TSTP Solution File: NUM317+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM317+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 : Wed May 31 12:24:51 EDT 2023

% Result   : Theorem 212.31s 27.08s
% Output   : CNFRefutation 213.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   50 (  22 unt;   0 def)
%            Number of atoms       :  131 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  154 (  73   ~;  71   |;   6   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-1 aty)
%            Number of variables   :   90 (;  90   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f130,axiom,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f268,axiom,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f269,axiom,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f270,axiom,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f275,axiom,
    ! [X,Y,Z] :
      ( ( rdn_positive_less(rdnn(X),rdnn(Y))
        & rdn_positive_less(rdnn(Y),rdnn(Z)) )
     => rdn_positive_less(rdnn(X),rdnn(Z)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f290,axiom,
    ! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
      ( ( rdn_translate(X,rdn_pos(RDN_X))
        & rdn_translate(Y,rdn_neg(RDN_Y))
        & rdn_positive_less(RDN_Y,RDN_X)
        & rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
        & rdn_translate(Z,rdn_pos(RDN_Z)) )
     => sum(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(f325,axiom,
    rdn_digit_add(rdnn(n2),rdnn(n3),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,
    sum(n5,nn2,n3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f403,negated_conjecture,
    ~ sum(n5,nn2,n3),
    inference(negated_conjecture,[status(cth)],[f402]) ).

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(f533,plain,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f671,plain,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    inference(cnf_transformation,[status(esa)],[f268]) ).

fof(f672,plain,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    inference(cnf_transformation,[status(esa)],[f269]) ).

fof(f673,plain,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    inference(cnf_transformation,[status(esa)],[f270]) ).

fof(f678,plain,
    ! [X,Y,Z] :
      ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
      | ~ rdn_positive_less(rdnn(Y),rdnn(Z))
      | rdn_positive_less(rdnn(X),rdnn(Z)) ),
    inference(pre_NNF_transformation,[status(esa)],[f275]) ).

fof(f679,plain,
    ! [X,Z] :
      ( ! [Y] :
          ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
          | ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
      | rdn_positive_less(rdnn(X),rdnn(Z)) ),
    inference(miniscoping,[status(esa)],[f678]) ).

fof(f680,plain,
    ! [X0,X1,X2] :
      ( ~ rdn_positive_less(rdnn(X0),rdnn(X1))
      | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | rdn_positive_less(rdnn(X0),rdnn(X2)) ),
    inference(cnf_transformation,[status(esa)],[f679]) ).

fof(f725,plain,
    ! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
      ( ~ rdn_translate(X,rdn_pos(RDN_X))
      | ~ rdn_translate(Y,rdn_neg(RDN_Y))
      | ~ rdn_positive_less(RDN_Y,RDN_X)
      | ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
      | ~ rdn_translate(Z,rdn_pos(RDN_Z))
      | sum(X,Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f290]) ).

fof(f726,plain,
    ! [X,Y,Z] :
      ( ! [RDN_Z] :
          ( ! [RDN_X,RDN_Y] :
              ( ~ rdn_translate(X,rdn_pos(RDN_X))
              | ~ rdn_translate(Y,rdn_neg(RDN_Y))
              | ~ rdn_positive_less(RDN_Y,RDN_X)
              | ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X) )
          | ~ rdn_translate(Z,rdn_pos(RDN_Z)) )
      | sum(X,Y,Z) ),
    inference(miniscoping,[status(esa)],[f725]) ).

fof(f727,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ rdn_translate(X0,rdn_pos(X1))
      | ~ rdn_translate(X2,rdn_neg(X3))
      | ~ rdn_positive_less(X3,X1)
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X1)
      | ~ rdn_translate(X5,rdn_pos(X4))
      | sum(X0,X2,X5) ),
    inference(cnf_transformation,[status(esa)],[f726]) ).

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(f784,plain,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[status(esa)],[f325]) ).

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

fof(f861,plain,
    ~ sum(n5,nn2,n3),
    inference(cnf_transformation,[status(esa)],[f403]) ).

fof(f12197,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
      | ~ rdn_translate(X4,rdn_pos(rdnn(X3)))
      | ~ rdn_translate(X5,rdn_neg(rdnn(X0)))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X3))
      | ~ rdn_translate(X6,rdn_pos(rdnn(X1)))
      | sum(X4,X5,X6) ),
    inference(resolution,[status(thm)],[f749,f727]) ).

fof(f35329,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
      | ~ rdn_translate(X3,rdn_pos(rdnn(X2)))
      | ~ rdn_positive_less(rdnn(n2),rdnn(X2))
      | ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
      | sum(X3,nn2,X4) ),
    inference(resolution,[status(thm)],[f12197,f533]) ).

fof(f35426,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
      | ~ rdn_translate(X3,rdn_pos(rdnn(X2)))
      | ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
      | sum(X3,nn2,X4)
      | ~ rdn_positive_less(rdnn(n2),rdnn(X5))
      | ~ rdn_positive_less(rdnn(X5),rdnn(X2)) ),
    inference(resolution,[status(thm)],[f35329,f680]) ).

fof(f35539,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
      | ~ rdn_translate(X3,rdn_pos(rdnn(X2)))
      | ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
      | sum(X3,nn2,X4)
      | ~ rdn_positive_less(rdnn(n3),rdnn(X2)) ),
    inference(resolution,[status(thm)],[f35426,f671]) ).

fof(f37079,plain,
    ( spl0_2751
  <=> rdn_positive_less(rdnn(n3),rdnn(n5)) ),
    introduced(split_symbol_definition) ).

fof(f37080,plain,
    ( rdn_positive_less(rdnn(n3),rdnn(n5))
    | ~ spl0_2751 ),
    inference(component_clause,[status(thm)],[f37079]) ).

fof(f37081,plain,
    ( ~ rdn_positive_less(rdnn(n3),rdnn(n5))
    | spl0_2751 ),
    inference(component_clause,[status(thm)],[f37079]) ).

fof(f37450,plain,
    ! [X0] :
      ( ~ rdn_positive_less(rdnn(n3),rdnn(X0))
      | ~ rdn_positive_less(rdnn(X0),rdnn(n5))
      | spl0_2751 ),
    inference(resolution,[status(thm)],[f37081,f680]) ).

fof(f39313,plain,
    ( ~ rdn_positive_less(rdnn(n4),rdnn(n5))
    | spl0_2751 ),
    inference(resolution,[status(thm)],[f37450,f672]) ).

fof(f39314,plain,
    ( $false
    | spl0_2751 ),
    inference(forward_subsumption_resolution,[status(thm)],[f39313,f673]) ).

fof(f39315,plain,
    spl0_2751,
    inference(contradiction_clause,[status(thm)],[f39314]) ).

fof(f39357,plain,
    ! [X0,X1,X2,X3] :
      ( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0))
      | ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
      | ~ rdn_translate(X3,rdn_pos(rdnn(X0)))
      | sum(X2,nn2,X3)
      | ~ spl0_2751 ),
    inference(resolution,[status(thm)],[f37080,f35539]) ).

fof(f42391,plain,
    ! [X0,X1,X2] :
      ( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(n5),rdnn(n0))
      | ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
      | ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
      | sum(X1,nn2,X2)
      | ~ spl0_2751 ),
    inference(resolution,[status(thm)],[f39357,f811]) ).

fof(f47326,plain,
    ! [X0,X1] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
      | ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
      | sum(X0,nn2,X1)
      | ~ spl0_2751 ),
    inference(resolution,[status(thm)],[f42391,f784]) ).

fof(f51965,plain,
    ! [X0] :
      ( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
      | sum(n5,nn2,X0)
      | ~ spl0_2751 ),
    inference(resolution,[status(thm)],[f47326,f409]) ).

fof(f61581,plain,
    ( sum(n5,nn2,n3)
    | ~ spl0_2751 ),
    inference(resolution,[status(thm)],[f51965,f407]) ).

fof(f61582,plain,
    ( $false
    | ~ spl0_2751 ),
    inference(forward_subsumption_resolution,[status(thm)],[f61581,f861]) ).

fof(f61583,plain,
    ~ spl0_2751,
    inference(contradiction_clause,[status(thm)],[f61582]) ).

fof(f61584,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f39315,f61583]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM317+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n003.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue May 30 09:56:53 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 212.31/27.08  % Refutation found
% 212.31/27.08  % SZS status Theorem for theBenchmark: Theorem is valid
% 212.31/27.08  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 213.66/27.33  % Elapsed time: 26.998323 seconds
% 213.66/27.33  % CPU time: 213.611602 seconds
% 213.66/27.33  % Memory used: 677.467 MB
%------------------------------------------------------------------------------