TSTP Solution File: NUN066+2 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 12:31:14 EDT 2023

% Result   : Theorem 0.19s 0.53s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   48 (   6 unt;   0 def)
%            Number of atoms       :  153 (  48 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  176 (  71   ~;  73   |;  31   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   0 con; 1-2 aty)
%            Number of variables   :  121 (; 102   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X1,X8] :
    ? [Y4] :
      ( ? [Y5] :
          ( ? [Y15] :
              ( r2(X8,Y15)
              & r3(X1,Y15,Y5) )
          & Y5 = Y4 )
      & ? [Y7] :
          ( r2(Y7,Y4)
          & r3(X1,X8,Y7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X3,X10] :
      ( ! [Y12] :
          ( ! [Y13] :
              ( ~ r2(X3,Y13)
              | Y13 != Y12 )
          | ~ r2(X10,Y12) )
      | X3 = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X5] :
    ? [Y8] :
      ( ? [Y17] :
          ( r1(Y17)
          & r4(X5,Y17,Y8) )
      & ? [Y18] :
          ( r1(Y18)
          & Y8 = Y18 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X7,Y10] :
      ( ! [Y20] :
          ( ~ r1(Y20)
          | Y20 != Y10 )
      | ~ r2(X7,Y10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ? [Y1] :
      ( ! [Y2] :
          ( ! [Y3] :
              ( ! [Y4] :
                  ( ~ r1(Y4)
                  | ~ r2(Y4,Y3) )
              | ~ r2(Y3,Y2) )
          | Y1 != Y2 )
      & ! [Y5] :
          ( ~ r1(Y5)
          | Y1 != Y5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ? [Y1] :
        ( ! [Y2] :
            ( ! [Y3] :
                ( ! [Y4] :
                    ( ~ r1(Y4)
                    | ~ r2(Y4,Y3) )
                | ~ r2(Y3,Y2) )
            | Y1 != Y2 )
        & ! [Y5] :
            ( ~ r1(Y5)
            | Y1 != Y5 ) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f34,plain,
    ! [X1,X8] :
      ( r2(X8,sk0_6(X8,X1))
      & r3(X1,sk0_6(X8,X1),sk0_5(X8,X1))
      & sk0_5(X8,X1) = sk0_4(X8,X1)
      & r2(sk0_7(X8,X1),sk0_4(X8,X1))
      & r3(X1,X8,sk0_7(X8,X1)) ),
    inference(skolemization,[status(esa)],[f5]) ).

fof(f35,plain,
    ! [X0,X1] : r2(X0,sk0_6(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r2(X3,X2)
      | X0 = X3 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f51,plain,
    ! [X5] :
      ( r1(sk0_15(X5))
      & r4(X5,sk0_15(X5),sk0_14(X5))
      & r1(sk0_16(X5))
      & sk0_14(X5) = sk0_16(X5) ),
    inference(skolemization,[status(esa)],[f9]) ).

fof(f54,plain,
    ! [X0] : r1(sk0_16(X0)),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f55,plain,
    ! [X0] : sk0_14(X0) = sk0_16(X0),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f62,plain,
    ! [Y10] :
      ( ! [Y20] :
          ( ~ r1(Y20)
          | Y20 != Y10 )
      | ! [X7] : ~ r2(X7,Y10) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | X0 != X1
      | ~ r2(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f62]) ).

fof(f64,plain,
    ! [Y1] :
      ( ? [Y2] :
          ( ? [Y3] :
              ( ? [Y4] :
                  ( r1(Y4)
                  & r2(Y4,Y3) )
              & r2(Y3,Y2) )
          & Y1 = Y2 )
      | ? [Y5] :
          ( r1(Y5)
          & Y1 = Y5 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f65,plain,
    ! [Y1,Y2] :
      ( pd0_5(Y2,Y1)
     => ( ? [Y3] :
            ( ? [Y4] :
                ( r1(Y4)
                & r2(Y4,Y3) )
            & r2(Y3,Y2) )
        & Y1 = Y2 ) ),
    introduced(predicate_definition,[f64]) ).

fof(f66,plain,
    ! [Y1] :
      ( ? [Y2] : pd0_5(Y2,Y1)
      | ? [Y5] :
          ( r1(Y5)
          & Y1 = Y5 ) ),
    inference(formula_renaming,[status(thm)],[f64,f65]) ).

fof(f67,plain,
    ! [Y1] :
      ( pd0_5(sk0_20(Y1),Y1)
      | ( r1(sk0_21(Y1))
        & Y1 = sk0_21(Y1) ) ),
    inference(skolemization,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [X0] :
      ( pd0_5(sk0_20(X0),X0)
      | r1(sk0_21(X0)) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f69,plain,
    ! [X0] :
      ( pd0_5(sk0_20(X0),X0)
      | X0 = sk0_21(X0) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f85,plain,
    ! [Y1,Y2] :
      ( ~ pd0_5(Y2,Y1)
      | ( ? [Y3] :
            ( ? [Y4] :
                ( r1(Y4)
                & r2(Y4,Y3) )
            & r2(Y3,Y2) )
        & Y1 = Y2 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f65]) ).

fof(f86,plain,
    ! [Y1,Y2] :
      ( ~ pd0_5(Y2,Y1)
      | ( r1(sk0_23(Y2,Y1))
        & r2(sk0_23(Y2,Y1),sk0_22(Y2,Y1))
        & r2(sk0_22(Y2,Y1),Y2)
        & Y1 = Y2 ) ),
    inference(skolemization,[status(esa)],[f85]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ~ pd0_5(X0,X1)
      | r2(sk0_23(X0,X1),sk0_22(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ pd0_5(X0,X1)
      | r2(sk0_22(X0,X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ pd0_5(X0,X1)
      | X1 = X0 ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f91,plain,
    ! [X0] :
      ( X0 = sk0_21(X0)
      | X0 = sk0_20(X0) ),
    inference(resolution,[status(thm)],[f69,f90]) ).

fof(f92,plain,
    ! [X0] :
      ( r1(sk0_21(X0))
      | X0 = sk0_20(X0) ),
    inference(resolution,[status(thm)],[f68,f90]) ).

fof(f94,plain,
    ! [X0] :
      ( r1(X0)
      | X0 = sk0_20(X0)
      | X0 = sk0_20(X0) ),
    inference(paramodulation,[status(thm)],[f91,f92]) ).

fof(f95,plain,
    ! [X0] :
      ( r1(X0)
      | X0 = sk0_20(X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f94]) ).

fof(f96,plain,
    ! [X0] :
      ( pd0_5(X0,X0)
      | r1(sk0_21(X0))
      | r1(X0) ),
    inference(paramodulation,[status(thm)],[f95,f68]) ).

fof(f97,plain,
    ! [X0] :
      ( pd0_5(X0,X0)
      | X0 = sk0_21(X0)
      | r1(X0) ),
    inference(paramodulation,[status(thm)],[f95,f69]) ).

fof(f101,plain,
    ! [X0,X1,X2,X3] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | X0 = sk0_22(X2,X3)
      | ~ pd0_5(X2,X3) ),
    inference(resolution,[status(thm)],[f46,f89]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_5(X0,X1)
      | ~ r1(X2)
      | X2 != sk0_22(X0,X1) ),
    inference(resolution,[status(thm)],[f88,f63]) ).

fof(f107,plain,
    ! [X0] : r1(sk0_14(X0)),
    inference(paramodulation,[status(thm)],[f55,f54]) ).

fof(f109,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | X0 != sk0_6(X1,X2) ),
    inference(resolution,[status(thm)],[f35,f63]) ).

fof(f116,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_5(X0,X1)
      | ~ r1(X2)
      | ~ r2(X2,X3)
      | X3 != X0
      | ~ pd0_5(X0,X1) ),
    inference(resolution,[status(thm)],[f106,f101]) ).

fof(f117,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_5(X0,X1)
      | ~ r1(X2)
      | ~ r2(X2,X3)
      | X3 != X0 ),
    inference(duplicate_literals_removal,[status(esa)],[f116]) ).

fof(f128,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | ~ r2(X0,X1)
      | X1 != X2
      | r1(sk0_21(X2))
      | r1(X2) ),
    inference(resolution,[status(thm)],[f117,f96]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | ~ r2(X0,X1)
      | X1 != X2
      | r1(sk0_21(X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f128,f63]) ).

fof(f130,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | ~ r2(X0,X1)
      | X1 != X2
      | X2 = sk0_21(X2)
      | r1(X2) ),
    inference(resolution,[status(thm)],[f117,f97]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | ~ r2(X0,X1)
      | X1 != X2
      | X2 = sk0_21(X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f130,f63]) ).

fof(f136,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | sk0_6(X0,X1) != X2
      | X2 = sk0_21(X2) ),
    inference(resolution,[status(thm)],[f131,f35]) ).

fof(f141,plain,
    ! [X0,X1,X2] :
      ( ~ r1(X0)
      | sk0_6(X0,X1) != X2
      | r1(sk0_21(X2)) ),
    inference(resolution,[status(thm)],[f129,f35]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | r1(sk0_21(sk0_6(X0,X1))) ),
    inference(equality_resolution,[status(esa)],[f141]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | sk0_6(X0,X1) = sk0_21(sk0_6(X0,X1)) ),
    inference(equality_resolution,[status(esa)],[f136]) ).

fof(f323,plain,
    ! [X0,X1] :
      ( ~ r1(sk0_21(sk0_6(X0,X1)))
      | ~ r1(X0) ),
    inference(resolution,[status(thm)],[f109,f179]) ).

fof(f324,plain,
    ! [X0] : ~ r1(X0),
    inference(forward_subsumption_resolution,[status(thm)],[f323,f156]) ).

fof(f337,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f107,f324]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n029.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 11:00:07 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 0.19/0.53  % Refutation found
% 0.19/0.53  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.53  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.55  % Elapsed time: 0.199658 seconds
% 0.19/0.55  % CPU time: 1.441175 seconds
% 0.19/0.55  % Memory used: 72.193 MB
%------------------------------------------------------------------------------