TSTP Solution File: SET578+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 20:39:51 EDT 2024

% Result   : Theorem 0.19s 0.41s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   74 (   4 unt;   0 def)
%            Number of atoms       :  211 (  14 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  219 (  82   ~;  90   |;  29   &)
%                                         (  15 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   9 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   91 (  80   !;  11   ?)

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

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

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

fof(f7,conjecture,
    ! [B,C,D] :
      ( ! [E] :
          ( member(E,B)
        <=> ( member(E,C)
            & member(E,D) ) )
     => B = intersection(C,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    ~ ! [B,C,D] :
        ( ! [E] :
            ( member(E,B)
          <=> ( member(E,C)
              & member(E,D) ) )
       => B = intersection(C,D) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

fof(f9,plain,
    ! [B,C,D] :
      ( ( ~ member(D,intersection(B,C))
        | ( member(D,B)
          & member(D,C) ) )
      & ( member(D,intersection(B,C))
        | ~ member(D,B)
        | ~ member(D,C) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f10,plain,
    ( ! [B,C,D] :
        ( ~ member(D,intersection(B,C))
        | ( member(D,B)
          & member(D,C) ) )
    & ! [B,C,D] :
        ( member(D,intersection(B,C))
        | ~ member(D,B)
        | ~ member(D,C) ) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f14,plain,
    ! [B,C] :
      ( ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
      & ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f15,plain,
    ( ! [B,C] :
        ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
    & ! [B,C] :
        ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f20,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f21,plain,
    ! [B,C] :
      ( ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
      & ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f23,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ( member(sk0_0(C,B),B)
          & ~ member(sk0_0(C,B),C) ) ) ),
    inference(skolemization,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f35,plain,
    ? [B,C,D] :
      ( ! [E] :
          ( member(E,B)
        <=> ( member(E,C)
            & member(E,D) ) )
      & B != intersection(C,D) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f36,plain,
    ? [B,C,D] :
      ( ! [E] :
          ( ( ~ member(E,B)
            | ( member(E,C)
              & member(E,D) ) )
          & ( member(E,B)
            | ~ member(E,C)
            | ~ member(E,D) ) )
      & B != intersection(C,D) ),
    inference(NNF_transformation,[status(esa)],[f35]) ).

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

fof(f38,plain,
    ( ! [E] :
        ( ~ member(E,sk0_2)
        | ( member(E,sk0_3)
          & member(E,sk0_4) ) )
    & ! [E] :
        ( member(E,sk0_2)
        | ~ member(E,sk0_3)
        | ~ member(E,sk0_4) )
    & sk0_2 != intersection(sk0_3,sk0_4) ),
    inference(skolemization,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f41,plain,
    ! [X0] :
      ( member(X0,sk0_2)
      | ~ member(X0,sk0_3)
      | ~ member(X0,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f42,plain,
    sk0_2 != intersection(sk0_3,sk0_4),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f43,plain,
    ! [X0] : subset(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f16]) ).

fof(f47,plain,
    ( spl0_0
  <=> subset(sk0_2,intersection(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f49,plain,
    ( ~ subset(sk0_2,intersection(sk0_3,sk0_4))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f47]) ).

fof(f50,plain,
    ( spl0_1
  <=> subset(intersection(sk0_3,sk0_4),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f52,plain,
    ( ~ subset(intersection(sk0_3,sk0_4),sk0_2)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f50]) ).

fof(f53,plain,
    ( ~ subset(sk0_2,intersection(sk0_3,sk0_4))
    | ~ subset(intersection(sk0_3,sk0_4),sk0_2) ),
    inference(resolution,[status(thm)],[f18,f42]) ).

fof(f54,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f53,f47,f50]) ).

fof(f57,plain,
    ( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f26,f49]) ).

fof(f58,plain,
    ( spl0_2
  <=> member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f60,plain,
    ( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_3)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f58]) ).

fof(f61,plain,
    ( spl0_3
  <=> member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f63,plain,
    ( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_4)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f61]) ).

fof(f64,plain,
    ( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_3)
    | ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_4)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f57,f13]) ).

fof(f65,plain,
    ( ~ spl0_2
    | ~ spl0_3
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f64,f58,f61,f47]) ).

fof(f69,plain,
    ( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_2)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f52,f26]) ).

fof(f70,plain,
    ( spl0_4
  <=> member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f72,plain,
    ( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_3)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f70]) ).

fof(f73,plain,
    ( spl0_5
  <=> member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f75,plain,
    ( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_4)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f73]) ).

fof(f76,plain,
    ( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_3)
    | ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_4)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f69,f41]) ).

fof(f77,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f76,f70,f73,f50]) ).

fof(f82,plain,
    ( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_2)
    | spl0_2 ),
    inference(resolution,[status(thm)],[f60,f39]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),intersection(X0,sk0_4))
      | spl0_5 ),
    inference(resolution,[status(thm)],[f75,f12]) ).

fof(f90,plain,
    ( subset(sk0_2,intersection(sk0_3,sk0_4))
    | spl0_2 ),
    inference(resolution,[status(thm)],[f82,f25]) ).

fof(f91,plain,
    ( $false
    | spl0_0
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f90,f49]) ).

fof(f92,plain,
    ( spl0_0
    | spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f91]) ).

fof(f94,plain,
    ! [X0] :
      ( ~ subset(X0,sk0_3)
      | ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),X0)
      | spl0_4 ),
    inference(resolution,[status(thm)],[f72,f24]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_3,X0))
      | spl0_4 ),
    inference(resolution,[status(thm)],[f72,f11]) ).

fof(f104,plain,
    ( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_2)
    | spl0_3 ),
    inference(resolution,[status(thm)],[f63,f40]) ).

fof(f113,plain,
    ( subset(sk0_2,intersection(sk0_3,sk0_4))
    | spl0_3 ),
    inference(resolution,[status(thm)],[f104,f25]) ).

fof(f114,plain,
    ( spl0_0
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f113,f47,f61]) ).

fof(f144,plain,
    ( spl0_10
  <=> member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f149,plain,
    ( spl0_11
  <=> subset(sk0_3,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f151,plain,
    ( ~ subset(sk0_3,sk0_3)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f149]) ).

fof(f152,plain,
    ( ~ subset(sk0_3,sk0_3)
    | ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_2)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f94,f39]) ).

fof(f153,plain,
    ( ~ spl0_11
    | ~ spl0_10
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f152,f149,f144,f70]) ).

fof(f157,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f151,f43]) ).

fof(f158,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f157]) ).

fof(f197,plain,
    ( subset(intersection(sk0_3,sk0_4),sk0_2)
    | spl0_5 ),
    inference(resolution,[status(thm)],[f88,f25]) ).

fof(f198,plain,
    ( $false
    | spl0_1
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f197,f52]) ).

fof(f199,plain,
    ( spl0_1
    | spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f198]) ).

fof(f218,plain,
    ( subset(intersection(sk0_3,sk0_4),sk0_2)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f96,f25]) ).

fof(f219,plain,
    ( $false
    | spl0_1
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f218,f52]) ).

fof(f220,plain,
    ( spl0_1
    | spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f219]) ).

fof(f221,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f54,f65,f77,f92,f114,f153,f158,f199,f220]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 21:33:29 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.19/0.41  % Refutation found
% 0.19/0.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42  % Elapsed time: 0.076865 seconds
% 0.19/0.42  % CPU time: 0.503173 seconds
% 0.19/0.42  % Total memory used: 66.086 MB
% 0.19/0.42  % Net memory used: 65.539 MB
%------------------------------------------------------------------------------