TSTP Solution File: SEU120+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU120+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 12:35:51 EDT 2023

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   41 (   3 unt;   0 def)
%            Number of atoms       :  101 (  18 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  111 (  51   ~;  36   |;  18   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   64 (;  49   !;  15   ?)

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

fof(f4,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> set_intersection2(A,B) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [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(f13,negated_conjecture,
    ~ ! [A,B] :
        ( ~ ( ~ disjoint(A,B)
            & ! [C] : ~ in(C,set_intersection2(A,B)) )
        & ~ ( ? [C] : in(C,set_intersection2(A,B))
            & disjoint(A,B) ) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f17,plain,
    ! [A] :
      ( ( A != empty_set
        | ! [B] : ~ in(B,A) )
      & ( A = empty_set
        | ? [B] : in(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

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

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

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

fof(f21,plain,
    ! [X0] :
      ( X0 = empty_set
      | in(sk0_0(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f22,plain,
    ! [A,B] :
      ( ( ~ disjoint(A,B)
        | set_intersection2(A,B) = empty_set )
      & ( disjoint(A,B)
        | set_intersection2(A,B) != empty_set ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f23,plain,
    ( ! [A,B] :
        ( ~ disjoint(A,B)
        | set_intersection2(A,B) = empty_set )
    & ! [A,B] :
        ( disjoint(A,B)
        | set_intersection2(A,B) != empty_set ) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_intersection2(X0,X1) = empty_set ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | set_intersection2(X0,X1) != empty_set ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f35,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)],[f13]) ).

fof(f36,plain,
    ! [A,B] :
      ( pd0_0(B,A)
     => ( ~ disjoint(A,B)
        & ! [C] : ~ in(C,set_intersection2(A,B)) ) ),
    introduced(predicate_definition,[f35]) ).

fof(f37,plain,
    ? [A,B] :
      ( pd0_0(B,A)
      | ( ? [C] : in(C,set_intersection2(A,B))
        & disjoint(A,B) ) ),
    inference(formula_renaming,[status(thm)],[f35,f36]) ).

fof(f38,plain,
    ( ? [A,B] : pd0_0(B,A)
    | ? [A,B] :
        ( ? [C] : in(C,set_intersection2(A,B))
        & disjoint(A,B) ) ),
    inference(miniscoping,[status(esa)],[f37]) ).

fof(f39,plain,
    ( pd0_0(sk0_4,sk0_3)
    | ( in(sk0_7,set_intersection2(sk0_5,sk0_6))
      & disjoint(sk0_5,sk0_6) ) ),
    inference(skolemization,[status(esa)],[f38]) ).

fof(f40,plain,
    ( pd0_0(sk0_4,sk0_3)
    | in(sk0_7,set_intersection2(sk0_5,sk0_6)) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f41,plain,
    ( pd0_0(sk0_4,sk0_3)
    | disjoint(sk0_5,sk0_6) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f42,plain,
    ! [A,B] :
      ( ~ pd0_0(B,A)
      | ( ~ disjoint(A,B)
        & ! [C] : ~ in(C,set_intersection2(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | ~ disjoint(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1)
      | ~ in(X2,set_intersection2(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f45,plain,
    ( spl0_0
  <=> pd0_0(sk0_4,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f46,plain,
    ( pd0_0(sk0_4,sk0_3)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f45]) ).

fof(f48,plain,
    ( spl0_1
  <=> in(sk0_7,set_intersection2(sk0_5,sk0_6)) ),
    introduced(split_symbol_definition) ).

fof(f49,plain,
    ( in(sk0_7,set_intersection2(sk0_5,sk0_6))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f48]) ).

fof(f51,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f40,f45,f48]) ).

fof(f52,plain,
    ( spl0_2
  <=> disjoint(sk0_5,sk0_6) ),
    introduced(split_symbol_definition) ).

fof(f53,plain,
    ( disjoint(sk0_5,sk0_6)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f52]) ).

fof(f55,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f41,f45,f52]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = empty_set
      | ~ pd0_0(X1,X0) ),
    inference(resolution,[status(thm)],[f21,f44]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | ~ pd0_0(X1,X0) ),
    inference(resolution,[status(thm)],[f25,f63]) ).

fof(f76,plain,
    ! [X0,X1] : ~ pd0_0(X0,X1),
    inference(forward_subsumption_resolution,[status(thm)],[f75,f43]) ).

fof(f82,plain,
    ( $false
    | ~ spl0_0 ),
    inference(backward_subsumption_resolution,[status(thm)],[f46,f76]) ).

fof(f83,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f82]) ).

fof(f93,plain,
    ( set_intersection2(sk0_5,sk0_6) != empty_set
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f49,f20]) ).

fof(f96,plain,
    ( ~ disjoint(sk0_5,sk0_6)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f93,f24]) ).

fof(f97,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f96,f53]) ).

fof(f98,plain,
    ( ~ spl0_2
    | ~ spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f97]) ).

fof(f99,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f51,f55,f83,f98]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU120+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n002.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 : Tue May 30 09:29:43 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.024670 seconds
% 0.13/0.38  % CPU time: 0.036234 seconds
% 0.13/0.38  % Memory used: 14.315 MB
%------------------------------------------------------------------------------