TSTP Solution File: NUN076+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 20:36:22 EDT 2024

% Result   : Theorem 0.20s 0.42s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   60 (  23 unt;   0 def)
%            Number of atoms       :  153 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  166 (  73   ~;  57   |;  34   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-1 aty)
%            Number of variables   :  140 ( 115   !;  25   ?)

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

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

fof(f5,axiom,
    ! [X20] : id(X20,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X21,X22] :
      ( ~ id(X21,X22)
      | id(X22,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X23,X24,X25] :
      ( ~ id(X23,X24)
      | id(X23,X25)
      | ~ id(X24,X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X4] :
    ? [Y9] :
      ( id(Y9,X4)
      & ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X5] :
    ? [Y8] :
      ( ? [Y17] :
          ( r1(Y17)
          & r4(X5,Y17,Y8) )
      & ? [Y18] :
          ( id(Y8,Y18)
          & r1(Y18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,conjecture,
    ? [Y1,Y2,Y3] :
      ( ? [Y4] :
          ( id(Y4,Y1)
          & ? [Y6] :
              ( r4(Y6,Y2,Y4)
              & ? [Y7] :
                  ( r2(Y7,Y6)
                  & ? [Y8] :
                      ( r1(Y8)
                      & r2(Y8,Y7) ) ) ) )
      & ? [Y5] :
          ( id(Y5,Y1)
          & r3(Y2,Y3,Y5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,negated_conjecture,
    ~ ? [Y1,Y2,Y3] :
        ( ? [Y4] :
            ( id(Y4,Y1)
            & ? [Y6] :
                ( r4(Y6,Y2,Y4)
                & ? [Y7] :
                    ( r2(Y7,Y6)
                    & ? [Y8] :
                        ( r1(Y8)
                        & r2(Y8,Y7) ) ) ) )
        & ? [Y5] :
            ( id(Y5,Y1)
            & r3(Y2,Y3,Y5) ) ),
    inference(negated_conjecture,[status(cth)],[f19]) ).

fof(f21,plain,
    ! [Y24,X19] :
      ( pd0_0(X19,Y24)
     => ( id(X19,Y24)
        & r1(X19) ) ),
    introduced(predicate_definition,[f1]) ).

fof(f22,plain,
    ? [Y24] :
    ! [X19] :
      ( pd0_0(X19,Y24)
      | ( ~ r1(X19)
        & ~ id(X19,Y24) ) ),
    inference(formula_renaming,[status(thm)],[f1,f21]) ).

fof(f23,plain,
    ! [X19] :
      ( pd0_0(X19,sk0_0)
      | ( ~ r1(X19)
        & ~ id(X19,sk0_0) ) ),
    inference(skolemization,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0] :
      ( pd0_0(X0,sk0_0)
      | ~ r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0] :
      ( pd0_0(X0,sk0_0)
      | ~ id(X0,sk0_0) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X11,Y21,X12] :
      ( pd0_1(X12,Y21,X11)
     => ( id(X12,Y21)
        & r2(X11,X12) ) ),
    introduced(predicate_definition,[f2]) ).

fof(f27,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( pd0_1(X12,Y21,X11)
      | ( ~ r2(X11,X12)
        & ~ id(X12,Y21) ) ),
    inference(formula_renaming,[status(thm)],[f2,f26]) ).

fof(f28,plain,
    ! [X11,X12] :
      ( pd0_1(X12,sk0_1(X11),X11)
      | ( ~ r2(X11,X12)
        & ~ id(X12,sk0_1(X11)) ) ),
    inference(skolemization,[status(esa)],[f27]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( pd0_1(X0,sk0_1(X1),X1)
      | ~ id(X0,sk0_1(X1)) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f41,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f43,plain,
    ! [X24,X25] :
      ( ! [X23] :
          ( ~ id(X23,X24)
          | id(X23,X25) )
      | ~ id(X24,X25) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ~ id(X0,X1)
      | id(X0,X2)
      | ~ id(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f74,plain,
    ! [X4] :
      ( id(sk0_12(X4),X4)
      & r1(sk0_13(X4))
      & r3(X4,sk0_13(X4),sk0_12(X4)) ),
    inference(skolemization,[status(esa)],[f15]) ).

fof(f75,plain,
    ! [X0] : id(sk0_12(X0),X0),
    inference(cnf_transformation,[status(esa)],[f74]) ).

fof(f77,plain,
    ! [X0] : r3(X0,sk0_13(X0),sk0_12(X0)),
    inference(cnf_transformation,[status(esa)],[f74]) ).

fof(f78,plain,
    ! [X5] :
      ( r1(sk0_15(X5))
      & r4(X5,sk0_15(X5),sk0_14(X5))
      & id(sk0_14(X5),sk0_16(X5))
      & r1(sk0_16(X5)) ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f79,plain,
    ! [X0] : r1(sk0_15(X0)),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f80,plain,
    ! [X0] : r4(X0,sk0_15(X0),sk0_14(X0)),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f81,plain,
    ! [X0] : id(sk0_14(X0),sk0_16(X0)),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f82,plain,
    ! [X0] : r1(sk0_16(X0)),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f91,plain,
    ! [Y1,Y2,Y3] :
      ( ! [Y4] :
          ( ~ id(Y4,Y1)
          | ! [Y6] :
              ( ~ r4(Y6,Y2,Y4)
              | ! [Y7] :
                  ( ~ r2(Y7,Y6)
                  | ! [Y8] :
                      ( ~ r1(Y8)
                      | ~ r2(Y8,Y7) ) ) ) )
      | ! [Y5] :
          ( ~ id(Y5,Y1)
          | ~ r3(Y2,Y3,Y5) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f92,plain,
    ! [Y1,Y2] :
      ( ! [Y4] :
          ( ~ id(Y4,Y1)
          | ! [Y6] :
              ( ~ r4(Y6,Y2,Y4)
              | ! [Y7] :
                  ( ~ r2(Y7,Y6)
                  | ! [Y8] :
                      ( ~ r1(Y8)
                      | ~ r2(Y8,Y7) ) ) ) )
      | ! [Y5] :
          ( ~ id(Y5,Y1)
          | ! [Y3] : ~ r3(Y2,Y3,Y5) ) ),
    inference(miniscoping,[status(esa)],[f91]) ).

fof(f93,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ id(X0,X1)
      | ~ r4(X2,X3,X0)
      | ~ r2(X4,X2)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ id(X6,X1)
      | ~ r3(X3,X7,X6) ),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f94,plain,
    ! [Y24,X19] :
      ( ~ pd0_0(X19,Y24)
      | ( id(X19,Y24)
        & r1(X19) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | id(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f97,plain,
    ! [X11,Y21,X12] :
      ( ~ pd0_1(X12,Y21,X11)
      | ( id(X12,Y21)
        & r2(X11,X12) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | r2(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f124,plain,
    ! [X0] : id(X0,sk0_12(X0)),
    inference(resolution,[status(thm)],[f75,f42]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X0,sk0_12(X1)) ),
    inference(resolution,[status(thm)],[f124,f44]) ).

fof(f167,plain,
    ! [X0] : pd0_0(sk0_16(X0),sk0_0),
    inference(resolution,[status(thm)],[f24,f82]) ).

fof(f168,plain,
    ! [X0] : pd0_0(sk0_15(X0),sk0_0),
    inference(resolution,[status(thm)],[f24,f79]) ).

fof(f179,plain,
    ! [X0] : id(sk0_15(X0),sk0_0),
    inference(resolution,[status(thm)],[f95,f168]) ).

fof(f180,plain,
    ! [X0] : id(sk0_16(X0),sk0_0),
    inference(resolution,[status(thm)],[f95,f167]) ).

fof(f188,plain,
    ! [X0] : id(sk0_0,sk0_15(X0)),
    inference(resolution,[status(thm)],[f179,f42]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( ~ id(X0,sk0_16(X1))
      | id(X0,sk0_0) ),
    inference(resolution,[status(thm)],[f180,f44]) ).

fof(f205,plain,
    ! [X0] : pd0_1(sk0_1(X0),sk0_1(X0),X0),
    inference(resolution,[status(thm)],[f30,f41]) ).

fof(f231,plain,
    ! [X0] : id(sk0_0,sk0_12(sk0_15(X0))),
    inference(resolution,[status(thm)],[f188,f125]) ).

fof(f273,plain,
    ! [X0] : id(sk0_12(sk0_15(X0)),sk0_0),
    inference(resolution,[status(thm)],[f231,f42]) ).

fof(f392,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ id(sk0_14(X0),X1)
      | ~ r2(X2,X0)
      | ~ r1(X3)
      | ~ r2(X3,X2)
      | ~ id(X4,X1)
      | ~ r3(sk0_15(X0),X5,X4) ),
    inference(resolution,[status(thm)],[f80,f93]) ).

fof(f394,plain,
    ! [X0] : r2(X0,sk0_1(X0)),
    inference(resolution,[status(thm)],[f99,f205]) ).

fof(f408,plain,
    ! [X0] : id(sk0_14(X0),sk0_0),
    inference(resolution,[status(thm)],[f191,f81]) ).

fof(f415,plain,
    ! [X0] : pd0_0(sk0_14(X0),sk0_0),
    inference(resolution,[status(thm)],[f408,f25]) ).

fof(f421,plain,
    ! [X0] : r1(sk0_14(X0)),
    inference(resolution,[status(thm)],[f415,f96]) ).

fof(f451,plain,
    ! [X0,X1,X2,X3] :
      ( ~ id(sk0_14(X0),X1)
      | ~ r2(X2,X0)
      | ~ r1(X3)
      | ~ r2(X3,X2)
      | ~ id(sk0_12(sk0_15(X0)),X1) ),
    inference(resolution,[status(thm)],[f392,f77]) ).

fof(f453,plain,
    ! [X0,X1,X2] :
      ( ~ id(sk0_14(X0),sk0_0)
      | ~ r2(X1,X0)
      | ~ r1(X2)
      | ~ r2(X2,X1) ),
    inference(resolution,[status(thm)],[f451,f273]) ).

fof(f454,plain,
    ! [X0,X1,X2] :
      ( ~ r2(X0,X1)
      | ~ r1(X2)
      | ~ r2(X2,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f453,f408]) ).

fof(f460,plain,
    ! [X0,X1] :
      ( ~ r2(sk0_1(X0),X1)
      | ~ r1(X0) ),
    inference(resolution,[status(thm)],[f454,f394]) ).

fof(f463,plain,
    ! [X0] : ~ r1(X0),
    inference(resolution,[status(thm)],[f460,f394]) ).

fof(f466,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f421,f463]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n009.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 22:33:41 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.20/0.42  % Refutation found
% 0.20/0.42  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.42  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.44  % Elapsed time: 0.090091 seconds
% 0.20/0.44  % CPU time: 0.635016 seconds
% 0.20/0.44  % Total memory used: 15.694 MB
% 0.20/0.44  % Net memory used: 15.137 MB
%------------------------------------------------------------------------------