TSTP Solution File: NUN057+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUN057+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 20:36:17 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   73 (  27 unt;   0 def)
%            Number of atoms       :  209 (  44 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  246 ( 110   ~;  85   |;  48   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  199 ( 169   !;  30   ?)

% 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(f8,axiom,
    ! [X4] :
    ? [Y9] :
      ( ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) )
      & Y9 = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ? [Y1] :
      ( ? [Y2] :
          ( Y1 = Y2
          & ? [Y3] :
              ( r2(Y3,Y2)
              & ? [Y4] :
                  ( r2(Y4,Y3)
                  & ? [Y6] :
                      ( r2(Y6,Y4)
                      & ? [Y8] :
                          ( r1(Y8)
                          & r2(Y8,Y6) ) ) ) ) )
      & ? [Y5] :
          ( r3(Y5,Y5,Y1)
          & ? [Y7] :
              ( r2(Y7,Y5)
              & ? [Y9] :
                  ( r1(Y9)
                  & r2(Y9,Y7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ? [Y1] :
        ( ? [Y2] :
            ( Y1 = Y2
            & ? [Y3] :
                ( r2(Y3,Y2)
                & ? [Y4] :
                    ( r2(Y4,Y3)
                    & ? [Y6] :
                        ( r2(Y6,Y4)
                        & ? [Y8] :
                            ( r1(Y8)
                            & r2(Y8,Y6) ) ) ) ) )
        & ? [Y5] :
            ( r3(Y5,Y5,Y1)
            & ? [Y7] :
                ( r2(Y7,Y5)
                & ? [Y9] :
                    ( r1(Y9)
                    & r2(Y9,Y7) ) ) ) ),
    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(f22,plain,
    ! [X0,X1] :
      ( pd0_1(X0,sk0_1(X1),X1)
      | r2(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

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(f39,plain,
    ! [X0,X1] : r3(X0,X1,sk0_7(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f47,plain,
    ! [X4] :
      ( r1(sk0_13(X4))
      & r3(X4,sk0_13(X4),sk0_12(X4))
      & sk0_12(X4) = X4 ),
    inference(skolemization,[status(esa)],[f8]) ).

fof(f48,plain,
    ! [X0] : r1(sk0_13(X0)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0] : r3(X0,sk0_13(X0),sk0_12(X0)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ! [X0] : sk0_12(X0) = X0,
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f64,plain,
    ! [Y1] :
      ( ! [Y2] :
          ( Y1 != Y2
          | ! [Y3] :
              ( ~ r2(Y3,Y2)
              | ! [Y4] :
                  ( ~ r2(Y4,Y3)
                  | ! [Y6] :
                      ( ~ r2(Y6,Y4)
                      | ! [Y8] :
                          ( ~ r1(Y8)
                          | ~ r2(Y8,Y6) ) ) ) ) )
      | ! [Y5] :
          ( ~ r3(Y5,Y5,Y1)
          | ! [Y7] :
              ( ~ r2(Y7,Y5)
              | ! [Y9] :
                  ( ~ r1(Y9)
                  | ~ r2(Y9,Y7) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f65,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
      ( X0 != X1
      | ~ r2(X2,X1)
      | ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ r3(X6,X6,X0)
      | ~ r2(X7,X6)
      | ~ r1(X8)
      | ~ r2(X8,X7) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [Y24,X19] :
      ( ~ pd0_0(X19,Y24)
      | ( ~ r1(X19)
        & X19 != Y24 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | ~ r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f69,plain,
    ! [X11,Y21,X12] :
      ( ~ pd0_1(X12,Y21,X11)
      | ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | ~ r2(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f72,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(f73,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_2(X0,X1,X2,X3)
      | ~ r3(X3,X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f72]) ).

fof(f83,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ r2(X0,X1)
      | ~ r2(X2,X0)
      | ~ r2(X3,X2)
      | ~ r1(X4)
      | ~ r2(X4,X3)
      | ~ r3(X5,X5,X1)
      | ~ r2(X6,X5)
      | ~ r1(X7)
      | ~ r2(X7,X6) ),
    inference(destructive_equality_resolution,[status(esa)],[f65]) ).

fof(f84,plain,
    ! [X0] : ~ pd0_0(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f68]) ).

fof(f85,plain,
    ! [X0,X1] : ~ pd0_1(X0,X0,X1),
    inference(destructive_equality_resolution,[status(esa)],[f71]) ).

fof(f88,plain,
    r1(sk0_0),
    inference(resolution,[status(thm)],[f17,f84]) ).

fof(f90,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ r2(X0,X1)
      | ~ r2(X2,X0)
      | ~ r2(X3,X2)
      | ~ r1(X4)
      | ~ r2(X4,X3)
      | ~ r3(X5,X5,X1)
      | ~ r2(X6,X5)
      | ~ r2(sk0_0,X6) ),
    inference(resolution,[status(thm)],[f88,f83]) ).

fof(f110,plain,
    ! [X0] :
      ( X0 = sk0_0
      | ~ r1(X0) ),
    inference(resolution,[status(thm)],[f18,f67]) ).

fof(f113,plain,
    ! [X0] : sk0_13(X0) = sk0_0,
    inference(resolution,[status(thm)],[f110,f48]) ).

fof(f117,plain,
    ! [X0] : r2(X0,sk0_1(X0)),
    inference(resolution,[status(thm)],[f22,f85]) ).

fof(f131,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ r2(X0,X1)
      | ~ r2(X2,X0)
      | ~ r2(X3,X2)
      | ~ r1(X4)
      | ~ r2(X4,X3)
      | ~ r3(X5,X5,X1)
      | ~ r2(sk0_1(sk0_0),X5) ),
    inference(resolution,[status(thm)],[f117,f90]) ).

fof(f140,plain,
    ! [X0] : r3(X0,sk0_0,sk0_12(X0)),
    inference(forward_demodulation,[status(thm)],[f113,f49]) ).

fof(f141,plain,
    ! [X0] : r3(X0,sk0_0,X0),
    inference(forward_demodulation,[status(thm)],[f50,f140]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | X1 = sk0_1(X0) ),
    inference(resolution,[status(thm)],[f70,f23]) ).

fof(f163,plain,
    ! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_4(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f37,f36]) ).

fof(f165,plain,
    ! [X0,X1] : sk0_4(X0,X1) = sk0_1(sk0_7(X0,X1)),
    inference(resolution,[status(thm)],[f162,f38]) ).

fof(f167,plain,
    ! [X0,X1] : sk0_6(X0,X1) = sk0_1(X0),
    inference(resolution,[status(thm)],[f162,f35]) ).

fof(f176,plain,
    ! [X0,X1] : r3(X0,sk0_1(X1),sk0_4(X1,X0)),
    inference(backward_demodulation,[status(thm)],[f167,f163]) ).

fof(f202,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ r2(X0,sk0_4(X1,sk0_1(X1)))
      | ~ r2(X2,X0)
      | ~ r2(X3,X2)
      | ~ r1(X4)
      | ~ r2(X4,X3)
      | ~ r2(sk0_1(sk0_0),sk0_1(X1)) ),
    inference(resolution,[status(thm)],[f176,f131]) ).

fof(f204,plain,
    ! [X0,X1,X2] :
      ( ~ r3(X0,X1,X2)
      | X2 = sk0_2(X1,X0) ),
    inference(resolution,[status(thm)],[f73,f28]) ).

fof(f206,plain,
    ! [X0,X1] : sk0_4(X0,X1) = sk0_2(sk0_1(X0),X1),
    inference(resolution,[status(thm)],[f204,f176]) ).

fof(f207,plain,
    ! [X0] : X0 = sk0_2(sk0_0,X0),
    inference(resolution,[status(thm)],[f204,f141]) ).

fof(f208,plain,
    ! [X0,X1] : sk0_7(X0,X1) = sk0_2(X0,X1),
    inference(resolution,[status(thm)],[f204,f39]) ).

fof(f215,plain,
    ! [X0,X1] : sk0_4(X0,X1) = sk0_1(sk0_2(X0,X1)),
    inference(backward_demodulation,[status(thm)],[f208,f165]) ).

fof(f217,plain,
    ! [X0,X1] : r2(sk0_2(X0,X1),sk0_4(X0,X1)),
    inference(backward_demodulation,[status(thm)],[f208,f38]) ).

fof(f229,plain,
    ! [X0] : sk0_4(sk0_0,X0) = sk0_1(X0),
    inference(paramodulation,[status(thm)],[f207,f215]) ).

fof(f256,plain,
    ! [X0,X1,X2,X3] :
      ( ~ r2(X0,sk0_4(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))))
      | ~ r2(X1,X0)
      | ~ r2(X2,X1)
      | ~ r1(X3)
      | ~ r2(X3,X2) ),
    inference(resolution,[status(thm)],[f202,f117]) ).

fof(f259,plain,
    ! [X0,X1,X2] :
      ( ~ r2(X0,sk0_2(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))))
      | ~ r2(X1,X0)
      | ~ r1(X2)
      | ~ r2(X2,X1) ),
    inference(resolution,[status(thm)],[f256,f217]) ).

fof(f260,plain,
    ! [X0,X1,X2] :
      ( ~ r2(X0,sk0_4(sk0_0,sk0_1(sk0_1(sk0_0))))
      | ~ r2(X1,X0)
      | ~ r1(X2)
      | ~ r2(X2,X1) ),
    inference(forward_demodulation,[status(thm)],[f206,f259]) ).

fof(f261,plain,
    ! [X0,X1,X2] :
      ( ~ r2(X0,sk0_1(sk0_1(sk0_1(sk0_0))))
      | ~ r2(X1,X0)
      | ~ r1(X2)
      | ~ r2(X2,X1) ),
    inference(forward_demodulation,[status(thm)],[f229,f260]) ).

fof(f262,plain,
    ! [X0,X1] :
      ( ~ r2(X0,sk0_1(sk0_1(sk0_0)))
      | ~ r1(X1)
      | ~ r2(X1,X0) ),
    inference(resolution,[status(thm)],[f261,f117]) ).

fof(f263,plain,
    ! [X0] :
      ( ~ r1(X0)
      | ~ r2(X0,sk0_1(sk0_0)) ),
    inference(resolution,[status(thm)],[f262,f117]) ).

fof(f264,plain,
    ~ r1(sk0_0),
    inference(resolution,[status(thm)],[f263,f117]) ).

fof(f265,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f264,f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUN057+2 : 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 : n008.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 22:39:43 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40  % Elapsed time: 0.037108 seconds
% 0.13/0.40  % CPU time: 0.138284 seconds
% 0.13/0.40  % Total memory used: 26.568 MB
% 0.13/0.40  % Net memory used: 26.502 MB
%------------------------------------------------------------------------------