TSTP Solution File: NUM561+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 12:29:42 EDT 2023

% Result   : Theorem 0.14s 0.36s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   36 (  10 unt;   1 def)
%            Number of atoms       :  128 (  24 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  150 (  58   ~;  59   |;  22   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-4 aty)
%            Number of variables   :   52 (;  44   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [W0] :
      ( aSet0(W0)
     => aSubsetOf0(W0,W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f64,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => aSet0(szDzozmdt0(W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f68,definition,
    ! [W0] :
      ( aFunction0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,szDzozmdt0(W0))
         => ! [W2] :
              ( W2 = sdtlcdtrc0(W0,W1)
            <=> ( aSet0(W2)
                & ! [W3] :
                    ( aElementOf0(W3,W2)
                  <=> ? [W4] :
                        ( aElementOf0(W4,W1)
                        & sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f69,hypothesis,
    aFunction0(xF),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f70,hypothesis,
    aElementOf0(xx,szDzozmdt0(xF)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f71,conjecture,
    aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f72,negated_conjecture,
    ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    inference(negated_conjecture,[status(cth)],[f71]) ).

fof(f107,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | aSubsetOf0(W0,W0) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | aSubsetOf0(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f281,plain,
    ! [W0] :
      ( ~ aFunction0(W0)
      | aSet0(szDzozmdt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f64]) ).

fof(f282,plain,
    ! [X0] :
      ( ~ aFunction0(X0)
      | aSet0(szDzozmdt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f281]) ).

fof(f298,plain,
    ! [W0] :
      ( ~ aFunction0(W0)
      | ! [W1] :
          ( ~ aSubsetOf0(W1,szDzozmdt0(W0))
          | ! [W2] :
              ( W2 = sdtlcdtrc0(W0,W1)
            <=> ( aSet0(W2)
                & ! [W3] :
                    ( aElementOf0(W3,W2)
                  <=> ? [W4] :
                        ( aElementOf0(W4,W1)
                        & sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f68]) ).

fof(f299,plain,
    ! [W0] :
      ( ~ aFunction0(W0)
      | ! [W1] :
          ( ~ aSubsetOf0(W1,szDzozmdt0(W0))
          | ! [W2] :
              ( ( W2 != sdtlcdtrc0(W0,W1)
                | ( aSet0(W2)
                  & ! [W3] :
                      ( ( ~ aElementOf0(W3,W2)
                        | ? [W4] :
                            ( aElementOf0(W4,W1)
                            & sdtlpdtrp0(W0,W4) = W3 ) )
                      & ( aElementOf0(W3,W2)
                        | ! [W4] :
                            ( ~ aElementOf0(W4,W1)
                            | sdtlpdtrp0(W0,W4) != W3 ) ) ) ) )
              & ( W2 = sdtlcdtrc0(W0,W1)
                | ~ aSet0(W2)
                | ? [W3] :
                    ( ( ~ aElementOf0(W3,W2)
                      | ! [W4] :
                          ( ~ aElementOf0(W4,W1)
                          | sdtlpdtrp0(W0,W4) != W3 ) )
                    & ( aElementOf0(W3,W2)
                      | ? [W4] :
                          ( aElementOf0(W4,W1)
                          & sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f298]) ).

fof(f300,plain,
    ! [W0] :
      ( ~ aFunction0(W0)
      | ! [W1] :
          ( ~ aSubsetOf0(W1,szDzozmdt0(W0))
          | ( ! [W2] :
                ( W2 != sdtlcdtrc0(W0,W1)
                | ( aSet0(W2)
                  & ! [W3] :
                      ( ~ aElementOf0(W3,W2)
                      | ? [W4] :
                          ( aElementOf0(W4,W1)
                          & sdtlpdtrp0(W0,W4) = W3 ) )
                  & ! [W3] :
                      ( aElementOf0(W3,W2)
                      | ! [W4] :
                          ( ~ aElementOf0(W4,W1)
                          | sdtlpdtrp0(W0,W4) != W3 ) ) ) )
            & ! [W2] :
                ( W2 = sdtlcdtrc0(W0,W1)
                | ~ aSet0(W2)
                | ? [W3] :
                    ( ( ~ aElementOf0(W3,W2)
                      | ! [W4] :
                          ( ~ aElementOf0(W4,W1)
                          | sdtlpdtrp0(W0,W4) != W3 ) )
                    & ( aElementOf0(W3,W2)
                      | ? [W4] :
                          ( aElementOf0(W4,W1)
                          & sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f299]) ).

fof(f301,plain,
    ! [W0] :
      ( ~ aFunction0(W0)
      | ! [W1] :
          ( ~ aSubsetOf0(W1,szDzozmdt0(W0))
          | ( ! [W2] :
                ( W2 != sdtlcdtrc0(W0,W1)
                | ( aSet0(W2)
                  & ! [W3] :
                      ( ~ aElementOf0(W3,W2)
                      | ( aElementOf0(sk0_13(W3,W2,W1,W0),W1)
                        & sdtlpdtrp0(W0,sk0_13(W3,W2,W1,W0)) = W3 ) )
                  & ! [W3] :
                      ( aElementOf0(W3,W2)
                      | ! [W4] :
                          ( ~ aElementOf0(W4,W1)
                          | sdtlpdtrp0(W0,W4) != W3 ) ) ) )
            & ! [W2] :
                ( W2 = sdtlcdtrc0(W0,W1)
                | ~ aSet0(W2)
                | ( ( ~ aElementOf0(sk0_14(W2,W1,W0),W2)
                    | ! [W4] :
                        ( ~ aElementOf0(W4,W1)
                        | sdtlpdtrp0(W0,W4) != sk0_14(W2,W1,W0) ) )
                  & ( aElementOf0(sk0_14(W2,W1,W0),W2)
                    | ( aElementOf0(sk0_15(W2,W1,W0),W1)
                      & sdtlpdtrp0(W0,sk0_15(W2,W1,W0)) = sk0_14(W2,W1,W0) ) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f300]) ).

fof(f305,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ aFunction0(X0)
      | ~ aSubsetOf0(X1,szDzozmdt0(X0))
      | X2 != sdtlcdtrc0(X0,X1)
      | aElementOf0(X3,X2)
      | ~ aElementOf0(X4,X1)
      | sdtlpdtrp0(X0,X4) != X3 ),
    inference(cnf_transformation,[status(esa)],[f301]) ).

fof(f309,plain,
    aFunction0(xF),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f310,plain,
    aElementOf0(xx,szDzozmdt0(xF)),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f311,plain,
    ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    inference(cnf_transformation,[status(esa)],[f72]) ).

fof(f352,plain,
    ! [X0,X1,X2] :
      ( ~ aFunction0(X0)
      | ~ aSubsetOf0(X1,szDzozmdt0(X0))
      | aElementOf0(sdtlpdtrp0(X0,X2),sdtlcdtrc0(X0,X1))
      | ~ aElementOf0(X2,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f305]) ).

fof(f354,plain,
    ( spl0_0
  <=> aFunction0(xF) ),
    introduced(split_symbol_definition) ).

fof(f356,plain,
    ( ~ aFunction0(xF)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f354]) ).

fof(f362,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f356,f309]) ).

fof(f363,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f362]) ).

fof(f364,plain,
    ( spl0_2
  <=> aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)) ),
    introduced(split_symbol_definition) ).

fof(f366,plain,
    ( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f364]) ).

fof(f367,plain,
    ( spl0_3
  <=> aElementOf0(xx,szDzozmdt0(xF)) ),
    introduced(split_symbol_definition) ).

fof(f369,plain,
    ( ~ aElementOf0(xx,szDzozmdt0(xF))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f367]) ).

fof(f370,plain,
    ( ~ aFunction0(xF)
    | ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
    | ~ aElementOf0(xx,szDzozmdt0(xF)) ),
    inference(resolution,[status(thm)],[f352,f311]) ).

fof(f371,plain,
    ( ~ spl0_0
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f370,f354,f364,f367]) ).

fof(f480,plain,
    ( ~ aSet0(szDzozmdt0(xF))
    | spl0_2 ),
    inference(resolution,[status(thm)],[f366,f108]) ).

fof(f481,plain,
    ( ~ aFunction0(xF)
    | spl0_2 ),
    inference(resolution,[status(thm)],[f480,f282]) ).

fof(f482,plain,
    ( ~ spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f481,f354,f364]) ).

fof(f483,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f369,f310]) ).

fof(f484,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f483]) ).

fof(f485,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f363,f371,f482,f484]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.33  % Computer : n007.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 09:39:32 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Drodi V3.5.1
% 0.14/0.36  % Refutation found
% 0.14/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58  % Elapsed time: 0.021831 seconds
% 0.20/0.58  % CPU time: 0.047749 seconds
% 0.20/0.58  % Memory used: 15.657 MB
%------------------------------------------------------------------------------