%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM335+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:30:36 EDT 2024

% Result   : Theorem 2.25s 0.69s
% Output   : CNFRefutation 2.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   42 (  17 unt;   0 def)
%            Number of atoms       :   94 (  11 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   93 (  41   ~;  37   |;   9   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :   87 (  86   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f287,axiom,
    ! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
      ( ( rdn_translate(X,rdn_pos(RDN_X))
        & rdn_translate(Y,rdn_pos(RDN_Y))
        & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
        & rdn_translate(Z,rdn_pos(RDN_Z)) )
     => sum(X,Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f295,axiom,
    ! [X,Y1,Y2,Z] :
      ( ( sum(X,Y1,Z)
        & sum(X,Y2,Z) )
     => Y1 = Y2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f296,axiom,
    ! [X,Y,Z] :
      ( sum(Y,Z,X)
    <=> difference(X,Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f297,axiom,
    ! [C,D1,D2,RD,ID] :
      ( ( rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
        & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f334,axiom,
    rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f352,axiom,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f402,conjecture,
    ! [X] :
      ( difference(n5,n3,X)
     => X = n2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f403,negated_conjecture,
    ~ ! [X] :
        ( difference(n5,n3,X)
       => X = n2 ),
    inference(negated_conjecture,[status(cth)],[f402]) ).

fof(f406,plain,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f407,plain,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f409,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f716,plain,
    ! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
      ( ~ rdn_translate(X,rdn_pos(RDN_X))
      | ~ rdn_translate(Y,rdn_pos(RDN_Y))
      | ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
      | ~ rdn_translate(Z,rdn_pos(RDN_Z))
      | sum(X,Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f287]) ).

fof(f717,plain,
    ! [X,Y,Z] :
      ( ! [RDN_Z] :
          ( ! [RDN_X,RDN_Y] :
              ( ~ rdn_translate(X,rdn_pos(RDN_X))
              | ~ rdn_translate(Y,rdn_pos(RDN_Y))
              | ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) )
          | ~ rdn_translate(Z,rdn_pos(RDN_Z)) )
      | sum(X,Y,Z) ),
    inference(miniscoping,[status(esa)],[f716]) ).

fof(f718,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ rdn_translate(X0,rdn_pos(X1))
      | ~ rdn_translate(X2,rdn_pos(X3))
      | ~ rdn_add_with_carry(rdnn(n0),X1,X3,X4)
      | ~ rdn_translate(X5,rdn_pos(X4))
      | sum(X0,X2,X5) ),
    inference(cnf_transformation,[status(esa)],[f717]) ).

fof(f740,plain,
    ! [X,Y1,Y2,Z] :
      ( ~ sum(X,Y1,Z)
      | ~ sum(X,Y2,Z)
      | Y1 = Y2 ),
    inference(pre_NNF_transformation,[status(esa)],[f295]) ).

fof(f741,plain,
    ! [Y1,Y2] :
      ( ! [X,Z] :
          ( ~ sum(X,Y1,Z)
          | ~ sum(X,Y2,Z) )
      | Y1 = Y2 ),
    inference(miniscoping,[status(esa)],[f740]) ).

fof(f742,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X3,X2)
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f741]) ).

fof(f743,plain,
    ! [X,Y,Z] :
      ( ( ~ sum(Y,Z,X)
        | difference(X,Y,Z) )
      & ( sum(Y,Z,X)
        | ~ difference(X,Y,Z) ) ),
    inference(NNF_transformation,[status(esa)],[f296]) ).

fof(f744,plain,
    ( ! [X,Y,Z] :
        ( ~ sum(Y,Z,X)
        | difference(X,Y,Z) )
    & ! [X,Y,Z] :
        ( sum(Y,Z,X)
        | ~ difference(X,Y,Z) ) ),
    inference(miniscoping,[status(esa)],[f743]) ).

fof(f746,plain,
    ! [X0,X1,X2] :
      ( sum(X0,X1,X2)
      | ~ difference(X2,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f744]) ).

fof(f747,plain,
    ! [C,D1,D2,RD,ID] :
      ( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
      | ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
      | rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
    inference(pre_NNF_transformation,[status(esa)],[f297]) ).

fof(f748,plain,
    ! [C,D1,D2,RD] :
      ( ! [ID] :
          ( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
          | ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) )
      | rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
    inference(miniscoping,[status(esa)],[f747]) ).

fof(f749,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
      | rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4)) ),
    inference(cnf_transformation,[status(esa)],[f748]) ).

fof(f793,plain,
    rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[status(esa)],[f334]) ).

fof(f811,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[status(esa)],[f352]) ).

fof(f861,plain,
    ? [X] :
      ( difference(n5,n3,X)
      & X != n2 ),
    inference(pre_NNF_transformation,[status(esa)],[f403]) ).

fof(f862,plain,
    ( difference(n5,n3,sk0_0)
    & sk0_0 != n2 ),
    inference(skolemization,[status(esa)],[f861]) ).

fof(f863,plain,
    difference(n5,n3,sk0_0),
    inference(cnf_transformation,[status(esa)],[f862]) ).

fof(f864,plain,
    sk0_0 != n2,
    inference(cnf_transformation,[status(esa)],[f862]) ).

fof(f865,plain,
    sum(n3,sk0_0,n5),
    inference(resolution,[status(thm)],[f746,f863]) ).

fof(f869,plain,
    ! [X0] :
      ( ~ sum(n3,X0,n5)
      | X0 = sk0_0 ),
    inference(resolution,[status(thm)],[f742,f865]) ).

fof(f2520,plain,
    ! [X0,X1] :
      ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
      | rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)) ),
    inference(resolution,[status(thm)],[f749,f811]) ).

fof(f2555,plain,
    rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)),
    inference(resolution,[status(thm)],[f2520,f793]) ).

fof(f2638,plain,
    ! [X0,X1,X2] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
      | ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
      | ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
      | sum(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f2555,f718]) ).

fof(f2978,plain,
    ! [X0,X1] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
      | ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
      | sum(X0,X1,n5) ),
    inference(resolution,[status(thm)],[f2638,f409]) ).

fof(f3166,plain,
    ! [X0] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
      | sum(n3,X0,n5) ),
    inference(resolution,[status(thm)],[f2978,f407]) ).

fof(f3167,plain,
    sum(n3,n2,n5),
    inference(resolution,[status(thm)],[f3166,f406]) ).

fof(f3168,plain,
    n2 = sk0_0,
    inference(resolution,[status(thm)],[f3167,f869]) ).

fof(f3169,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f3168,f864]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM335+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n006.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
% 0.13/0.35  % DateTime : Mon Apr 29 20:34:05 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.21/0.36  % Drodi V3.6.0
% 2.25/0.69  % Refutation found
% 2.25/0.69  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.25/0.69  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.66/0.71  % Elapsed time: 0.360364 seconds
% 2.66/0.71  % CPU time: 2.687022 seconds
% 2.66/0.71  % Total memory used: 109.059 MB
% 2.66/0.71  % Net memory used: 107.068 MB
%------------------------------------------------------------------------------