TSTP Solution File: SEU110+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 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 20:41:02 EDT 2024

% Result   : Theorem 3.69s 0.85s
% Output   : CNFRefutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   50 (   7 unt;   0 def)
%            Number of atoms       :  170 (  11 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  196 (  76   ~;  81   |;  26   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   95 (  89   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B] :
      ( preboolean(B)
     => ( B = finite_subsets(A)
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A] : preboolean(finite_subsets(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(B,C) )
     => subset(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f27,conjecture,
    ! [A,B] :
      ( subset(A,B)
     => subset(finite_subsets(A),finite_subsets(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,negated_conjecture,
    ~ ! [A,B] :
        ( subset(A,B)
       => subset(finite_subsets(A),finite_subsets(B)) ),
    inference(negated_conjecture,[status(cth)],[f27]) ).

fof(f50,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f51,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)],[f50]) ).

fof(f52,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)],[f51]) ).

fof(f53,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f52]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f57,plain,
    ! [A,B] :
      ( ~ preboolean(B)
      | ( B = finite_subsets(A)
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f58,plain,
    ! [A,B] :
      ( ~ preboolean(B)
      | ( ( B != finite_subsets(A)
          | ! [C] :
              ( ( ~ in(C,B)
                | ( subset(C,A)
                  & finite(C) ) )
              & ( in(C,B)
                | ~ subset(C,A)
                | ~ finite(C) ) ) )
        & ( B = finite_subsets(A)
          | ? [C] :
              ( ( ~ in(C,B)
                | ~ subset(C,A)
                | ~ finite(C) )
              & ( in(C,B)
                | ( subset(C,A)
                  & finite(C) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [B] :
      ( ~ preboolean(B)
      | ( ! [A] :
            ( B != finite_subsets(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ( subset(C,A)
                    & finite(C) ) )
              & ! [C] :
                  ( in(C,B)
                  | ~ subset(C,A)
                  | ~ finite(C) ) ) )
        & ! [A] :
            ( B = finite_subsets(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ~ subset(C,A)
                  | ~ finite(C) )
                & ( in(C,B)
                  | ( subset(C,A)
                    & finite(C) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f58]) ).

fof(f60,plain,
    ! [B] :
      ( ~ preboolean(B)
      | ( ! [A] :
            ( B != finite_subsets(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ( subset(C,A)
                    & finite(C) ) )
              & ! [C] :
                  ( in(C,B)
                  | ~ subset(C,A)
                  | ~ finite(C) ) ) )
        & ! [A] :
            ( B = finite_subsets(A)
            | ( ( ~ in(sk0_1(A,B),B)
                | ~ subset(sk0_1(A,B),A)
                | ~ finite(sk0_1(A,B)) )
              & ( in(sk0_1(A,B),B)
                | ( subset(sk0_1(A,B),A)
                  & finite(sk0_1(A,B)) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f59]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ~ preboolean(X0)
      | X0 != finite_subsets(X1)
      | ~ in(X2,X0)
      | subset(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ preboolean(X0)
      | X0 != finite_subsets(X1)
      | ~ in(X2,X0)
      | finite(X2) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ~ preboolean(X0)
      | X0 != finite_subsets(X1)
      | in(X2,X0)
      | ~ subset(X2,X1)
      | ~ finite(X2) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f67,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f127,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(B,C)
      | subset(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f128,plain,
    ! [A,C] :
      ( ! [B] :
          ( ~ subset(A,B)
          | ~ subset(B,C) )
      | subset(A,C) ),
    inference(miniscoping,[status(esa)],[f127]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X2)
      | subset(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f130,plain,
    ? [A,B] :
      ( subset(A,B)
      & ~ subset(finite_subsets(A),finite_subsets(B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f131,plain,
    ( subset(sk0_12,sk0_13)
    & ~ subset(finite_subsets(sk0_12),finite_subsets(sk0_13)) ),
    inference(skolemization,[status(esa)],[f130]) ).

fof(f132,plain,
    subset(sk0_12,sk0_13),
    inference(cnf_transformation,[status(esa)],[f131]) ).

fof(f133,plain,
    ~ subset(finite_subsets(sk0_12),finite_subsets(sk0_13)),
    inference(cnf_transformation,[status(esa)],[f131]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ preboolean(finite_subsets(X0))
      | ~ in(X1,finite_subsets(X0))
      | subset(X1,X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f61]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ~ preboolean(finite_subsets(X0))
      | ~ in(X1,finite_subsets(X0))
      | finite(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f62]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ~ preboolean(finite_subsets(X0))
      | in(X1,finite_subsets(X0))
      | ~ subset(X1,X0)
      | ~ finite(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f158,plain,
    ! [X0] :
      ( ~ subset(X0,sk0_12)
      | subset(X0,sk0_13) ),
    inference(resolution,[status(thm)],[f129,f132]) ).

fof(f1485,plain,
    ! [X0,X1] :
      ( ~ in(X0,finite_subsets(X1))
      | subset(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f154,f67]) ).

fof(f1487,plain,
    ! [X0,X1] :
      ( subset(sk0_0(X0,finite_subsets(X1)),X1)
      | subset(finite_subsets(X1),X0) ),
    inference(resolution,[status(thm)],[f1485,f55]) ).

fof(f1488,plain,
    ! [X0,X1] :
      ( ~ in(X0,finite_subsets(X1))
      | finite(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f155,f67]) ).

fof(f1490,plain,
    ! [X0,X1] :
      ( finite(sk0_0(X0,finite_subsets(X1)))
      | subset(finite_subsets(X1),X0) ),
    inference(resolution,[status(thm)],[f1488,f55]) ).

fof(f1491,plain,
    ! [X0,X1] :
      ( in(X0,finite_subsets(X1))
      | ~ subset(X0,X1)
      | ~ finite(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f156,f67]) ).

fof(f1493,plain,
    ! [X0,X1] :
      ( ~ subset(sk0_0(finite_subsets(X0),X1),X0)
      | ~ finite(sk0_0(finite_subsets(X0),X1))
      | subset(X1,finite_subsets(X0)) ),
    inference(resolution,[status(thm)],[f1491,f56]) ).

fof(f4760,plain,
    ! [X0] :
      ( subset(finite_subsets(sk0_12),X0)
      | subset(sk0_0(X0,finite_subsets(sk0_12)),sk0_13) ),
    inference(resolution,[status(thm)],[f1487,f158]) ).

fof(f5237,plain,
    ( spl0_454
  <=> finite(sk0_0(finite_subsets(sk0_13),finite_subsets(sk0_12))) ),
    introduced(split_symbol_definition) ).

fof(f5239,plain,
    ( ~ finite(sk0_0(finite_subsets(sk0_13),finite_subsets(sk0_12)))
    | spl0_454 ),
    inference(component_clause,[status(thm)],[f5237]) ).

fof(f5240,plain,
    ( spl0_455
  <=> subset(finite_subsets(sk0_12),finite_subsets(sk0_13)) ),
    introduced(split_symbol_definition) ).

fof(f5241,plain,
    ( subset(finite_subsets(sk0_12),finite_subsets(sk0_13))
    | ~ spl0_455 ),
    inference(component_clause,[status(thm)],[f5240]) ).

fof(f5243,plain,
    ( ~ finite(sk0_0(finite_subsets(sk0_13),finite_subsets(sk0_12)))
    | subset(finite_subsets(sk0_12),finite_subsets(sk0_13))
    | subset(finite_subsets(sk0_12),finite_subsets(sk0_13)) ),
    inference(resolution,[status(thm)],[f1493,f4760]) ).

fof(f5244,plain,
    ( ~ spl0_454
    | spl0_455 ),
    inference(split_clause,[status(thm)],[f5243,f5237,f5240]) ).

fof(f5362,plain,
    ( subset(finite_subsets(sk0_12),finite_subsets(sk0_13))
    | spl0_454 ),
    inference(resolution,[status(thm)],[f5239,f1490]) ).

fof(f5363,plain,
    ( $false
    | spl0_454 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5362,f133]) ).

fof(f5364,plain,
    spl0_454,
    inference(contradiction_clause,[status(thm)],[f5363]) ).

fof(f5365,plain,
    ( $false
    | ~ spl0_455 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5241,f133]) ).

fof(f5366,plain,
    ~ spl0_455,
    inference(contradiction_clause,[status(thm)],[f5365]) ).

fof(f5367,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f5244,f5364,f5366]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n005.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 : Mon Apr 29 19:44:26 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.6.0
% 3.69/0.85  % Refutation found
% 3.69/0.85  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.69/0.85  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.69/0.88  % Elapsed time: 0.550373 seconds
% 3.69/0.88  % CPU time: 4.194538 seconds
% 3.69/0.88  % Total memory used: 81.055 MB
% 3.69/0.88  % Net memory used: 79.139 MB
%------------------------------------------------------------------------------