TSTP Solution File: NUM926+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM926+4 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n023.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 : Thu Aug 31 12:16:58 EDT 2023

% Result   : Theorem 7.44s 2.25s
% Output   : Refutation 7.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   40 (  16 unt;   0 def)
%            Number of atoms       :  109 (  30 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  107 (  38   ~;  30   |;  26   &)
%                                         (   1 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  17 con; 0-2 aty)
%            Number of variables   :   42 (;  20   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f38698,plain,
    $false,
    inference(subsumption_resolution,[],[f38697,f16692]) ).

fof(f16692,plain,
    is_int(one_one_int),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    is_int(one_one_int),
    file('/export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).

fof(f38697,plain,
    ~ is_int(one_one_int),
    inference(subsumption_resolution,[],[f38696,f16700]) ).

fof(f16700,plain,
    is_int(t),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,axiom,
    is_int(t),
    file('/export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',gsy_v_t____) ).

fof(f38696,plain,
    ( ~ is_int(t)
    | ~ is_int(one_one_int) ),
    inference(subsumption_resolution,[],[f38695,f16873]) ).

fof(f16873,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
    file('/export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',fact_0_tpos) ).

fof(f38695,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t))
    | ~ is_int(t)
    | ~ is_int(one_one_int) ),
    inference(subsumption_resolution,[],[f38254,f37701]) ).

fof(f37701,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
    inference(resolution,[],[f25397,f25634]) ).

fof(f25634,plain,
    ( sQ742_eqProxy(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),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK43),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,sK44),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    inference(equality_proxy_replacement,[],[f17046,f25360]) ).

fof(f25360,plain,
    ! [X0,X1] :
      ( sQ742_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ742_eqProxy])]) ).

fof(f17046,plain,
    ( 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) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK43),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,sK44),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    inference(cnf_transformation,[],[f14537]) ).

fof(f14537,plain,
    ( ( 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) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK43),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,sK44),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
      & is_int(sK44)
      & is_int(sK43) )
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f10570,f14536]) ).

fof(f14536,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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)))))
        & is_int(X1)
        & is_int(X0) )
   => ( 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) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK43),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,sK44),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
      & is_int(sK44)
      & is_int(sK43) ) ),
    introduced(choice_axiom,[]) ).

fof(f10570,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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)))))
        & is_int(X1)
        & is_int(X0) )
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
    inference(ennf_transformation,[],[f5484]) ).

fof(f5484,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
   => ? [X0,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,pls))))),m)),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,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)))))
        & is_int(X1)
        & is_int(X0) ) ),
    inference(rectify,[],[f62]) ).

fof(f62,axiom,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
   => ? [X3,X4] :
        ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X3),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,X4),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)
        & is_int(X4)
        & is_int(X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(f25397,plain,
    ! [X0,X1] : ~ sQ742_eqProxy(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),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)))))),
    inference(equality_proxy_replacement,[],[f16690,f25360]) ).

fof(f16690,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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))))),
    inference(cnf_transformation,[],[f10567]) ).

fof(f10567,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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))))),
    inference(ennf_transformation,[],[f5482]) ).

fof(f5482,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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))))),
    inference(rectify,[],[f5481]) ).

fof(f5481,negated_conjecture,
    ~ ? [X3,X4] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X3),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,X4),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,[],[f5480]) ).

fof(f5480,conjecture,
    ? [X3,X4] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X3),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,X4),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/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',conj_0) ).

fof(f38254,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t))
    | ~ is_int(t)
    | ~ is_int(one_one_int) ),
    inference(resolution,[],[f37700,f27778]) ).

fof(f27778,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | sQ742_eqProxy(X0,X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(equality_proxy_replacement,[],[f20641,f25360]) ).

fof(f20641,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | X0 = X1
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(cnf_transformation,[],[f12523]) ).

fof(f12523,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | X0 = X1
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(flattening,[],[f12522]) ).

fof(f12522,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | X0 = X1
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ is_int(X1)
      | ~ is_int(X0) ),
    inference(ennf_transformation,[],[f8393]) ).

fof(f8393,plain,
    ! [X0,X1] :
      ( ( is_int(X1)
        & is_int(X0) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => ( X0 != X1
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ) ),
    inference(rectify,[],[f1071]) ).

fof(f1071,axiom,
    ! [X289,X290] :
      ( ( is_int(X290)
        & is_int(X289) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X289),X290))
       => ( X289 != X290
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X289),X290)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',fact_1011_order__le__neq__implies__less) ).

fof(f37700,plain,
    ~ sQ742_eqProxy(one_one_int,t),
    inference(resolution,[],[f25397,f25631]) ).

fof(f25631,plain,
    ( sQ742_eqProxy(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),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK41),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,sK42),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
    | ~ sQ742_eqProxy(one_one_int,t) ),
    inference(equality_proxy_replacement,[],[f17043,f25360,f25360]) ).

fof(f17043,plain,
    ( 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) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK41),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,sK42),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
    | one_one_int != t ),
    inference(cnf_transformation,[],[f14535]) ).

fof(f14535,plain,
    ( ( 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) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK41),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,sK42),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
      & is_int(sK42)
      & is_int(sK41) )
    | one_one_int != t ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f10569,f14534]) ).

fof(f14534,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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)))))
        & is_int(X1)
        & is_int(X0) )
   => ( 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) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,sK41),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,sK42),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
      & is_int(sK42)
      & is_int(sK41) ) ),
    introduced(choice_axiom,[]) ).

fof(f10569,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,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),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,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)))))
        & is_int(X1)
        & is_int(X0) )
    | one_one_int != t ),
    inference(ennf_transformation,[],[f5483]) ).

fof(f5483,plain,
    ( one_one_int = t
   => ? [X0,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,pls))))),m)),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,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)))))
        & is_int(X1)
        & is_int(X0) ) ),
    inference(rectify,[],[f61]) ).

fof(f61,axiom,
    ( one_one_int = t
   => ? [X3,X4] :
        ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X3),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,X4),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)
        & is_int(X4)
        & is_int(X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.87/0.91  % Problem    : NUM926+4 : TPTP v8.1.2. Released v5.3.0.
% 0.87/0.92  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.95/1.13  % Computer : n023.cluster.edu
% 0.95/1.13  % Model    : x86_64 x86_64
% 0.95/1.13  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.95/1.13  % Memory   : 8042.1875MB
% 0.95/1.13  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.95/1.13  % CPULimit   : 300
% 0.95/1.13  % WCLimit    : 300
% 0.95/1.13  % DateTime   : Fri Aug 25 09:55:42 EDT 2023
% 0.95/1.13  % CPUTime    : 
% 0.95/1.13  This is a FOF_THM_RFO_SEQ problem
% 0.95/1.13  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.AppM15vAL4/Vampire---4.8_30075
% 0.95/1.13  % (30183)Running in auto input_syntax mode. Trying TPTP
% 0.98/1.33  % (30190)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_394 on Vampire---4 for (394ds/0Mi)
% 0.98/1.36  % (30186)ott-11_3:1_afr=on:anc=all_dependent:bd=preordered:bce=on:er=filter:fsd=off:fde=unused:nm=4:sos=all:sac=on:tgt=full:urr=on_476 on Vampire---4 for (476ds/0Mi)
% 0.98/1.36  % (30188)dis+3_3:2_aac=none:fsd=off:fde=none:lcm=reverse:nm=32:nicw=on:sos=on:sac=on:sp=occurrence_419 on Vampire---4 for (419ds/0Mi)
% 0.98/1.36  % (30189)dis+1011_2:1_add=off:afr=on:er=known:fde=unused:nwc=1.3:nicw=on:sas=z3:sims=off:sos=on:sac=on:tgt=full_398 on Vampire---4 for (398ds/0Mi)
% 0.98/1.36  % (30184)dis+1011_3_av=off:bd=off:er=known:fsd=off:fde=unused:irw=on:nm=64:nwc=1.3:sos=on:sp=reverse_arity_577 on Vampire---4 for (577ds/0Mi)
% 0.98/1.36  % (30185)dis-1002_1_bd=off:fsd=off:fsr=off:fde=none:nwc=1.3:sims=off:sos=all_501 on Vampire---4 for (501ds/0Mi)
% 0.98/1.36  % (30187)ott+1010_3_aac=none:bs=unit_only:bce=on:ep=R:er=filter:fsd=off:fde=none:gsp=on:irw=on:lcm=predicate:nwc=10.0:sos=all:sp=occurrence_449 on Vampire---4 for (449ds/0Mi)
% 7.44/2.24  % (30187)First to succeed.
% 7.44/2.25  % (30187)Refutation found. Thanks to Tanya!
% 7.44/2.25  % SZS status Theorem for Vampire---4
% 7.44/2.25  % SZS output start Proof for Vampire---4
% See solution above
% 7.44/2.25  % (30187)------------------------------
% 7.44/2.25  % (30187)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 7.44/2.25  % (30187)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 7.44/2.25  % (30187)Termination reason: Refutation
% 7.44/2.25  
% 7.44/2.25  % (30187)Memory used [KB]: 46054
% 7.44/2.25  % (30187)Time elapsed: 0.876 s
% 7.44/2.25  % (30187)------------------------------
% 7.44/2.25  % (30187)------------------------------
% 7.44/2.25  % (30183)Success in time 1.104 s
% 7.44/2.25  % Vampire---4.8 exiting
%------------------------------------------------------------------------------