TSTP Solution File: NUM926+5 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 20:36:09 EDT 2024

% Result   : Theorem 0.20s 0.40s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   49 (  19 unt;   0 def)
%            Number of atoms       :   89 (  44 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   75 (  35   ~;  28   |;   5   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   9 con; 0-3 aty)
%            Number of variables   :   44 (  32   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f28,axiom,
    ord_less_eq(int,one_one(int),t),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f29,axiom,
    ( t = one_one(int)
   => ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ( ord_less(int,one_one(int),t)
   => ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f50,axiom,
    ! [Z_1,W_1] :
      ( ord_less(int,Z_1,W_1)
    <=> ( ord_less_eq(int,Z_1,W_1)
        & Z_1 != W_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f113,axiom,
    ! [Z,W] : times_times(int,Z,W) = times_times(int,W,Z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f114,axiom,
    ! [K_1] : number_number_of(int,K_1) = K_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f117,axiom,
    ! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f142,conjecture,
    ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f143,negated_conjecture,
    ~ ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    inference(negated_conjecture,[status(cth)],[f142]) ).

fof(f216,plain,
    ord_less_eq(int,one_one(int),t),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f217,plain,
    ( t != one_one(int)
    | ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(pre_NNF_transformation,[status(esa)],[f29]) ).

fof(f218,plain,
    ( t != one_one(int)
    | plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(skolemization,[status(esa)],[f217]) ).

fof(f219,plain,
    ( t != one_one(int)
    | plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

fof(f220,plain,
    ( ~ ord_less(int,one_one(int),t)
    | ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f221,plain,
    ( ~ ord_less(int,one_one(int),t)
    | plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(skolemization,[status(esa)],[f220]) ).

fof(f222,plain,
    ( ~ ord_less(int,one_one(int),t)
    | plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(cnf_transformation,[status(esa)],[f221]) ).

fof(f253,plain,
    ! [Z_1,W_1] :
      ( ( ~ ord_less(int,Z_1,W_1)
        | ( ord_less_eq(int,Z_1,W_1)
          & Z_1 != W_1 ) )
      & ( ord_less(int,Z_1,W_1)
        | ~ ord_less_eq(int,Z_1,W_1)
        | Z_1 = W_1 ) ),
    inference(NNF_transformation,[status(esa)],[f50]) ).

fof(f254,plain,
    ( ! [Z_1,W_1] :
        ( ~ ord_less(int,Z_1,W_1)
        | ( ord_less_eq(int,Z_1,W_1)
          & Z_1 != W_1 ) )
    & ! [Z_1,W_1] :
        ( ord_less(int,Z_1,W_1)
        | ~ ord_less_eq(int,Z_1,W_1)
        | Z_1 = W_1 ) ),
    inference(miniscoping,[status(esa)],[f253]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ord_less(int,X0,X1)
      | ~ ord_less_eq(int,X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f254]) ).

fof(f433,plain,
    ! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f434,plain,
    ! [X0] : number_number_of(int,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f437,plain,
    ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
    inference(cnf_transformation,[status(esa)],[f117]) ).

fof(f486,plain,
    ! [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    inference(pre_NNF_transformation,[status(esa)],[f143]) ).

fof(f487,plain,
    ! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    inference(cnf_transformation,[status(esa)],[f486]) ).

fof(f488,plain,
    ( spl0_0
  <=> t = one_one(int) ),
    introduced(split_symbol_definition) ).

fof(f491,plain,
    ( spl0_1
  <=> plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    introduced(split_symbol_definition) ).

fof(f492,plain,
    ( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f491]) ).

fof(f494,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f219,f488,f491]) ).

fof(f495,plain,
    ( spl0_2
  <=> ord_less(int,one_one(int),t) ),
    introduced(split_symbol_definition) ).

fof(f498,plain,
    ( spl0_3
  <=> plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    introduced(split_symbol_definition) ).

fof(f499,plain,
    ( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f498]) ).

fof(f501,plain,
    ( ~ spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f222,f495,f498]) ).

fof(f503,plain,
    ! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),
    inference(backward_demodulation,[status(thm)],[f434,f487]) ).

fof(f512,plain,
    ! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),
    inference(paramodulation,[status(thm)],[f437,f503]) ).

fof(f513,plain,
    ! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,bit0(bit0(bit1(pls))),m)),
    inference(forward_demodulation,[status(thm)],[f437,f512]) ).

fof(f514,plain,
    ! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),
    inference(forward_demodulation,[status(thm)],[f433,f513]) ).

fof(f1029,plain,
    ( ord_less(int,one_one(int),t)
    | one_one(int) = t ),
    inference(resolution,[status(thm)],[f257,f216]) ).

fof(f1030,plain,
    ( spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f1029,f495,f488]) ).

fof(f1033,plain,
    ( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f437,f499]) ).

fof(f1034,plain,
    ( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls))))))
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f433,f1033]) ).

fof(f1035,plain,
    ( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f434,f1034]) ).

fof(f1036,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1035,f514]) ).

fof(f1037,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f1036]) ).

fof(f1038,plain,
    ( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f437,f492]) ).

fof(f1039,plain,
    ( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls))))))
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f433,f1038]) ).

fof(f1040,plain,
    ( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f434,f1039]) ).

fof(f1041,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1040,f514]) ).

fof(f1042,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f1041]) ).

fof(f1043,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f494,f501,f1030,f1037,f1042]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Apr 29 20:54:36 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.20/0.40  % Refutation found
% 0.20/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.42  % Elapsed time: 0.069368 seconds
% 0.20/0.42  % CPU time: 0.388819 seconds
% 0.20/0.42  % Total memory used: 72.177 MB
% 0.20/0.42  % Net memory used: 72.056 MB
%------------------------------------------------------------------------------