TSTP Solution File: SEU164+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 20:41:18 EDT 2024

% Result   : Theorem 3.69s 0.86s
% Output   : CNFRefutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   43 (  11 unt;   0 def)
%            Number of atoms       :  171 (  39 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  200 (  72   ~;  90   |;  31   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-3 aty)
%            Number of variables   :  116 ( 104   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] :
      ( B = powerset(A)
    <=> ! [C] :
          ( in(C,B)
        <=> subset(C,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B] :
      ( B = union(A)
    <=> ! [C] :
          ( in(C,B)
        <=> ? [D] :
              ( in(C,D)
              & in(D,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A] : union(powerset(A)) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A] : union(powerset(A)) = A,
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f22,plain,
    ! [A,B] :
      ( ( B != powerset(A)
        | ! [C] :
            ( ( ~ in(C,B)
              | subset(C,A) )
            & ( in(C,B)
              | ~ subset(C,A) ) ) )
      & ( B = powerset(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | ~ subset(C,A) )
            & ( in(C,B)
              | subset(C,A) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f23,plain,
    ( ! [A,B] :
        ( B != powerset(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | subset(C,A) )
          & ! [C] :
              ( in(C,B)
              | ~ subset(C,A) ) ) )
    & ! [A,B] :
        ( B = powerset(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | ~ subset(C,A) )
            & ( in(C,B)
              | subset(C,A) ) ) ) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f24,plain,
    ( ! [A,B] :
        ( B != powerset(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | subset(C,A) )
          & ! [C] :
              ( in(C,B)
              | ~ subset(C,A) ) ) )
    & ! [A,B] :
        ( B = powerset(A)
        | ( ( ~ in(sk0_1(B,A),B)
            | ~ subset(sk0_1(B,A),A) )
          & ( in(sk0_1(B,A),B)
            | subset(sk0_1(B,A),A) ) ) ) ),
    inference(skolemization,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( X0 != powerset(X1)
      | ~ in(X2,X0)
      | subset(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( X0 != powerset(X1)
      | in(X2,X0)
      | ~ subset(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f29,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f30,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f29]) ).

fof(f31,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_2(B,A),A)
          & ~ in(sk0_2(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f36,plain,
    ! [A,B] :
      ( ( B != union(A)
        | ! [C] :
            ( ( ~ in(C,B)
              | ? [D] :
                  ( in(C,D)
                  & in(D,A) ) )
            & ( in(C,B)
              | ! [D] :
                  ( ~ in(C,D)
                  | ~ in(D,A) ) ) ) )
      & ( B = union(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | ! [D] :
                  ( ~ in(C,D)
                  | ~ in(D,A) ) )
            & ( in(C,B)
              | ? [D] :
                  ( in(C,D)
                  & in(D,A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f37,plain,
    ( ! [A,B] :
        ( B != union(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | ? [D] :
                  ( in(C,D)
                  & in(D,A) ) )
          & ! [C] :
              ( in(C,B)
              | ! [D] :
                  ( ~ in(C,D)
                  | ~ in(D,A) ) ) ) )
    & ! [A,B] :
        ( B = union(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | ! [D] :
                  ( ~ in(C,D)
                  | ~ in(D,A) ) )
            & ( in(C,B)
              | ? [D] :
                  ( in(C,D)
                  & in(D,A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f36]) ).

fof(f38,plain,
    ( ! [A,B] :
        ( B != union(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | ( in(C,sk0_3(C,B,A))
                & in(sk0_3(C,B,A),A) ) )
          & ! [C] :
              ( in(C,B)
              | ! [D] :
                  ( ~ in(C,D)
                  | ~ in(D,A) ) ) ) )
    & ! [A,B] :
        ( B = union(A)
        | ( ( ~ in(sk0_4(B,A),B)
            | ! [D] :
                ( ~ in(sk0_4(B,A),D)
                | ~ in(D,A) ) )
          & ( in(sk0_4(B,A),B)
            | ( in(sk0_4(B,A),sk0_5(B,A))
              & in(sk0_5(B,A),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f37]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( X0 = union(X1)
      | ~ in(sk0_4(X0,X1),X0)
      | ~ in(sk0_4(X0,X1),X2)
      | ~ in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( X0 = union(X1)
      | in(sk0_4(X0,X1),X0)
      | in(sk0_4(X0,X1),sk0_5(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( X0 = union(X1)
      | in(sk0_4(X0,X1),X0)
      | in(sk0_5(X0,X1),X1) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f53,plain,
    ! [A] : subset(A,A),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f54,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f60,plain,
    ? [A] : union(powerset(A)) != A,
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f61,plain,
    union(powerset(sk0_9)) != sk0_9,
    inference(skolemization,[status(esa)],[f60]) ).

fof(f62,plain,
    union(powerset(sk0_9)) != sk0_9,
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ in(X0,powerset(X1))
      | subset(X0,X1) ),
    inference(equality_resolution,[status(esa)],[f25]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( in(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(equality_resolution,[status(esa)],[f26]) ).

fof(f67,plain,
    ! [X0] : in(X0,powerset(X0)),
    inference(resolution,[status(thm)],[f54,f65]) ).

fof(f707,plain,
    ! [X0,X1] :
      ( X0 = union(X1)
      | ~ in(sk0_4(X0,X1),X0)
      | ~ in(X0,X1)
      | X0 = union(X1)
      | in(sk0_5(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f42,f44]) ).

fof(f708,plain,
    ! [X0,X1] :
      ( X0 = union(X1)
      | ~ in(sk0_4(X0,X1),X0)
      | ~ in(X0,X1)
      | in(sk0_5(X0,X1),X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f707]) ).

fof(f709,plain,
    ! [X0,X1] :
      ( X0 = union(X1)
      | ~ in(X0,X1)
      | in(sk0_5(X0,X1),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f708,f44]) ).

fof(f761,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | in(sk0_5(X0,powerset(X0)),powerset(X0)) ),
    inference(resolution,[status(thm)],[f709,f67]) ).

fof(f809,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | subset(sk0_5(X0,powerset(X0)),X0) ),
    inference(resolution,[status(thm)],[f761,f64]) ).

fof(f821,plain,
    ! [X0,X1] :
      ( X0 = union(powerset(X0))
      | ~ in(X1,sk0_5(X0,powerset(X0)))
      | in(X1,X0) ),
    inference(resolution,[status(thm)],[f809,f33]) ).

fof(f826,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | in(sk0_4(X0,powerset(X0)),X0)
      | X0 = union(powerset(X0))
      | in(sk0_4(X0,powerset(X0)),X0) ),
    inference(resolution,[status(thm)],[f821,f43]) ).

fof(f827,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | in(sk0_4(X0,powerset(X0)),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f826]) ).

fof(f834,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | X0 = union(powerset(X0))
      | ~ in(sk0_4(X0,powerset(X0)),X0)
      | ~ in(X0,powerset(X0)) ),
    inference(resolution,[status(thm)],[f827,f42]) ).

fof(f835,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | ~ in(sk0_4(X0,powerset(X0)),X0)
      | ~ in(X0,powerset(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f834]) ).

fof(f836,plain,
    ! [X0] :
      ( X0 = union(powerset(X0))
      | ~ in(X0,powerset(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f835,f827]) ).

fof(f868,plain,
    ! [X0] : X0 = union(powerset(X0)),
    inference(resolution,[status(thm)],[f836,f67]) ).

fof(f869,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f62,f868]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.03/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 19:35:19 EDT 2024
% 0.21/0.35  % CPUTime  : 
% 0.21/0.37  % Drodi V3.6.0
% 3.69/0.86  % Refutation found
% 3.69/0.86  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.69/0.86  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.69/0.89  % Elapsed time: 0.516767 seconds
% 3.69/0.89  % CPU time: 3.887184 seconds
% 3.69/0.89  % Total memory used: 84.112 MB
% 3.69/0.89  % Net memory used: 82.130 MB
%------------------------------------------------------------------------------