TSTP Solution File: SET592+3 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 20:39:54 EDT 2024

% Result   : Theorem 0.09s 0.29s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   57 (  10 unt;   0 def)
%            Number of atoms       :  150 (  18 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  153 (  60   ~;  55   |;  27   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   83 (  73   !;  10   ?)

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

fof(f3,axiom,
    ! [B] : ~ member(B,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f5,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [B] :
      ( empty(B)
    <=> ! [C] : ~ member(C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(B,D)
        & intersection(C,D) = empty_set )
     => B = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [B,C,D] :
        ( ( subset(B,C)
          & subset(B,D)
          & intersection(C,D) = empty_set )
       => B = empty_set ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f13,plain,
    ! [B] :
      ( ~ subset(B,empty_set)
      | B = empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f14,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | X0 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f17,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f18,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)],[f4]) ).

fof(f19,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)],[f18]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f23,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f24,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)],[f23]) ).

fof(f25,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)],[f24]) ).

fof(f26,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)],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f35,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f37,plain,
    ! [B] :
      ( ( ~ empty(B)
        | ! [C] : ~ member(C,B) )
      & ( empty(B)
        | ? [C] : member(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f9]) ).

fof(f38,plain,
    ( ! [B] :
        ( ~ empty(B)
        | ! [C] : ~ member(C,B) )
    & ! [B] :
        ( empty(B)
        | ? [C] : member(C,B) ) ),
    inference(miniscoping,[status(esa)],[f37]) ).

fof(f39,plain,
    ( ! [B] :
        ( ~ empty(B)
        | ! [C] : ~ member(C,B) )
    & ! [B] :
        ( empty(B)
        | member(sk0_1(B),B) ) ),
    inference(skolemization,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ empty(X0)
      | ~ member(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f41,plain,
    ! [X0] :
      ( empty(X0)
      | member(sk0_1(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f49,plain,
    ? [B,C,D] :
      ( subset(B,C)
      & subset(B,D)
      & intersection(C,D) = empty_set
      & B != empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f50,plain,
    ? [B] :
      ( ? [C,D] :
          ( subset(B,C)
          & subset(B,D)
          & intersection(C,D) = empty_set )
      & B != empty_set ),
    inference(miniscoping,[status(esa)],[f49]) ).

fof(f51,plain,
    ( subset(sk0_3,sk0_4)
    & subset(sk0_3,sk0_5)
    & intersection(sk0_4,sk0_5) = empty_set
    & sk0_3 != empty_set ),
    inference(skolemization,[status(esa)],[f50]) ).

fof(f52,plain,
    subset(sk0_3,sk0_4),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f53,plain,
    subset(sk0_3,sk0_5),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f54,plain,
    intersection(sk0_4,sk0_5) = empty_set,
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f55,plain,
    sk0_3 != empty_set,
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f80,plain,
    ! [X0] :
      ( ~ member(X0,sk0_3)
      | member(X0,sk0_5) ),
    inference(resolution,[status(thm)],[f27,f53]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ member(X0,sk0_3)
      | member(X0,sk0_4) ),
    inference(resolution,[status(thm)],[f27,f52]) ).

fof(f89,plain,
    ( spl0_4
  <=> member(sk0_1(sk0_3),sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f90,plain,
    ( member(sk0_1(sk0_3),sk0_5)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f89]) ).

fof(f92,plain,
    ( spl0_5
  <=> empty(sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f93,plain,
    ( empty(sk0_3)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f92]) ).

fof(f95,plain,
    ( member(sk0_1(sk0_3),sk0_5)
    | empty(sk0_3) ),
    inference(resolution,[status(thm)],[f80,f41]) ).

fof(f96,plain,
    ( spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f95,f89,f92]) ).

fof(f97,plain,
    ( spl0_6
  <=> member(sk0_1(sk0_3),sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f98,plain,
    ( member(sk0_1(sk0_3),sk0_4)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f97]) ).

fof(f100,plain,
    ( member(sk0_1(sk0_3),sk0_4)
    | empty(sk0_3) ),
    inference(resolution,[status(thm)],[f81,f41]) ).

fof(f101,plain,
    ( spl0_6
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f100,f97,f92]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ empty(X0) ),
    inference(resolution,[status(thm)],[f28,f40]) ).

fof(f197,plain,
    ! [X0] :
      ( subset(sk0_3,X0)
      | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f93,f107]) ).

fof(f198,plain,
    ( sk0_3 = empty_set
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f197,f14]) ).

fof(f199,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f198,f55]) ).

fof(f200,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f199]) ).

fof(f203,plain,
    ! [X0] :
      ( member(sk0_1(sk0_3),intersection(sk0_5,X0))
      | ~ member(sk0_1(sk0_3),X0)
      | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f90,f22]) ).

fof(f221,plain,
    ( member(sk0_1(sk0_3),intersection(sk0_5,sk0_4))
    | ~ spl0_4
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f203,f98]) ).

fof(f222,plain,
    ( member(sk0_1(sk0_3),intersection(sk0_4,sk0_5))
    | ~ spl0_4
    | ~ spl0_6 ),
    inference(forward_demodulation,[status(thm)],[f35,f221]) ).

fof(f223,plain,
    ( member(sk0_1(sk0_3),empty_set)
    | ~ spl0_4
    | ~ spl0_6 ),
    inference(forward_demodulation,[status(thm)],[f54,f222]) ).

fof(f224,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f223,f17]) ).

fof(f225,plain,
    ( ~ spl0_4
    | ~ spl0_6 ),
    inference(contradiction_clause,[status(thm)],[f224]) ).

fof(f226,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f96,f101,f200,f225]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09  % Problem  : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Mon Apr 29 21:43:05 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.09/0.29  % Drodi V3.6.0
% 0.09/0.29  % Refutation found
% 0.09/0.29  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.29  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.30  % Elapsed time: 0.013977 seconds
% 0.09/0.30  % CPU time: 0.028291 seconds
% 0.09/0.30  % Total memory used: 13.018 MB
% 0.09/0.30  % Net memory used: 12.933 MB
%------------------------------------------------------------------------------