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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : NUM926+7 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 01:42:02 PM UTC 2026

% Result   : Theorem 0.21s 0.65s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   63 (  32 unt;   0 def)
%            Number of atoms       :  106 (  67 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   81 (  38   ~;  34   |;   5   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  10 con; 0-4 aty)
%            Number of variables   :   54 (  42   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f51,hypothesis,
    ! [B_1_1] : ti(int,bit0(B_1_1)) = bit0(B_1_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f53,hypothesis,
    ! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f57,axiom,
    ! [B_1_1,X_a] :
      ( number(X_a)
     => ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f97,axiom,
    ti(int,t) = t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f98,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f99,axiom,
    ( t = one_one(int)
   => ? [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f100,axiom,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))
   => ? [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f120,axiom,
    ! [Z_2,W_1] :
      ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
    <=> ( ti(int,Z_2) != ti(int,W_1)
        & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f186,axiom,
    ! [K_1] : number_number_of(int,K_1) = ti(int,K_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f258,axiom,
    one_one(int) = number_number_of(int,bit1(pls)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1149,axiom,
    number(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1255,conjecture,
    ? [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1256,negated_conjecture,
    ~ ? [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
    inference(negated_conjecture,[status(cth)],[f1255]) ).

fof(f1357,plain,
    ! [X0] : ti(int,bit0(X0)) = bit0(X0),
    inference(cnf_transformation,[status(thm)],[f51]) ).

fof(f1359,plain,
    ! [X0] : ti(int,bit1(X0)) = bit1(X0),
    inference(cnf_transformation,[status(thm)],[f53]) ).

fof(f1365,plain,
    ! [B_1_1,X_a] :
      ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1)
      | ~ number(X_a) ),
    inference(pre_NNF_transformation,[status(thm)],[f57]) ).

fof(f1366,plain,
    ! [X_a] :
      ( ! [B_1_1] : ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1)
      | ~ number(X_a) ),
    inference(miniscoping,[status(thm)],[f1365]) ).

fof(f1367,plain,
    ! [X0,X1] :
      ( ti(X0,number_number_of(X0,X1)) = number_number_of(X0,X1)
      | ~ number(X0) ),
    inference(cnf_transformation,[status(thm)],[f1366]) ).

fof(f1417,plain,
    ti(int,t) = t,
    inference(cnf_transformation,[status(thm)],[f97]) ).

fof(f1418,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
    inference(cnf_transformation,[status(thm)],[f98]) ).

fof(f1419,plain,
    ( ? [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | t != one_one(int) ),
    inference(pre_NNF_transformation,[status(thm)],[f99]) ).

fof(f1420,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK0_skl),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK1_skl),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | t != one_one(int) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f1419]) ).

fof(f1421,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK0_skl),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK1_skl),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | t != one_one(int) ),
    inference(cnf_transformation,[status(thm)],[f1420]) ).

fof(f1422,plain,
    ( ? [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(pre_NNF_transformation,[status(thm)],[f100]) ).

fof(f1423,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK2_skl),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK3_skl),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f1422]) ).

fof(f1424,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK2_skl),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK3_skl),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(cnf_transformation,[status(thm)],[f1423]) ).

fof(f1455,plain,
    ! [Z_2,W_1] :
      ( ( ti(int,Z_2) = ti(int,W_1)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) )
      & ( ( ti(int,Z_2) != ti(int,W_1)
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) )
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) ) ),
    inference(NNF_transformation,[status(thm)],[f120]) ).

fof(f1456,plain,
    ( ! [Z_2,W_1] :
        ( ti(int,Z_2) = ti(int,W_1)
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
        | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) )
    & ! [Z_2,W_1] :
        ( ( ti(int,Z_2) != ti(int,W_1)
          & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) )
        | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) ) ),
    inference(miniscoping,[status(thm)],[f1455]) ).

fof(f1459,plain,
    ! [X0,X1] :
      ( ti(int,X0) = ti(int,X1)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ),
    inference(cnf_transformation,[status(thm)],[f1456]) ).

fof(f1641,plain,
    ! [X0] : number_number_of(int,X0) = ti(int,X0),
    inference(cnf_transformation,[status(thm)],[f186]) ).

fof(f1809,plain,
    one_one(int) = number_number_of(int,bit1(pls)),
    inference(cnf_transformation,[status(thm)],[f258]) ).

fof(f4394,plain,
    number(int),
    inference(cnf_transformation,[status(thm)],[f1149]) ).

fof(f4502,plain,
    ! [X,Y] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,Y),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
    inference(pre_NNF_transformation,[status(thm)],[f1256]) ).

fof(f4503,plain,
    ! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
    inference(cnf_transformation,[status(thm)],[f4502]) ).

fof(f5788,plain,
    ( ti(int,one_one(int)) = number_number_of(int,bit1(pls))
    | ~ number(int) ),
    inference(paramodulation,[status(thm)],[f1809,f1367]) ).

fof(f5794,plain,
    ( ti(int,one_one(int)) = one_one(int)
    | ~ number(int) ),
    inference(forward_demodulation,[status(thm)],[f1809,f5788]) ).

fof(f5795,plain,
    ti(int,one_one(int)) = one_one(int),
    inference(forward_subsumption_resolution,[status(thm)],[f5794,f4394]) ).

fof(f6111,plain,
    number_number_of(int,t) = t,
    inference(backward_demodulation,[status(thm)],[f1641,f1417]) ).

fof(f6117,plain,
    ! [X0] : number_number_of(int,bit1(X0)) = bit1(X0),
    inference(backward_demodulation,[status(thm)],[f1641,f1359]) ).

fof(f6118,plain,
    ! [X0] : number_number_of(int,bit0(X0)) = bit0(X0),
    inference(backward_demodulation,[status(thm)],[f1641,f1357]) ).

fof(f6287,plain,
    one_one(int) = bit1(pls),
    inference(backward_demodulation,[status(thm)],[f6117,f1809]) ).

fof(f6364,plain,
    ! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(one_one(int))))),m)),one_one(int)),
    inference(backward_demodulation,[status(thm)],[f6287,f4503]) ).

fof(f6425,plain,
    ! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(one_one(int))))),m)),one_one(int)),
    inference(forward_demodulation,[status(thm)],[f6287,f6364]) ).

fof(f6426,plain,
    ! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(one_one(int))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(one_one(int))))),m)),one_one(int)),
    inference(forward_demodulation,[status(thm)],[f6287,f6425]) ).

fof(f6689,plain,
    ! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(one_one(int))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,bit0(bit0(one_one(int)))),m)),one_one(int)),
    inference(forward_demodulation,[status(thm)],[f6118,f6426]) ).

fof(f6892,plain,
    number_number_of(int,one_one(int)) = one_one(int),
    inference(forward_demodulation,[status(thm)],[f1641,f5795]) ).

fof(f7559,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK0_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK1_skl),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | t != one_one(int) ),
    inference(forward_demodulation,[status(thm)],[f6287,f1421]) ).

fof(f7560,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK0_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK1_skl),number_number_of(nat,bit0(one_one(int))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | t != one_one(int) ),
    inference(forward_demodulation,[status(thm)],[f6287,f7559]) ).

fof(f7561,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK0_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK1_skl),number_number_of(nat,bit0(one_one(int))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,bit0(bit0(bit1(pls)))),m)),one_one(int))
    | t != one_one(int) ),
    inference(forward_demodulation,[status(thm)],[f6118,f7560]) ).

fof(f7562,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK0_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK1_skl),number_number_of(nat,bit0(one_one(int))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,bit0(bit0(one_one(int)))),m)),one_one(int))
    | t != one_one(int) ),
    inference(forward_demodulation,[status(thm)],[f6287,f7561]) ).

fof(f7563,plain,
    t != one_one(int),
    inference(forward_subsumption_resolution,[status(thm)],[f7562,f6689]) ).

fof(f7719,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK2_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK3_skl),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(forward_demodulation,[status(thm)],[f6287,f1424]) ).

fof(f7720,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK2_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK3_skl),number_number_of(nat,bit0(one_one(int))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(forward_demodulation,[status(thm)],[f6287,f7719]) ).

fof(f7721,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK2_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK3_skl),number_number_of(nat,bit0(one_one(int))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,bit0(bit0(bit1(pls)))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(forward_demodulation,[status(thm)],[f6118,f7720]) ).

fof(f7722,plain,
    ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK2_skl),number_number_of(nat,bit0(one_one(int))))),hAPP(nat,int,power_power(int,sK3_skl),number_number_of(nat,bit0(one_one(int))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,bit0(bit0(one_one(int)))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(forward_demodulation,[status(thm)],[f6287,f7721]) ).

fof(f7723,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
    inference(forward_subsumption_resolution,[status(thm)],[f7722,f6689]) ).

fof(f8786,plain,
    ! [X0,X1] :
      ( number_number_of(int,X0) = ti(int,X1)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ),
    inference(forward_demodulation,[status(thm)],[f1641,f1459]) ).

fof(f8787,plain,
    ! [X0,X1] :
      ( number_number_of(int,X0) = number_number_of(int,X1)
      | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
      | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ),
    inference(forward_demodulation,[status(thm)],[f1641,f8786]) ).

fof(f8788,plain,
    ( number_number_of(int,one_one(int)) = number_number_of(int,t)
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(resolution,[status(thm)],[f8787,f1418]) ).

fof(f8801,plain,
    ( one_one(int) = number_number_of(int,t)
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(forward_demodulation,[status(thm)],[f6892,f8788]) ).

fof(f8802,plain,
    ( one_one(int) = t
    | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(forward_demodulation,[status(thm)],[f6111,f8801]) ).

fof(f8803,plain,
    one_one(int) = t,
    inference(forward_subsumption_resolution,[status(thm)],[f8802,f7723]) ).

fof(f8885,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f8803,f7563]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM926+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35  % Computer : n005.cluster.edu
% 0.09/0.35  % Model    : x86_64 x86_64
% 0.09/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35  % Memory   : 8046.5625MB
% 0.09/0.35  % OS       : Linux 6.8.0-71-generic
% 0.09/0.35  % CPULimit : 300
% 0.09/0.35  % WCLimit  : 300
% 0.09/0.35  % DateTime : Mon Sep 21 03:18:33 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.21/0.49  % Drodi V4.1.1
% 0.21/0.65  % Refutation found
% 0.21/0.65  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.65  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.63/0.72  % Elapsed time: 0.357581 seconds
% 0.63/0.72  % CPU time: 1.398745 seconds
% 0.63/0.72  % Total memory used: 238.373 MB
% 0.63/0.72  % Net memory used: 237.479 MB
%------------------------------------------------------------------------------