TSTP Solution File: NUM926+4 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM926+4 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 20:36:08 EDT 2024

% Result   : Theorem 7.76s 1.62s
% Output   : CNFRefutation 8.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   65 (  25 unt;   0 def)
%            Number of atoms       :  136 (  47 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  121 (  50   ~;  43   |;  17   &)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  18 con; 0-2 aty)
%            Number of variables   :   37 (  25   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,hypothesis,
    is_int(one_one_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f59,axiom,
    is_int(t),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f60,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f61,axiom,
    ( t = one_one_int
   => ? [X,Y] :
        ( is_int(X)
        & is_int(Y)
        & hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f62,axiom,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
   => ? [X,Y] :
        ( is_int(X)
        & is_int(Y)
        & hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f92,axiom,
    ! [X_49] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_49),X_49) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_49),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f125,axiom,
    ! [Z_2,W_1] :
      ( ( is_int(Z_2)
        & is_int(W_1) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1))
      <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1))
          & Z_2 != W_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f704,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5480,conjecture,
    ? [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5481,negated_conjecture,
    ~ ? [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int),
    inference(negated_conjecture,[status(cth)],[f5480]) ).

fof(f5487,plain,
    is_int(one_one_int),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f5547,plain,
    is_int(t),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f5548,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f5549,plain,
    ( t != one_one_int
    | ? [X,Y] :
        ( is_int(X)
        & is_int(Y)
        & hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f61]) ).

fof(f5550,plain,
    ( t != one_one_int
    | ( is_int(sk0_0)
      & is_int(sk0_1)
      & hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
    inference(skolemization,[status(esa)],[f5549]) ).

fof(f5553,plain,
    ( t != one_one_int
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ),
    inference(cnf_transformation,[status(esa)],[f5550]) ).

fof(f5554,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | ? [X,Y] :
        ( is_int(X)
        & is_int(Y)
        & hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f62]) ).

fof(f5555,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | ( is_int(sk0_2)
      & is_int(sk0_3)
      & hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
    inference(skolemization,[status(esa)],[f5554]) ).

fof(f5558,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ),
    inference(cnf_transformation,[status(esa)],[f5555]) ).

fof(f5588,plain,
    ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X0) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f5624,plain,
    ! [Z_2,W_1] :
      ( ~ is_int(Z_2)
      | ~ is_int(W_1)
      | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1))
      <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1))
          & Z_2 != W_1 ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f125]) ).

fof(f5625,plain,
    ! [Z_2,W_1] :
      ( ~ is_int(Z_2)
      | ~ is_int(W_1)
      | ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1))
          | ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1))
            & Z_2 != W_1 ) )
        & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1))
          | Z_2 = W_1 ) ) ),
    inference(NNF_transformation,[status(esa)],[f5624]) ).

fof(f5628,plain,
    ! [X0,X1] :
      ( ~ is_int(X0)
      | ~ is_int(X1)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f5625]) ).

fof(f6768,plain,
    pls = zero_zero_int,
    inference(cnf_transformation,[status(esa)],[f704]) ).

fof(f19089,plain,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int),
    inference(pre_NNF_transformation,[status(esa)],[f5481]) ).

fof(f19090,plain,
    ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int),
    inference(cnf_transformation,[status(esa)],[f19089]) ).

fof(f19376,plain,
    ( spl0_0
  <=> t = one_one_int ),
    introduced(split_symbol_definition) ).

fof(f19387,plain,
    ( spl0_3
  <=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ),
    introduced(split_symbol_definition) ).

fof(f19388,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f19387]) ).

fof(f19390,plain,
    ( ~ spl0_0
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f5553,f19376,f19387]) ).

fof(f19391,plain,
    ( spl0_4
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    introduced(split_symbol_definition) ).

fof(f19402,plain,
    ( spl0_7
  <=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ),
    introduced(split_symbol_definition) ).

fof(f19403,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f19402]) ).

fof(f19405,plain,
    ( ~ spl0_4
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f5558,f19391,f19402]) ).

fof(f19951,plain,
    ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int),
    inference(backward_demodulation,[status(thm)],[f6768,f19090]) ).

fof(f19952,plain,
    ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int),
    inference(forward_demodulation,[status(thm)],[f6768,f19951]) ).

fof(f19953,plain,
    ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int),
    inference(forward_demodulation,[status(thm)],[f6768,f19952]) ).

fof(f20757,plain,
    ! [X0] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X0) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int)))),
    inference(forward_demodulation,[status(thm)],[f6768,f5588]) ).

fof(f20802,plain,
    ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int),
    inference(paramodulation,[status(thm)],[f20757,f19953]) ).

fof(f20811,plain,
    ! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X0)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int),
    inference(paramodulation,[status(thm)],[f20757,f20802]) ).

fof(f32144,plain,
    ( spl0_17
  <=> is_int(t) ),
    introduced(split_symbol_definition) ).

fof(f32146,plain,
    ( ~ is_int(t)
    | spl0_17 ),
    inference(component_clause,[status(thm)],[f32144]) ).

fof(f32158,plain,
    ( spl0_21
  <=> is_int(one_one_int) ),
    introduced(split_symbol_definition) ).

fof(f32160,plain,
    ( ~ is_int(one_one_int)
    | spl0_21 ),
    inference(component_clause,[status(thm)],[f32158]) ).

fof(f32166,plain,
    ( $false
    | spl0_21 ),
    inference(forward_subsumption_resolution,[status(thm)],[f32160,f5487]) ).

fof(f32167,plain,
    spl0_21,
    inference(contradiction_clause,[status(thm)],[f32166]) ).

fof(f32172,plain,
    ( $false
    | spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f32146,f5547]) ).

fof(f32173,plain,
    spl0_17,
    inference(contradiction_clause,[status(thm)],[f32172]) ).

fof(f32175,plain,
    ( ~ is_int(one_one_int)
    | ~ is_int(t)
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | one_one_int = t ),
    inference(resolution,[status(thm)],[f5628,f5548]) ).

fof(f32176,plain,
    ( ~ spl0_21
    | ~ spl0_17
    | spl0_4
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f32175,f32158,f32144,f19391,f19376]) ).

fof(f32187,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f6768,f19403]) ).

fof(f32188,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_2),sk0_2)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f20757,f32187]) ).

fof(f32189,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_2),sk0_2)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f6768,f32188]) ).

fof(f32190,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_2),sk0_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_3),sk0_3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f20757,f32189]) ).

fof(f32191,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_2),sk0_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_3),sk0_3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int)
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f6768,f32190]) ).

fof(f32192,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f32191,f20811]) ).

fof(f32193,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f32192]) ).

fof(f32194,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_0),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f6768,f19388]) ).

fof(f32195,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_0),sk0_0)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f20757,f32194]) ).

fof(f32196,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_0),sk0_0)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sk0_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f6768,f32195]) ).

fof(f32197,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_0),sk0_0)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_1),sk0_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f20757,f32196]) ).

fof(f32198,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_0),sk0_0)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sk0_1),sk0_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))),m)),one_one_int)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f6768,f32197]) ).

fof(f32199,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f32198,f20811]) ).

fof(f32200,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f32199]) ).

fof(f32201,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f19390,f19405,f32167,f32173,f32176,f32193,f32200]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM926+4 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n015.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 21:00:17 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.47/0.66  % Drodi V3.6.0
% 7.76/1.62  % Refutation found
% 7.76/1.62  % SZS status Theorem for theBenchmark: Theorem is valid
% 7.76/1.62  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.29/1.72  % Elapsed time: 1.364388 seconds
% 8.29/1.72  % CPU time: 8.176016 seconds
% 8.29/1.72  % Total memory used: 674.863 MB
% 8.29/1.72  % Net memory used: 669.641 MB
%------------------------------------------------------------------------------