TSTP Solution File: NUN068+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUN068+2 : 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 20:36:20 EDT 2024

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   77 (   9 unt;   0 def)
%            Number of atoms       :  190 (  86 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  176 (  63   ~;  85   |;  25   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  139 ( 126   !;  13   ?)

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

fof(f2,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ r2(X11,X12)
        & X12 != Y21 )
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    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(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] :
              ( ~ r1(Y3)
              | ~ r2(Y3,Y2) )
          | Y1 != Y2 )
      & ! [Y4] :
          ( ~ r1(Y4)
          | Y1 != Y4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ? [Y1] :
        ( ! [Y2] :
            ( ! [Y3] :
                ( ~ r1(Y3)
                | ~ r2(Y3,Y2) )
            | Y1 != Y2 )
        & ! [Y4] :
            ( ~ r1(Y4)
            | Y1 != Y4 ) ),
    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(f46,plain,
    ! [X0,X1,X2,X3] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r2(X3,X2)
      | X0 = X3 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

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

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

fof(f66,plain,
    ! [Y1] :
      ( ? [Y2] : pd0_5(Y2,Y1)
      | ? [Y4] :
          ( r1(Y4)
          & Y1 = Y4 ) ),
    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(f70,plain,
    ! [Y24,X19] :
      ( ~ pd0_0(X19,Y24)
      | ( ~ r1(X19)
        & X19 != Y24 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | ~ r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f73,plain,
    ! [X11,Y21,X12] :
      ( ~ pd0_1(X12,Y21,X11)
      | ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f73]) ).

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

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

fof(f87,plain,
    ! [X0,X1] :
      ( ~ pd0_5(X0,X1)
      | r1(sk0_22(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

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

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

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ~ r2(X0,X1)
      | ~ r2(X2,X1)
      | X0 = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f46]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | ~ r2(X1,X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f92,plain,
    ! [X0] : ~ pd0_0(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f72]) ).

fof(f93,plain,
    ! [X0,X1] : ~ pd0_1(X0,X0,X1),
    inference(destructive_equality_resolution,[status(esa)],[f75]) ).

fof(f96,plain,
    ! [X0] :
      ( X0 = sk0_21(X0)
      | X0 = sk0_20(X0) ),
    inference(resolution,[status(thm)],[f69,f89]) ).

fof(f97,plain,
    ! [X0] :
      ( r1(sk0_22(sk0_20(X0),X0))
      | X0 = sk0_21(X0) ),
    inference(resolution,[status(thm)],[f87,f69]) ).

fof(f98,plain,
    ! [X0] :
      ( r1(sk0_21(X0))
      | r1(sk0_22(sk0_20(X0),X0)) ),
    inference(resolution,[status(thm)],[f68,f87]) ).

fof(f99,plain,
    ! [X0] :
      ( r1(sk0_21(X0))
      | X0 = sk0_20(X0) ),
    inference(resolution,[status(thm)],[f68,f89]) ).

fof(f100,plain,
    ! [X0] :
      ( r2(sk0_22(sk0_20(X0),X0),sk0_20(X0))
      | r1(sk0_21(X0)) ),
    inference(resolution,[status(thm)],[f88,f68]) ).

fof(f101,plain,
    ! [X0] :
      ( r2(sk0_22(sk0_20(X0),X0),sk0_20(X0))
      | X0 = sk0_21(X0) ),
    inference(resolution,[status(thm)],[f88,f69]) ).

fof(f102,plain,
    ! [X0] :
      ( r1(X0)
      | X0 = sk0_20(X0)
      | X0 = sk0_20(X0) ),
    inference(paramodulation,[status(thm)],[f96,f99]) ).

fof(f103,plain,
    ! [X0] :
      ( r1(X0)
      | X0 = sk0_20(X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f102]) ).

fof(f127,plain,
    r1(sk0_0),
    inference(resolution,[status(thm)],[f17,f92]) ).

fof(f128,plain,
    ! [X0] : r2(X0,sk0_1(X0)),
    inference(resolution,[status(thm)],[f22,f93]) ).

fof(f568,plain,
    ! [X0,X1] :
      ( ~ r2(X0,sk0_1(X1))
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f128,f90]) ).

fof(f569,plain,
    ! [X0] : ~ r1(sk0_1(X0)),
    inference(resolution,[status(thm)],[f128,f91]) ).

fof(f570,plain,
    ! [X0] : sk0_1(X0) = sk0_20(sk0_1(X0)),
    inference(resolution,[status(thm)],[f569,f103]) ).

fof(f571,plain,
    ! [X0] :
      ( ~ r1(X0)
      | X0 = sk0_0 ),
    inference(resolution,[status(thm)],[f71,f18]) ).

fof(f581,plain,
    ! [X0] :
      ( sk0_22(sk0_20(X0),X0) = sk0_0
      | r1(sk0_21(X0)) ),
    inference(resolution,[status(thm)],[f571,f98]) ).

fof(f582,plain,
    ! [X0] :
      ( sk0_22(sk0_20(X0),X0) = sk0_0
      | X0 = sk0_21(X0) ),
    inference(resolution,[status(thm)],[f571,f97]) ).

fof(f839,plain,
    ! [X0] :
      ( r2(sk0_0,sk0_20(X0))
      | X0 = sk0_21(X0)
      | X0 = sk0_21(X0) ),
    inference(paramodulation,[status(thm)],[f582,f101]) ).

fof(f840,plain,
    ! [X0] :
      ( r2(sk0_0,sk0_20(X0))
      | X0 = sk0_21(X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f839]) ).

fof(f860,plain,
    ! [X0] :
      ( r2(sk0_0,sk0_1(X0))
      | sk0_1(X0) = sk0_21(sk0_1(X0)) ),
    inference(paramodulation,[status(thm)],[f570,f840]) ).

fof(f865,plain,
    ! [X0] :
      ( sk0_22(sk0_20(X0),X0) = sk0_0
      | sk0_21(X0) = sk0_0 ),
    inference(resolution,[status(thm)],[f581,f571]) ).

fof(f1021,plain,
    ! [X0] :
      ( r2(sk0_0,sk0_20(X0))
      | r1(sk0_21(X0))
      | sk0_21(X0) = sk0_0 ),
    inference(paramodulation,[status(thm)],[f865,f100]) ).

fof(f1022,plain,
    ! [X0] :
      ( r2(sk0_0,sk0_20(X0))
      | sk0_21(X0) = sk0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1021,f571]) ).

fof(f1039,plain,
    ! [X0] :
      ( r2(sk0_0,sk0_1(X0))
      | sk0_21(sk0_1(X0)) = sk0_0 ),
    inference(paramodulation,[status(thm)],[f570,f1022]) ).

fof(f1377,plain,
    ! [X0] :
      ( X0 = sk0_0
      | sk0_1(X0) = sk0_21(sk0_1(X0)) ),
    inference(resolution,[status(thm)],[f568,f860]) ).

fof(f1378,plain,
    ! [X0] :
      ( X0 = sk0_0
      | sk0_21(sk0_1(X0)) = sk0_0 ),
    inference(resolution,[status(thm)],[f568,f1039]) ).

fof(f1411,plain,
    ! [X0] :
      ( X0 = sk0_0
      | sk0_1(X0) = sk0_0
      | X0 = sk0_0 ),
    inference(paramodulation,[status(thm)],[f1378,f1377]) ).

fof(f1412,plain,
    ! [X0] :
      ( X0 = sk0_0
      | sk0_1(X0) = sk0_0 ),
    inference(duplicate_literals_removal,[status(esa)],[f1411]) ).

fof(f1436,plain,
    ! [X0,X1] :
      ( ~ r2(X0,sk0_0)
      | X1 = X0
      | X1 = sk0_0 ),
    inference(paramodulation,[status(thm)],[f1412,f568]) ).

fof(f1461,plain,
    ! [X0] :
      ( r2(X0,sk0_0)
      | X0 = sk0_0 ),
    inference(paramodulation,[status(thm)],[f1412,f128]) ).

fof(f1578,plain,
    ! [X0,X1] :
      ( X0 = X1
      | X0 = sk0_0
      | X1 = sk0_0 ),
    inference(resolution,[status(thm)],[f1436,f1461]) ).

fof(f1606,plain,
    ! [X0,X1] :
      ( r1(X0)
      | X0 = X1
      | X1 = sk0_0 ),
    inference(paramodulation,[status(thm)],[f1578,f127]) ).

fof(f1661,plain,
    ! [X0,X1] :
      ( sk0_1(X0) = X1
      | X1 = sk0_0 ),
    inference(resolution,[status(thm)],[f1606,f569]) ).

fof(f1758,plain,
    ! [X0,X1] :
      ( r2(X0,X1)
      | X1 = sk0_0 ),
    inference(paramodulation,[status(thm)],[f1661,f128]) ).

fof(f1799,plain,
    ! [X0,X1,X2] :
      ( X0 = sk0_0
      | ~ r2(X1,X0)
      | X2 = X1 ),
    inference(resolution,[status(thm)],[f1758,f90]) ).

fof(f1800,plain,
    ! [X0,X1,X2] :
      ( X0 = sk0_0
      | X1 = X2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1799,f1758]) ).

fof(f1851,plain,
    ! [X0,X1] :
      ( sk0_0 != X0
      | X1 = X0 ),
    inference(equality_factoring,[status(esa)],[f1800]) ).

fof(f1852,plain,
    ! [X0] : X0 = sk0_0,
    inference(destructive_equality_resolution,[status(esa)],[f1851]) ).

fof(f1874,plain,
    ! [X0] : r1(X0),
    inference(paramodulation,[status(thm)],[f1852,f127]) ).

fof(f1876,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f569,f1874]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29  % Computer : n009.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Mon Apr 29 22:33:26 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.09/0.30  % Drodi V3.6.0
% 0.13/0.35  % Refutation found
% 0.13/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.073640 seconds
% 0.13/0.37  % CPU time: 0.466610 seconds
% 0.13/0.37  % Total memory used: 66.998 MB
% 0.13/0.37  % Net memory used: 66.347 MB
%------------------------------------------------------------------------------