TSTP Solution File: SET002+4 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET002+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:38:34 EDT 2024

% Result   : Theorem 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   30 (   9 unt;   0 def)
%            Number of atoms       :   86 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   89 (  33   ~;  36   |;  15   &)
%                                         (   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    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   71 (  68   !;   3   ?)

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

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

fof(f5,axiom,
    ! [X,A,B] :
      ( member(X,union(A,B))
    <=> ( member(X,A)
        | member(X,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [A] : equal_set(union(A,A),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [A] : equal_set(union(A,A),A),
    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(f35,plain,
    ! [X,A,B] :
      ( ( ~ member(X,union(A,B))
        | member(X,A)
        | member(X,B) )
      & ( member(X,union(A,B))
        | ( ~ member(X,A)
          & ~ member(X,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f36,plain,
    ( ! [X,A,B] :
        ( ~ member(X,union(A,B))
        | member(X,A)
        | member(X,B) )
    & ! [X,A,B] :
        ( member(X,union(A,B))
        | ( ~ member(X,A)
          & ~ member(X,B) ) ) ),
    inference(miniscoping,[status(esa)],[f35]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f68,plain,
    ? [A] : ~ equal_set(union(A,A),A),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

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

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

fof(f77,plain,
    ! [X0,X1,X2] :
      ( subset(union(X0,X1),X2)
      | member(sk0_0(X2,union(X0,X1)),X0)
      | member(sk0_0(X2,union(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f19,f37]) ).

fof(f107,plain,
    ! [X0] :
      ( subset(union(X0,X0),X0)
      | subset(union(X0,X0),X0) ),
    inference(resolution,[status(thm)],[f20,f77]) ).

fof(f108,plain,
    ! [X0] : subset(union(X0,X0),X0),
    inference(duplicate_literals_removal,[status(esa)],[f107]) ).

fof(f117,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f20,f39]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1,X0))
      | subset(X0,union(X1,X0)) ),
    inference(resolution,[status(thm)],[f117,f19]) ).

fof(f200,plain,
    ! [X0,X1] : subset(X0,union(X1,X0)),
    inference(duplicate_literals_removal,[status(esa)],[f199]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( equal_set(union(X0,X1),X1)
      | ~ subset(union(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f200,f25]) ).

fof(f217,plain,
    ! [X0] : equal_set(union(X0,X0),X0),
    inference(resolution,[status(thm)],[f208,f108]) ).

fof(f218,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f70,f217]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET002+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 21:51:10 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.36  % Refutation found
% 0.14/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38  % Elapsed time: 0.023211 seconds
% 0.20/0.38  % CPU time: 0.049338 seconds
% 0.20/0.38  % Total memory used: 12.938 MB
% 0.20/0.38  % Net memory used: 12.905 MB
%------------------------------------------------------------------------------