TSTP Solution File: SEU132+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU132+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 20:41:07 EDT 2024

% Result   : Theorem 79.81s 10.46s
% Output   : CNFRefutation 80.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   43 (   7 unt;   0 def)
%            Number of atoms       :  138 (  10 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  157 (  62   ~;  61   |;  25   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   97 (  87   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B,C] :
      ( C = set_difference(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & ~ in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f35,conjecture,
    ! [A,B,C] :
      ( subset(A,B)
     => subset(set_difference(A,C),set_difference(B,C)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,negated_conjecture,
    ~ ! [A,B,C] :
        ( subset(A,B)
       => subset(set_difference(A,C),set_difference(B,C)) ),
    inference(negated_conjecture,[status(cth)],[f35]) ).

fof(f70,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f71,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)],[f70]) ).

fof(f72,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)],[f71]) ).

fof(f73,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_2(B,A),A)
          & ~ in(sk0_2(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f72]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f73]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_2(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f73]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_2(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f73]) ).

fof(f86,plain,
    ! [A,B,C] :
      ( ( C != set_difference(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & ~ in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | in(D,B) ) ) )
      & ( C = set_difference(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)],[f9]) ).

fof(f87,plain,
    ( ! [A,B,C] :
        ( C != set_difference(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_difference(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)],[f86]) ).

fof(f88,plain,
    ( ! [A,B,C] :
        ( C != set_difference(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_difference(A,B)
        | ( ( ~ in(sk0_4(C,B,A),C)
            | ~ in(sk0_4(C,B,A),A)
            | in(sk0_4(C,B,A),B) )
          & ( in(sk0_4(C,B,A),C)
            | ( in(sk0_4(C,B,A),A)
              & ~ in(sk0_4(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f87]) ).

fof(f89,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_difference(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f88]) ).

fof(f90,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_difference(X1,X2)
      | ~ in(X3,X0)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f88]) ).

fof(f91,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_difference(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f88]) ).

fof(f143,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & ~ subset(set_difference(A,C),set_difference(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f144,plain,
    ? [A,B] :
      ( subset(A,B)
      & ? [C] : ~ subset(set_difference(A,C),set_difference(B,C)) ),
    inference(miniscoping,[status(esa)],[f143]) ).

fof(f145,plain,
    ( subset(sk0_8,sk0_9)
    & ~ subset(set_difference(sk0_8,sk0_10),set_difference(sk0_9,sk0_10)) ),
    inference(skolemization,[status(esa)],[f144]) ).

fof(f146,plain,
    subset(sk0_8,sk0_9),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f147,plain,
    ~ subset(set_difference(sk0_8,sk0_10),set_difference(sk0_9,sk0_10)),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f183,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_difference(X1,X2))
      | in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f89]) ).

fof(f184,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_difference(X1,X2))
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f90]) ).

fof(f185,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_difference(X1,X2))
      | ~ in(X0,X1)
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f91]) ).

fof(f228,plain,
    ! [X0] :
      ( ~ in(X0,sk0_8)
      | in(X0,sk0_9) ),
    inference(resolution,[status(thm)],[f74,f146]) ).

fof(f3048,plain,
    ! [X0,X1,X2] :
      ( subset(set_difference(X0,X1),X2)
      | ~ in(sk0_2(X2,set_difference(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f75,f184]) ).

fof(f3049,plain,
    ! [X0,X1,X2] :
      ( subset(set_difference(X0,X1),X2)
      | in(sk0_2(X2,set_difference(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f75,f183]) ).

fof(f3056,plain,
    ! [X0,X1,X2] :
      ( subset(X0,set_difference(X1,X2))
      | ~ in(sk0_2(set_difference(X1,X2),X0),X1)
      | in(sk0_2(set_difference(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f76,f185]) ).

fof(f15736,plain,
    ~ in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_10),
    inference(resolution,[status(thm)],[f3048,f147]) ).

fof(f17985,plain,
    in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_8),
    inference(resolution,[status(thm)],[f3049,f147]) ).

fof(f18068,plain,
    ( spl0_158
  <=> in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f18070,plain,
    ( ~ in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_9)
    | spl0_158 ),
    inference(component_clause,[status(thm)],[f18068]) ).

fof(f18071,plain,
    ( spl0_159
  <=> in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_10) ),
    introduced(split_symbol_definition) ).

fof(f18072,plain,
    ( in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_10)
    | ~ spl0_159 ),
    inference(component_clause,[status(thm)],[f18071]) ).

fof(f18074,plain,
    ( ~ in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_9)
    | in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_10) ),
    inference(resolution,[status(thm)],[f3056,f147]) ).

fof(f18075,plain,
    ( ~ spl0_158
    | spl0_159 ),
    inference(split_clause,[status(thm)],[f18074,f18068,f18071]) ).

fof(f18187,plain,
    ( $false
    | ~ spl0_159 ),
    inference(forward_subsumption_resolution,[status(thm)],[f18072,f15736]) ).

fof(f18188,plain,
    ~ spl0_159,
    inference(contradiction_clause,[status(thm)],[f18187]) ).

fof(f19775,plain,
    ( ~ in(sk0_2(set_difference(sk0_9,sk0_10),set_difference(sk0_8,sk0_10)),sk0_8)
    | spl0_158 ),
    inference(resolution,[status(thm)],[f18070,f228]) ).

fof(f19776,plain,
    ( $false
    | spl0_158 ),
    inference(forward_subsumption_resolution,[status(thm)],[f19775,f17985]) ).

fof(f19777,plain,
    spl0_158,
    inference(contradiction_clause,[status(thm)],[f19776]) ).

fof(f19778,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f18075,f18188,f19777]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SEU132+2 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n025.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Mon Apr 29 19:56:55 EDT 2024
% 0.09/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.6.0
% 79.81/10.46  % Refutation found
% 79.81/10.46  % SZS status Theorem for theBenchmark: Theorem is valid
% 79.81/10.46  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 81.06/10.60  % Elapsed time: 10.272895 seconds
% 81.06/10.60  % CPU time: 81.008204 seconds
% 81.06/10.60  % Total memory used: 443.457 MB
% 81.06/10.60  % Net memory used: 425.428 MB
%------------------------------------------------------------------------------