TSTP Solution File: SET916+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 : Wed May 31 12:35:31 EDT 2023

% Result   : Theorem 0.09s 0.34s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   52 (   7 unt;   0 def)
%            Number of atoms       :  195 (  55 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  237 (  94   ~;  89   |;  45   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :  110 (; 100   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A,B,C] :
      ( C = unordered_pair(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( D = A
            | D = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] : ~ in(C,set_intersection2(A,B)) )
      & ~ ( ? [C] : in(C,set_intersection2(A,B))
          & disjoint(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A,B,C] :
      ~ ( ~ in(A,B)
        & ~ in(C,B)
        & ~ disjoint(unordered_pair(A,C),B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A,B,C] :
        ~ ( ~ in(A,B)
          & ~ in(C,B)
          & ~ disjoint(unordered_pair(A,C),B) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f17,plain,
    ! [A,B,C] :
      ( ( C != unordered_pair(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | D = A
              | D = B )
            & ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
      & ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f18,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f19,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ( ( ~ in(sk0_0(C,B,A),C)
            | ( sk0_0(C,B,A) != A
              & sk0_0(C,B,A) != B ) )
          & ( in(sk0_0(C,B,A),C)
            | sk0_0(C,B,A) = A
            | sk0_0(C,B,A) = B ) ) ) ),
    inference(skolemization,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | ~ in(X3,X0)
      | X3 = X1
      | X3 = X2 ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f26,plain,
    ! [A,B,C] :
      ( ( C != set_intersection2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
      & ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f27,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f28,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ( ( ~ in(sk0_1(C,B,A),C)
            | ~ in(sk0_1(C,B,A),A)
            | ~ in(sk0_1(C,B,A),B) )
          & ( in(sk0_1(C,B,A),C)
            | ( in(sk0_1(C,B,A),A)
              & in(sk0_1(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f27]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f43,plain,
    ! [A,B] :
      ( ( disjoint(A,B)
        | ? [C] : in(C,set_intersection2(A,B)) )
      & ( ! [C] : ~ in(C,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f44,plain,
    ( ! [A,B] :
        ( disjoint(A,B)
        | ? [C] : in(C,set_intersection2(A,B)) )
    & ! [A,B] :
        ( ! [C] : ~ in(C,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    inference(miniscoping,[status(esa)],[f43]) ).

fof(f45,plain,
    ( ! [A,B] :
        ( disjoint(A,B)
        | in(sk0_4(B,A),set_intersection2(A,B)) )
    & ! [A,B] :
        ( ! [C] : ~ in(C,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    inference(skolemization,[status(esa)],[f44]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_4(X1,X0),set_intersection2(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f48,plain,
    ? [A,B,C] :
      ( ~ in(A,B)
      & ~ in(C,B)
      & ~ disjoint(unordered_pair(A,C),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f49,plain,
    ( ~ in(sk0_5,sk0_6)
    & ~ in(sk0_7,sk0_6)
    & ~ disjoint(unordered_pair(sk0_5,sk0_7),sk0_6) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f50,plain,
    ~ in(sk0_5,sk0_6),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ~ in(sk0_7,sk0_6),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    ~ disjoint(unordered_pair(sk0_5,sk0_7),sk0_6),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f20]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f29]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f30]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_4(X1,X0),X1) ),
    inference(resolution,[status(thm)],[f46,f57]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_4(X1,X0),X0) ),
    inference(resolution,[status(thm)],[f46,f56]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( disjoint(unordered_pair(X0,X1),X2)
      | sk0_4(X2,unordered_pair(X0,X1)) = X0
      | sk0_4(X2,unordered_pair(X0,X1)) = X1 ),
    inference(resolution,[status(thm)],[f79,f53]) ).

fof(f119,plain,
    ( spl0_0
  <=> sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_5 ),
    introduced(split_symbol_definition) ).

fof(f120,plain,
    ( sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_5
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f119]) ).

fof(f122,plain,
    ( spl0_1
  <=> sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_7 ),
    introduced(split_symbol_definition) ).

fof(f123,plain,
    ( sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_7
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f122]) ).

fof(f125,plain,
    ( sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_5
    | sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_7 ),
    inference(resolution,[status(thm)],[f92,f52]) ).

fof(f126,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f125,f119,f122]) ).

fof(f134,plain,
    ( spl0_2
  <=> disjoint(unordered_pair(sk0_5,sk0_7),sk0_6) ),
    introduced(split_symbol_definition) ).

fof(f135,plain,
    ( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f134]) ).

fof(f167,plain,
    ( spl0_9
  <=> in(sk0_5,sk0_6) ),
    introduced(split_symbol_definition) ).

fof(f168,plain,
    ( in(sk0_5,sk0_6)
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f167]) ).

fof(f170,plain,
    ( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
    | in(sk0_5,sk0_6)
    | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f120,f78]) ).

fof(f171,plain,
    ( spl0_2
    | spl0_9
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f170,f134,f167,f119]) ).

fof(f177,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f135,f52]) ).

fof(f178,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f177]) ).

fof(f209,plain,
    ( spl0_17
  <=> in(sk0_7,sk0_6) ),
    introduced(split_symbol_definition) ).

fof(f210,plain,
    ( in(sk0_7,sk0_6)
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f209]) ).

fof(f212,plain,
    ( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
    | in(sk0_7,sk0_6)
    | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f123,f78]) ).

fof(f213,plain,
    ( spl0_2
    | spl0_17
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f212,f134,f209,f122]) ).

fof(f220,plain,
    ( $false
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f210,f51]) ).

fof(f221,plain,
    ~ spl0_17,
    inference(contradiction_clause,[status(thm)],[f220]) ).

fof(f223,plain,
    ( $false
    | ~ spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f168,f50]) ).

fof(f224,plain,
    ~ spl0_9,
    inference(contradiction_clause,[status(thm)],[f223]) ).

fof(f225,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f126,f171,f178,f213,f221,f224]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33  % Computer : n016.cluster.edu
% 0.09/0.33  % Model    : x86_64 x86_64
% 0.09/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33  % Memory   : 8042.1875MB
% 0.09/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33  % CPULimit : 300
% 0.09/0.33  % WCLimit  : 300
% 0.09/0.33  % DateTime : Tue May 30 10:49:14 EDT 2023
% 0.09/0.33  % CPUTime  : 
% 0.09/0.34  % Drodi V3.5.1
% 0.09/0.34  % Refutation found
% 0.09/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.56  % Elapsed time: 0.014549 seconds
% 0.16/0.56  % CPU time: 0.015201 seconds
% 0.16/0.56  % Memory used: 3.692 MB
%------------------------------------------------------------------------------