TSTP Solution File: SET798+4 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% 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 20:40:22 EDT 2024

% Result   : Theorem 0.09s 0.31s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   28 (   5 unt;   0 def)
%            Number of atoms       :   99 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  106 (  35   ~;  33   |;  26   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   85 (  76   !;   9   ?)

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

fof(f15,axiom,
    ! [R,E,M] :
      ( lower_bound(M,R,E)
    <=> ! [X] :
          ( member(X,E)
         => apply(R,M,X) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,conjecture,
    ! [R,E] :
      ( order(R,E)
     => ! [X,Y] :
          ( ( subset(X,E)
            & subset(Y,E)
            & subset(X,Y) )
         => ! [M] :
              ( lower_bound(M,R,Y)
             => lower_bound(M,R,X) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,negated_conjecture,
    ~ ! [R,E] :
        ( order(R,E)
       => ! [X,Y] :
            ( ( subset(X,E)
              & subset(Y,E)
              & subset(X,Y) )
           => ! [M] :
                ( lower_bound(M,R,Y)
               => lower_bound(M,R,X) ) ) ),
    inference(negated_conjecture,[status(cth)],[f22]) ).

fof(f24,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( ~ member(X,A)
          | member(X,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f25,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
      & ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(miniscoping,[status(esa)],[f25]) ).

fof(f27,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( member(sk0_0(B,A),A)
          & ~ member(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f109,plain,
    ! [R,E,M] :
      ( lower_bound(M,R,E)
    <=> ! [X] :
          ( ~ member(X,E)
          | apply(R,M,X) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f110,plain,
    ! [R,E,M] :
      ( ( ~ lower_bound(M,R,E)
        | ! [X] :
            ( ~ member(X,E)
            | apply(R,M,X) ) )
      & ( lower_bound(M,R,E)
        | ? [X] :
            ( member(X,E)
            & ~ apply(R,M,X) ) ) ),
    inference(NNF_transformation,[status(esa)],[f109]) ).

fof(f111,plain,
    ( ! [R,E,M] :
        ( ~ lower_bound(M,R,E)
        | ! [X] :
            ( ~ member(X,E)
            | apply(R,M,X) ) )
    & ! [R,E,M] :
        ( lower_bound(M,R,E)
        | ? [X] :
            ( member(X,E)
            & ~ apply(R,M,X) ) ) ),
    inference(miniscoping,[status(esa)],[f110]) ).

fof(f112,plain,
    ( ! [R,E,M] :
        ( ~ lower_bound(M,R,E)
        | ! [X] :
            ( ~ member(X,E)
            | apply(R,M,X) ) )
    & ! [R,E,M] :
        ( lower_bound(M,R,E)
        | ( member(sk0_9(M,E,R),E)
          & ~ apply(R,M,sk0_9(M,E,R)) ) ) ),
    inference(skolemization,[status(esa)],[f111]) ).

fof(f113,plain,
    ! [X0,X1,X2,X3] :
      ( ~ lower_bound(X0,X1,X2)
      | ~ member(X3,X2)
      | apply(X1,X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f112]) ).

fof(f114,plain,
    ! [X0,X1,X2] :
      ( lower_bound(X0,X1,X2)
      | member(sk0_9(X0,X2,X1),X2) ),
    inference(cnf_transformation,[status(esa)],[f112]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( lower_bound(X0,X1,X2)
      | ~ apply(X1,X0,sk0_9(X0,X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f112]) ).

fof(f170,plain,
    ? [R,E] :
      ( order(R,E)
      & ? [X,Y] :
          ( subset(X,E)
          & subset(Y,E)
          & subset(X,Y)
          & ? [M] :
              ( lower_bound(M,R,Y)
              & ~ lower_bound(M,R,X) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f23]) ).

fof(f171,plain,
    ( order(sk0_16,sk0_17)
    & subset(sk0_18,sk0_17)
    & subset(sk0_19,sk0_17)
    & subset(sk0_18,sk0_19)
    & lower_bound(sk0_20,sk0_16,sk0_19)
    & ~ lower_bound(sk0_20,sk0_16,sk0_18) ),
    inference(skolemization,[status(esa)],[f170]) ).

fof(f175,plain,
    subset(sk0_18,sk0_19),
    inference(cnf_transformation,[status(esa)],[f171]) ).

fof(f176,plain,
    lower_bound(sk0_20,sk0_16,sk0_19),
    inference(cnf_transformation,[status(esa)],[f171]) ).

fof(f177,plain,
    ~ lower_bound(sk0_20,sk0_16,sk0_18),
    inference(cnf_transformation,[status(esa)],[f171]) ).

fof(f199,plain,
    ! [X0] :
      ( ~ member(X0,sk0_19)
      | apply(sk0_16,sk0_20,X0) ),
    inference(resolution,[status(thm)],[f113,f176]) ).

fof(f241,plain,
    ! [X0,X1,X2,X3] :
      ( lower_bound(X0,X1,X2)
      | ~ subset(X2,X3)
      | member(sk0_9(X0,X2,X1),X3) ),
    inference(resolution,[status(thm)],[f114,f28]) ).

fof(f242,plain,
    ! [X0] :
      ( lower_bound(sk0_20,sk0_16,X0)
      | ~ member(sk0_9(sk0_20,X0,sk0_16),sk0_19) ),
    inference(resolution,[status(thm)],[f115,f199]) ).

fof(f268,plain,
    ! [X0] :
      ( lower_bound(sk0_20,sk0_16,X0)
      | lower_bound(sk0_20,sk0_16,X0)
      | ~ subset(X0,sk0_19) ),
    inference(resolution,[status(thm)],[f242,f241]) ).

fof(f269,plain,
    ! [X0] :
      ( lower_bound(sk0_20,sk0_16,X0)
      | ~ subset(X0,sk0_19) ),
    inference(duplicate_literals_removal,[status(esa)],[f268]) ).

fof(f275,plain,
    ~ subset(sk0_18,sk0_19),
    inference(resolution,[status(thm)],[f269,f177]) ).

fof(f276,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f275,f175]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.09  % 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
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Mon Apr 29 21:53:05 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.09/0.30  % Drodi V3.6.0
% 0.09/0.31  % Refutation found
% 0.09/0.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.32  % Elapsed time: 0.031501 seconds
% 0.14/0.32  % CPU time: 0.144805 seconds
% 0.14/0.32  % Total memory used: 27.894 MB
% 0.14/0.32  % Net memory used: 27.819 MB
%------------------------------------------------------------------------------