)
          | member(X,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f15,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
      & ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f17,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( member(sk0_0(B,A),A)
          & ~ member(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    ! [A,B] :
      ( ( ~ equal_set(A,B)
        | ( subset(A,B)
          & subset(B,A) ) )
      & ( equal_set(A,B)
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f22,plain,
    ( ! [A,B] :
        ( ~ equal_set(A,B)
        | ( subset(A,B)
          & subset(B,A) ) )
    & ! [A,B] :
        ( equal_set(A,B)
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f40,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f41,plain,
    ! [B,A,E] :
      ( ( ~ member(B,difference(E,A))
        | ( member(B,E)
          & ~ member(B,A) ) )
      & ( member(B,difference(E,A))
        | ~ member(B,E)
        | member(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f42,plain,
    ( ! [B,A,E] :
        ( ~ member(B,difference(E,A))
        | ( member(B,E)
          & ~ member(B,A) ) )
    & ! [B,A,E] :
        ( member(B,difference(E,A))
        | ~ member(B,E)
        | member(B,A) ) ),
    inference(miniscoping,[status(esa)],[f41]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,difference(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X1,X2))
      | ~ member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f68,plain,
    ? [E] : ~ equal_set(difference(E,empty_set),E),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f69,plain,
    ~ equal_set(difference(sk0_3,empty_set),sk0_3),
    inference(skolemization,[status(esa)],[f68]) ).

fof(f70,plain,
    ~ equal_set(difference(sk0_3,empty_set),sk0_3),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( subset(difference(X0,X1),X2)
      | member(sk0_0(X2,difference(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f19,f43]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),difference(X0,X2))
      | member(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f19,f45]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( subset(difference(X0,X1),X0)
      | subset(difference(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f20,f75]) ).

fof(f93,plain,
    ! [X0,X1] : subset(difference(X0,X1),X0),
    inference(duplicate_literals_removal,[status(esa)],[f92]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( subset(X0,difference(X0,X1))
      | subset(X0,difference(X0,X1))
      | member(sk0_0(difference(X0,X1),X0),X1) ),
    inference(resolution,[status(thm)],[f20,f77]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( subset(X0,difference(X0,X1))
      | member(sk0_0(difference(X0,X1),X0),X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f94]) ).

fof(f116,plain,
    ! [X0] : subset(X0,difference(X0,empty_set)),
    inference(resolution,[status(thm)],[f95,f40]) ).

fof(f120,plain,
    ! [X0] :
      ( equal_set(difference(X0,empty_set),X0)
      | ~ subset(difference(X0,empty_set),X0) ),
    inference(resolution,[status(thm)],[f116,f25]) ).

fof(f121,plain,
    ! [X0] : equal_set(difference(X0,empty_set),X0),
    inference(forward_subsumption_resolution,[status(thm)],[f120,f93]) ).

fof(f122,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f70,f121]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35  % Computer : n005.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Mon Apr 29 21:39:56 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.12/0.37  % Drodi V3.6.0
% 0.12/0.37  % Refutation found
% 0.12/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39  % Elapsed time: 0.022525 seconds
% 0.12/0.39  % CPU time: 0.052129 seconds
% 0.12/0.39  % Total memory used: 13.284 MB
% 0.12/0.39  % Net memory used: 13.235 MB
%------------------------------------------------------------------------------