TSTP Solution File: AGT026+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : AGT026+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 11:58:32 EDT 2023

% Result   : Theorem 10.16s 1.82s
% Output   : CNFRefutation 10.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   75 (  28 unt;   0 def)
%            Number of atoms       :  183 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  190 (  82   ~;  80   |;  17   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   6 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;  16 con; 0-2 aty)
%            Number of variables   :  130 (; 126   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,N,M,P] :
      ( ( accept_population(A,P,N)
        & less(M,N) )
     => accept_population(A,P,M) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [A] :
      ( ( accept_population(A,atheist,n75)
        & accept_population(A,christian,n24)
        & accept_population(A,muslim,n1)
        & accept_population(A,native,n0)
        & accept_population(A,other,n0) )
    <=> accept_city(A,towna) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f362,axiom,
    accept_population(muslimcountrybhumanitarianorganization,other,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f472,axiom,
    accept_population(muslimcountrybhumanitarianorganization,native,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f473,axiom,
    accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f635,axiom,
    ~ accept_city(muslimcountrybhumanitarianorganization,towna),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f661,axiom,
    rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f712,axiom,
    rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f737,axiom,
    rdn_translate(n100,rdn_pos(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f893,axiom,
    rdn_non_zero_digit(rdnn(n1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f912,axiom,
    ! [Ds,Os,Db,Ob] :
      ( rdn_positive_less(Os,Ob)
     => rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f914,axiom,
    ! [D,Db,Ob] :
      ( rdn_non_zero(Ob)
     => rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f915,axiom,
    ! [X] :
      ( rdn_non_zero_digit(rdnn(X))
     => rdn_non_zero(rdnn(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f917,axiom,
    ! [X,Y,RDN_X,RDN_Y] :
      ( ( rdn_translate(X,rdn_pos(RDN_X))
        & rdn_translate(Y,rdn_pos(RDN_Y))
        & rdn_positive_less(RDN_X,RDN_Y) )
     => less(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f923,conjecture,
    ? [X,Y] : ~ accept_population(X,Y,n100),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f924,negated_conjecture,
    ~ ? [X,Y] : ~ accept_population(X,Y,n100),
    inference(negated_conjecture,[status(cth)],[f923]) ).

fof(f934,plain,
    ! [A,N,M,P] :
      ( ~ accept_population(A,P,N)
      | ~ less(M,N)
      | accept_population(A,P,M) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f935,plain,
    ! [A,M,P] :
      ( ! [N] :
          ( ~ accept_population(A,P,N)
          | ~ less(M,N) )
      | accept_population(A,P,M) ),
    inference(miniscoping,[status(esa)],[f934]) ).

fof(f936,plain,
    ! [X0,X1,X2,X3] :
      ( ~ accept_population(X0,X1,X2)
      | ~ less(X3,X2)
      | accept_population(X0,X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f935]) ).

fof(f1011,plain,
    ! [A] :
      ( ( ~ accept_population(A,atheist,n75)
        | ~ accept_population(A,christian,n24)
        | ~ accept_population(A,muslim,n1)
        | ~ accept_population(A,native,n0)
        | ~ accept_population(A,other,n0)
        | accept_city(A,towna) )
      & ( ( accept_population(A,atheist,n75)
          & accept_population(A,christian,n24)
          & accept_population(A,muslim,n1)
          & accept_population(A,native,n0)
          & accept_population(A,other,n0) )
        | ~ accept_city(A,towna) ) ),
    inference(NNF_transformation,[status(esa)],[f16]) ).

fof(f1012,plain,
    ( ! [A] :
        ( ~ accept_population(A,atheist,n75)
        | ~ accept_population(A,christian,n24)
        | ~ accept_population(A,muslim,n1)
        | ~ accept_population(A,native,n0)
        | ~ accept_population(A,other,n0)
        | accept_city(A,towna) )
    & ! [A] :
        ( ( accept_population(A,atheist,n75)
          & accept_population(A,christian,n24)
          & accept_population(A,muslim,n1)
          & accept_population(A,native,n0)
          & accept_population(A,other,n0) )
        | ~ accept_city(A,towna) ) ),
    inference(miniscoping,[status(esa)],[f1011]) ).

fof(f1013,plain,
    ! [X0] :
      ( ~ accept_population(X0,atheist,n75)
      | ~ accept_population(X0,christian,n24)
      | ~ accept_population(X0,muslim,n1)
      | ~ accept_population(X0,native,n0)
      | ~ accept_population(X0,other,n0)
      | accept_city(X0,towna) ),
    inference(cnf_transformation,[status(esa)],[f1012]) ).

fof(f1392,plain,
    accept_population(muslimcountrybhumanitarianorganization,other,n0),
    inference(cnf_transformation,[status(esa)],[f362]) ).

fof(f1502,plain,
    accept_population(muslimcountrybhumanitarianorganization,native,n0),
    inference(cnf_transformation,[status(esa)],[f472]) ).

fof(f1503,plain,
    accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
    inference(cnf_transformation,[status(esa)],[f473]) ).

fof(f1665,plain,
    ~ accept_city(muslimcountrybhumanitarianorganization,towna),
    inference(cnf_transformation,[status(esa)],[f635]) ).

fof(f1691,plain,
    rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
    inference(cnf_transformation,[status(esa)],[f661]) ).

fof(f1742,plain,
    rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
    inference(cnf_transformation,[status(esa)],[f712]) ).

fof(f1767,plain,
    rdn_translate(n100,rdn_pos(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
    inference(cnf_transformation,[status(esa)],[f737]) ).

fof(f1923,plain,
    rdn_non_zero_digit(rdnn(n1)),
    inference(cnf_transformation,[status(esa)],[f893]) ).

fof(f1944,plain,
    ! [Ds,Os,Db,Ob] :
      ( ~ rdn_positive_less(Os,Ob)
      | rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
    inference(pre_NNF_transformation,[status(esa)],[f912]) ).

fof(f1945,plain,
    ! [Os,Ob] :
      ( ~ rdn_positive_less(Os,Ob)
      | ! [Ds,Db] : rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
    inference(miniscoping,[status(esa)],[f1944]) ).

fof(f1946,plain,
    ! [X0,X1,X2,X3] :
      ( ~ rdn_positive_less(X0,X1)
      | rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1)) ),
    inference(cnf_transformation,[status(esa)],[f1945]) ).

fof(f1949,plain,
    ! [D,Db,Ob] :
      ( ~ rdn_non_zero(Ob)
      | rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
    inference(pre_NNF_transformation,[status(esa)],[f914]) ).

fof(f1950,plain,
    ! [Ob] :
      ( ~ rdn_non_zero(Ob)
      | ! [D,Db] : rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
    inference(miniscoping,[status(esa)],[f1949]) ).

fof(f1951,plain,
    ! [X0,X1,X2] :
      ( ~ rdn_non_zero(X0)
      | rdn_positive_less(rdnn(X1),rdn(rdnn(X2),X0)) ),
    inference(cnf_transformation,[status(esa)],[f1950]) ).

fof(f1952,plain,
    ! [X] :
      ( ~ rdn_non_zero_digit(rdnn(X))
      | rdn_non_zero(rdnn(X)) ),
    inference(pre_NNF_transformation,[status(esa)],[f915]) ).

fof(f1953,plain,
    ! [X0] :
      ( ~ rdn_non_zero_digit(rdnn(X0))
      | rdn_non_zero(rdnn(X0)) ),
    inference(cnf_transformation,[status(esa)],[f1952]) ).

fof(f1957,plain,
    ! [X,Y,RDN_X,RDN_Y] :
      ( ~ rdn_translate(X,rdn_pos(RDN_X))
      | ~ rdn_translate(Y,rdn_pos(RDN_Y))
      | ~ rdn_positive_less(RDN_X,RDN_Y)
      | less(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f917]) ).

fof(f1958,plain,
    ! [X,Y] :
      ( ! [RDN_X,RDN_Y] :
          ( ~ rdn_translate(X,rdn_pos(RDN_X))
          | ~ rdn_translate(Y,rdn_pos(RDN_Y))
          | ~ rdn_positive_less(RDN_X,RDN_Y) )
      | less(X,Y) ),
    inference(miniscoping,[status(esa)],[f1957]) ).

fof(f1959,plain,
    ! [X0,X1,X2,X3] :
      ( ~ rdn_translate(X0,rdn_pos(X1))
      | ~ rdn_translate(X2,rdn_pos(X3))
      | ~ rdn_positive_less(X1,X3)
      | less(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f1958]) ).

fof(f1979,plain,
    ! [X,Y] : accept_population(X,Y,n100),
    inference(pre_NNF_transformation,[status(esa)],[f924]) ).

fof(f1980,plain,
    ! [X0,X1] : accept_population(X0,X1,n100),
    inference(cnf_transformation,[status(esa)],[f1979]) ).

fof(f2835,plain,
    ( spl0_144
  <=> accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
    introduced(split_symbol_definition) ).

fof(f2837,plain,
    ( ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
    | spl0_144 ),
    inference(component_clause,[status(thm)],[f2835]) ).

fof(f2841,plain,
    ( $false
    | spl0_144 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2837,f1392]) ).

fof(f2842,plain,
    spl0_144,
    inference(contradiction_clause,[status(thm)],[f2841]) ).

fof(f3508,plain,
    ( spl0_273
  <=> accept_city(muslimcountrybhumanitarianorganization,towna) ),
    introduced(split_symbol_definition) ).

fof(f3509,plain,
    ( accept_city(muslimcountrybhumanitarianorganization,towna)
    | ~ spl0_273 ),
    inference(component_clause,[status(thm)],[f3508]) ).

fof(f3567,plain,
    ( spl0_287
  <=> accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
    introduced(split_symbol_definition) ).

fof(f3569,plain,
    ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
    | spl0_287 ),
    inference(component_clause,[status(thm)],[f3567]) ).

fof(f3570,plain,
    ( spl0_288
  <=> accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
    introduced(split_symbol_definition) ).

fof(f3572,plain,
    ( ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
    | spl0_288 ),
    inference(component_clause,[status(thm)],[f3570]) ).

fof(f3588,plain,
    ( spl0_289
  <=> accept_population(muslimcountrybhumanitarianorganization,native,n0) ),
    introduced(split_symbol_definition) ).

fof(f3590,plain,
    ( ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
    | spl0_289 ),
    inference(component_clause,[status(thm)],[f3588]) ).

fof(f3591,plain,
    ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
    | ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
    | ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
    | ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
    | accept_city(muslimcountrybhumanitarianorganization,towna) ),
    inference(resolution,[status(thm)],[f1503,f1013]) ).

fof(f3592,plain,
    ( ~ spl0_287
    | ~ spl0_288
    | ~ spl0_289
    | ~ spl0_144
    | spl0_273 ),
    inference(split_clause,[status(thm)],[f3591,f3567,f3570,f3588,f2835,f3508]) ).

fof(f3622,plain,
    ( $false
    | spl0_289 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3590,f1502]) ).

fof(f3623,plain,
    spl0_289,
    inference(contradiction_clause,[status(thm)],[f3622]) ).

fof(f5254,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ rdn_translate(X0,rdn_pos(X1))
      | ~ rdn_translate(X2,rdn_pos(X3))
      | ~ rdn_positive_less(X1,X3)
      | ~ accept_population(X4,X5,X2)
      | accept_population(X4,X5,X0) ),
    inference(resolution,[status(thm)],[f1959,f936]) ).

fof(f5260,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2)))
      | ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),X5)))
      | ~ accept_population(X6,X7,X3)
      | accept_population(X6,X7,X0)
      | ~ rdn_positive_less(X2,X5) ),
    inference(resolution,[status(thm)],[f5254,f1946]) ).

fof(f5284,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
      | ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdn(rdnn(X5),X6))))
      | ~ accept_population(X7,X8,X3)
      | accept_population(X7,X8,X0)
      | ~ rdn_non_zero(X6) ),
    inference(resolution,[status(thm)],[f5260,f1951]) ).

fof(f5364,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
      | ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdn(rdnn(X5),rdnn(X6)))))
      | ~ accept_population(X7,X8,X3)
      | accept_population(X7,X8,X0)
      | ~ rdn_non_zero_digit(rdnn(X6)) ),
    inference(resolution,[status(thm)],[f5284,f1953]) ).

fof(f5386,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
      | ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdn(rdnn(X5),rdnn(n1)))))
      | ~ accept_population(X6,X7,X3)
      | accept_population(X6,X7,X0) ),
    inference(resolution,[status(thm)],[f5364,f1923]) ).

fof(f5414,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
      | ~ accept_population(X3,X4,n100)
      | accept_population(X3,X4,X0) ),
    inference(resolution,[status(thm)],[f5386,f1767]) ).

fof(f5415,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
      | accept_population(X3,X4,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f5414,f1980]) ).

fof(f5480,plain,
    ! [X0,X1] : accept_population(X0,X1,n75),
    inference(resolution,[status(thm)],[f5415,f1742]) ).

fof(f5538,plain,
    ! [X0,X1] : accept_population(X0,X1,n24),
    inference(resolution,[status(thm)],[f5415,f1691]) ).

fof(f5553,plain,
    ( $false
    | spl0_287 ),
    inference(backward_subsumption_resolution,[status(thm)],[f3569,f5480]) ).

fof(f5554,plain,
    spl0_287,
    inference(contradiction_clause,[status(thm)],[f5553]) ).

fof(f5781,plain,
    ( $false
    | spl0_288 ),
    inference(backward_subsumption_resolution,[status(thm)],[f3572,f5538]) ).

fof(f5782,plain,
    spl0_288,
    inference(contradiction_clause,[status(thm)],[f5781]) ).

fof(f5855,plain,
    ( $false
    | ~ spl0_273 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3509,f1665]) ).

fof(f5856,plain,
    ~ spl0_273,
    inference(contradiction_clause,[status(thm)],[f5855]) ).

fof(f5857,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2842,f3592,f3623,f5554,f5782,f5856]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.28  % Problem  : AGT026+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.06/0.28  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.50  % Computer : n029.cluster.edu
% 0.06/0.50  % Model    : x86_64 x86_64
% 0.06/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.50  % Memory   : 8042.1875MB
% 0.06/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.50  % CPULimit : 300
% 0.06/0.50  % WCLimit  : 300
% 0.06/0.50  % DateTime : Tue May 30 11:06:37 EDT 2023
% 0.06/0.50  % CPUTime  : 
% 0.06/0.51  % Drodi V3.5.1
% 10.16/1.82  % Refutation found
% 10.16/1.82  % SZS status Theorem for theBenchmark: Theorem is valid
% 10.16/1.82  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.16/1.85  % Elapsed time: 1.343021 seconds
% 10.16/1.85  % CPU time: 10.515640 seconds
% 10.16/1.85  % Memory used: 161.604 MB
%------------------------------------------------------------------------------