TSTP Solution File: SET803+4 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 20:40:23 EDT 2024

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   32 (   9 unt;   0 def)
%            Number of atoms       :  131 (  22 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  155 (  56   ~;  47   |;  42   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   99 (  83   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [R,E,M] :
      ( greatest(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( member(X,E)
           => apply(R,X,M) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [R,E,M] :
      ( max(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( ( member(X,E)
              & apply(R,M,X) )
           => M = X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [R,E] :
      ( order(R,E)
     => ! [M1,M2] :
          ( ( max(M1,R,E)
            & max(M2,R,E)
            & M1 != M2 )
         => ~ ? [M] : greatest(M,R,E) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [R,E] :
        ( order(R,E)
       => ! [M1,M2] :
            ( ( max(M1,R,E)
              & max(M2,R,E)
              & M1 != M2 )
           => ~ ? [M] : greatest(M,R,E) ) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f51,plain,
    ! [R,E,M] :
      ( greatest(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( ~ member(X,E)
            | apply(R,X,M) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f52,plain,
    ! [R,E,M] :
      ( ( ~ greatest(M,R,E)
        | ( member(M,E)
          & ! [X] :
              ( ~ member(X,E)
              | apply(R,X,M) ) ) )
      & ( greatest(M,R,E)
        | ~ member(M,E)
        | ? [X] :
            ( member(X,E)
            & ~ apply(R,X,M) ) ) ),
    inference(NNF_transformation,[status(esa)],[f51]) ).

fof(f53,plain,
    ( ! [R,E,M] :
        ( ~ greatest(M,R,E)
        | ( member(M,E)
          & ! [X] :
              ( ~ member(X,E)
              | apply(R,X,M) ) ) )
    & ! [R,E,M] :
        ( greatest(M,R,E)
        | ~ member(M,E)
        | ? [X] :
            ( member(X,E)
            & ~ apply(R,X,M) ) ) ),
    inference(miniscoping,[status(esa)],[f52]) ).

fof(f54,plain,
    ( ! [R,E,M] :
        ( ~ greatest(M,R,E)
        | ( member(M,E)
          & ! [X] :
              ( ~ member(X,E)
              | apply(R,X,M) ) ) )
    & ! [R,E,M] :
        ( greatest(M,R,E)
        | ~ member(M,E)
        | ( member(sk0_7(M,E,R),E)
          & ~ apply(R,sk0_7(M,E,R),M) ) ) ),
    inference(skolemization,[status(esa)],[f53]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ~ greatest(X0,X1,X2)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3] :
      ( ~ greatest(X0,X1,X2)
      | ~ member(X3,X2)
      | apply(X1,X3,X0) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f67,plain,
    ! [R,E,M] :
      ( max(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( ~ member(X,E)
            | ~ apply(R,M,X)
            | M = X ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f68,plain,
    ! [R,E,M] :
      ( ( ~ max(M,R,E)
        | ( member(M,E)
          & ! [X] :
              ( ~ member(X,E)
              | ~ apply(R,M,X)
              | M = X ) ) )
      & ( max(M,R,E)
        | ~ member(M,E)
        | ? [X] :
            ( member(X,E)
            & apply(R,M,X)
            & M != X ) ) ),
    inference(NNF_transformation,[status(esa)],[f67]) ).

fof(f69,plain,
    ( ! [R,E,M] :
        ( ~ max(M,R,E)
        | ( member(M,E)
          & ! [X] :
              ( ~ member(X,E)
              | ~ apply(R,M,X)
              | M = X ) ) )
    & ! [R,E,M] :
        ( max(M,R,E)
        | ~ member(M,E)
        | ? [X] :
            ( member(X,E)
            & apply(R,M,X)
            & M != X ) ) ),
    inference(miniscoping,[status(esa)],[f68]) ).

fof(f70,plain,
    ( ! [R,E,M] :
        ( ~ max(M,R,E)
        | ( member(M,E)
          & ! [X] :
              ( ~ member(X,E)
              | ~ apply(R,M,X)
              | M = X ) ) )
    & ! [R,E,M] :
        ( max(M,R,E)
        | ~ member(M,E)
        | ( member(sk0_9(M,E,R),E)
          & apply(R,M,sk0_9(M,E,R))
          & M != sk0_9(M,E,R) ) ) ),
    inference(skolemization,[status(esa)],[f69]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ~ max(X0,X1,X2)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3] :
      ( ~ max(X0,X1,X2)
      | ~ member(X3,X2)
      | ~ apply(X1,X0,X3)
      | X0 = X3 ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f105,plain,
    ? [R,E] :
      ( order(R,E)
      & ? [M1,M2] :
          ( max(M1,R,E)
          & max(M2,R,E)
          & M1 != M2
          & ? [M] : greatest(M,R,E) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f106,plain,
    ? [R,E] :
      ( order(R,E)
      & ? [M1,M2] :
          ( max(M1,R,E)
          & max(M2,R,E)
          & M1 != M2 )
      & ? [M] : greatest(M,R,E) ),
    inference(miniscoping,[status(esa)],[f105]) ).

fof(f107,plain,
    ( order(sk0_13,sk0_14)
    & max(sk0_15,sk0_13,sk0_14)
    & max(sk0_16,sk0_13,sk0_14)
    & sk0_15 != sk0_16
    & greatest(sk0_17,sk0_13,sk0_14) ),
    inference(skolemization,[status(esa)],[f106]) ).

fof(f109,plain,
    max(sk0_15,sk0_13,sk0_14),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f110,plain,
    max(sk0_16,sk0_13,sk0_14),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f111,plain,
    sk0_15 != sk0_16,
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f112,plain,
    greatest(sk0_17,sk0_13,sk0_14),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f130,plain,
    member(sk0_17,sk0_14),
    inference(resolution,[status(thm)],[f55,f112]) ).

fof(f133,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ max(X0,X1,X2)
      | ~ member(X3,X2)
      | X0 = X3
      | ~ greatest(X3,X1,X4)
      | ~ member(X0,X4) ),
    inference(resolution,[status(thm)],[f72,f56]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ max(X0,sk0_13,X1)
      | ~ member(sk0_17,X1)
      | X0 = sk0_17
      | ~ member(X0,sk0_14) ),
    inference(resolution,[status(thm)],[f133,f112]) ).

fof(f135,plain,
    ! [X0] :
      ( ~ max(X0,sk0_13,sk0_14)
      | X0 = sk0_17
      | ~ member(X0,sk0_14) ),
    inference(resolution,[status(thm)],[f134,f130]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ max(X0,sk0_13,sk0_14)
      | X0 = sk0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f135,f71]) ).

fof(f137,plain,
    sk0_16 = sk0_17,
    inference(resolution,[status(thm)],[f136,f110]) ).

fof(f138,plain,
    sk0_15 = sk0_17,
    inference(resolution,[status(thm)],[f136,f109]) ).

fof(f151,plain,
    sk0_15 = sk0_16,
    inference(forward_demodulation,[status(thm)],[f137,f138]) ).

fof(f152,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f151,f111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 21:47:59 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.022141 seconds
% 0.13/0.37  % CPU time: 0.034438 seconds
% 0.13/0.37  % Total memory used: 11.496 MB
% 0.13/0.37  % Net memory used: 11.454 MB
%------------------------------------------------------------------------------