TSTP Solution File: NUM328+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM328+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : Tue Apr 30 20:30:36 EDT 2024

% Result   : Theorem 23.99s 3.43s
% Output   : CNFRefutation 23.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   22 (  11 unt;   0 def)
%            Number of atoms       :   51 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   55 (  26   ~;  23   |;   4   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-4 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   58 (  54   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    rdn_translate(n0,rdn_pos(rdnn(n0))),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f302,axiom,
    rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f402,conjecture,
    ? [X,Y] : sum(X,Y,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f403,negated_conjecture,
    ~ ? [X,Y] : sum(X,Y,X),
    inference(negated_conjecture,[status(cth)],[f402]) ).

fof(f404,plain,
    rdn_translate(n0,rdn_pos(rdnn(n0))),
    inference(cnf_transformation,[status(esa)],[f1]) ).

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(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(f761,plain,
    rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
    inference(cnf_transformation,[status(esa)],[f302]) ).

fof(f861,plain,
    ! [X,Y] : ~ sum(X,Y,X),
    inference(pre_NNF_transformation,[status(esa)],[f403]) ).

fof(f862,plain,
    ! [X0,X1] : ~ sum(X0,X1,X0),
    inference(cnf_transformation,[status(esa)],[f861]) ).

fof(f5447,plain,
    ! [X0,X1] :
      ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n0),rdnn(n0))
      | rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n0)) ),
    inference(resolution,[status(thm)],[f761,f749]) ).

fof(f11113,plain,
    rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
    inference(resolution,[status(thm)],[f5447,f761]) ).

fof(f11141,plain,
    ! [X0,X1,X2] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n0)))
      | ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
      | ~ rdn_translate(X2,rdn_pos(rdnn(n0)))
      | sum(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f11113,f718]) ).

fof(f11143,plain,
    ! [X0] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n0)))
      | sum(X0,n0,n0) ),
    inference(resolution,[status(thm)],[f11141,f404]) ).

fof(f11147,plain,
    sum(n0,n0,n0),
    inference(resolution,[status(thm)],[f11143,f404]) ).

fof(f11148,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f11147,f862]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : NUM328+1 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n017.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon Apr 29 20:15:03 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.6.0
% 23.99/3.43  % Refutation found
% 23.99/3.43  % SZS status Theorem for theBenchmark: Theorem is valid
% 23.99/3.43  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.66/3.52  % Elapsed time: 3.188621 seconds
% 24.66/3.52  % CPU time: 24.947299 seconds
% 24.66/3.52  % Total memory used: 287.145 MB
% 24.66/3.52  % Net memory used: 278.774 MB
%------------------------------------------------------------------------------