TSTP Solution File: NUN085+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 12:31:18 EDT 2023

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   68 (  29 unt;   0 def)
%            Number of atoms       :  150 (  46 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  143 (  61   ~;  43   |;  36   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  120 (; 105   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( ~ r1(X19)
        & X19 != Y24 )
      | ( r1(X19)
        & X19 = Y24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ r2(X11,X12)
        & X12 != Y21 )
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X13,X14] :
    ? [Y22] :
    ! [X15] :
      ( ( ~ r3(X13,X14,X15)
        & X15 != Y22 )
      | ( r3(X13,X14,X15)
        & X15 = Y22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X7,Y10] :
      ( ! [Y20] :
          ( ~ r1(Y20)
          | Y20 != Y10 )
      | ~ r2(X7,Y10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [Y1] :
      ( ! [Y2] :
          ( ! [Y3] :
              ( ~ r1(Y3)
              | ~ r3(Y3,Y2,Y1) )
          | ! [Y4] :
              ( ~ r1(Y4)
              | ~ r2(Y4,Y2) ) )
      | ! [Y5] :
          ( Y1 != Y5
          | ~ r1(Y5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [Y1] :
        ( ! [Y2] :
            ( ! [Y3] :
                ( ~ r1(Y3)
                | ~ r3(Y3,Y2,Y1) )
            | ! [Y4] :
                ( ~ r1(Y4)
                | ~ r2(Y4,Y2) ) )
        | ! [Y5] :
            ( Y1 != Y5
            | ~ r1(Y5) ) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [Y24,X19] :
      ( pd0_0(X19,Y24)
     => ( ~ r1(X19)
        & X19 != Y24 ) ),
    introduced(predicate_definition,[f1]) ).

fof(f15,plain,
    ? [Y24] :
    ! [X19] :
      ( pd0_0(X19,Y24)
      | ( r1(X19)
        & X19 = Y24 ) ),
    inference(formula_renaming,[status(thm)],[f1,f14]) ).

fof(f16,plain,
    ! [X19] :
      ( pd0_0(X19,sk0_0)
      | ( r1(X19)
        & X19 = sk0_0 ) ),
    inference(skolemization,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0] :
      ( pd0_0(X0,sk0_0)
      | r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0] :
      ( pd0_0(X0,sk0_0)
      | X0 = sk0_0 ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X11,Y21,X12] :
      ( pd0_1(X12,Y21,X11)
     => ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    introduced(predicate_definition,[f2]) ).

fof(f20,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( pd0_1(X12,Y21,X11)
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    inference(formula_renaming,[status(thm)],[f2,f19]) ).

fof(f21,plain,
    ! [X11,X12] :
      ( pd0_1(X12,sk0_1(X11),X11)
      | ( r2(X11,X12)
        & X12 = sk0_1(X11) ) ),
    inference(skolemization,[status(esa)],[f20]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( pd0_1(X0,sk0_1(X1),X1)
      | X0 = sk0_1(X1) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f24,plain,
    ! [X13,X14,Y22,X15] :
      ( pd0_2(X15,Y22,X14,X13)
     => ( ~ r3(X13,X14,X15)
        & X15 != Y22 ) ),
    introduced(predicate_definition,[f3]) ).

fof(f25,plain,
    ! [X13,X14] :
    ? [Y22] :
    ! [X15] :
      ( pd0_2(X15,Y22,X14,X13)
      | ( r3(X13,X14,X15)
        & X15 = Y22 ) ),
    inference(formula_renaming,[status(thm)],[f3,f24]) ).

fof(f26,plain,
    ! [X13,X14,X15] :
      ( pd0_2(X15,sk0_2(X14,X13),X14,X13)
      | ( r3(X13,X14,X15)
        & X15 = sk0_2(X14,X13) ) ),
    inference(skolemization,[status(esa)],[f25]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( pd0_2(X0,sk0_2(X1,X2),X1,X2)
      | X0 = sk0_2(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

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(f36,plain,
    ! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_5(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f37,plain,
    ! [X0,X1] : sk0_5(X0,X1) = sk0_4(X0,X1),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f38,plain,
    ! [X0,X1] : r2(sk0_7(X0,X1),sk0_4(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

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] :
              ( r1(Y3)
              & r3(Y3,Y2,Y1) )
          & ? [Y4] :
              ( r1(Y4)
              & r2(Y4,Y2) ) )
      & ? [Y5] :
          ( Y1 = Y5
          & r1(Y5) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f65,plain,
    ( r1(sk0_22)
    & r3(sk0_22,sk0_21,sk0_20)
    & r1(sk0_23)
    & r2(sk0_23,sk0_21)
    & sk0_20 = sk0_24
    & r1(sk0_24) ),
    inference(skolemization,[status(esa)],[f64]) ).

fof(f66,plain,
    r1(sk0_22),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f67,plain,
    r3(sk0_22,sk0_21,sk0_20),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f68,plain,
    r1(sk0_23),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f69,plain,
    r2(sk0_23,sk0_21),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f70,plain,
    sk0_20 = sk0_24,
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f71,plain,
    r1(sk0_24),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f72,plain,
    ! [Y24,X19] :
      ( ~ pd0_0(X19,Y24)
      | ( ~ r1(X19)
        & X19 != Y24 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | ~ r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f72]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f72]) ).

fof(f75,plain,
    ! [X11,Y21,X12] :
      ( ~ pd0_1(X12,Y21,X11)
      | ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | ~ r2(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f75]) ).

fof(f78,plain,
    ! [X13,X14,Y22,X15] :
      ( ~ pd0_2(X15,Y22,X14,X13)
      | ( ~ r3(X13,X14,X15)
        & X15 != Y22 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f79,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_2(X0,X1,X2,X3)
      | ~ r3(X3,X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | ~ r2(X1,X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f89,plain,
    ! [X0] : ~ pd0_0(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f74]) ).

fof(f93,plain,
    r1(sk0_20),
    inference(forward_demodulation,[status(thm)],[f70,f71]) ).

fof(f96,plain,
    r1(sk0_0),
    inference(resolution,[status(thm)],[f17,f89]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ r1(X0)
      | X0 = sk0_0 ),
    inference(resolution,[status(thm)],[f73,f18]) ).

fof(f106,plain,
    sk0_20 = sk0_0,
    inference(resolution,[status(thm)],[f102,f93]) ).

fof(f107,plain,
    sk0_23 = sk0_0,
    inference(resolution,[status(thm)],[f102,f68]) ).

fof(f108,plain,
    sk0_22 = sk0_0,
    inference(resolution,[status(thm)],[f102,f66]) ).

fof(f109,plain,
    r3(sk0_22,sk0_21,sk0_0),
    inference(backward_demodulation,[status(thm)],[f106,f67]) ).

fof(f113,plain,
    r2(sk0_0,sk0_21),
    inference(backward_demodulation,[status(thm)],[f107,f69]) ).

fof(f120,plain,
    r3(sk0_0,sk0_21,sk0_0),
    inference(forward_demodulation,[status(thm)],[f108,f109]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | X1 = sk0_1(X0) ),
    inference(resolution,[status(thm)],[f76,f23]) ).

fof(f133,plain,
    sk0_21 = sk0_1(sk0_0),
    inference(resolution,[status(thm)],[f132,f113]) ).

fof(f139,plain,
    ! [X0] :
      ( pd0_1(X0,sk0_21,sk0_0)
      | X0 = sk0_1(sk0_0) ),
    inference(paramodulation,[status(thm)],[f133,f23]) ).

fof(f140,plain,
    ! [X0] :
      ( pd0_1(X0,sk0_21,sk0_0)
      | X0 = sk0_21 ),
    inference(forward_demodulation,[status(thm)],[f133,f139]) ).

fof(f142,plain,
    ! [X0] :
      ( X0 = sk0_21
      | ~ r2(sk0_0,X0) ),
    inference(resolution,[status(thm)],[f140,f76]) ).

fof(f145,plain,
    ! [X0] : sk0_6(sk0_0,X0) = sk0_21,
    inference(resolution,[status(thm)],[f142,f35]) ).

fof(f153,plain,
    ! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_4(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f37,f36]) ).

fof(f154,plain,
    ! [X0] : r3(X0,sk0_21,sk0_4(sk0_0,X0)),
    inference(paramodulation,[status(thm)],[f145,f153]) ).

fof(f166,plain,
    ! [X0,X1] : ~ r1(sk0_4(X0,X1)),
    inference(resolution,[status(thm)],[f38,f88]) ).

fof(f181,plain,
    ! [X0,X1,X2] :
      ( ~ r3(X0,X1,X2)
      | X2 = sk0_2(X1,X0) ),
    inference(resolution,[status(thm)],[f79,f28]) ).

fof(f183,plain,
    sk0_0 = sk0_2(sk0_21,sk0_0),
    inference(resolution,[status(thm)],[f181,f120]) ).

fof(f185,plain,
    ! [X0] : sk0_4(sk0_0,X0) = sk0_2(sk0_21,X0),
    inference(resolution,[status(thm)],[f181,f154]) ).

fof(f213,plain,
    ! [X0] : ~ r1(sk0_2(sk0_21,X0)),
    inference(paramodulation,[status(thm)],[f185,f166]) ).

fof(f214,plain,
    ~ r1(sk0_0),
    inference(paramodulation,[status(thm)],[f183,f213]) ).

fof(f215,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f214,f96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 10:11:40 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.63  % Elapsed time: 0.066823 seconds
% 0.19/0.63  % CPU time: 0.025080 seconds
% 0.19/0.63  % Memory used: 3.752 MB
%------------------------------------------------------------------------------