TSTP Solution File: ITP269_1 by Z3---4.8.9.0

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%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ITP269_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%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 : Sat Sep 17 04:18:04 EDT 2022

% Result   : Theorem 2.37s 2.55s
% Output   : Proof 3.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   35 (   3 unt;  31 typ;   0 def)
%            Number of atoms       :    5 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    2 (   1   ~;   0   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Maximal term depth    :   21 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   23 (  13   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  13 usr;  13 prp; 0-1 aty)
%            Number of functors    :   30 (  30 usr;  18 con; 0-3 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pp_type,type,
    pp: bool > $o ).

tff(aa_nat_bool_type,type,
    aa_nat_bool: ( fun_nat_bool * nat ) > bool ).

tff(aa_nat_nat_type,type,
    aa_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(deg_type,type,
    deg: nat ).

tff(aa_nat_fun_nat_nat_type,type,
    aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).

tff(aa_num_nat_type,type,
    aa_num_nat: ( fun_num_nat * num ) > nat ).

tff(aa_num_num_type,type,
    aa_num_num: ( fun_num_num * num ) > num ).

tff(one_type,type,
    one: num ).

tff(bit0_type,type,
    bit0: fun_num_num ).

tff(numeral_numeral_nat_type,type,
    numeral_numeral_nat: fun_num_nat ).

tff(power_power_nat_type,type,
    power_power_nat: fun_nat_fun_nat_nat ).

tff(aa_nat_fun_nat_bool_type,type,
    aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).

tff(ma_type,type,
    ma: nat ).

tff(the_nat_type,type,
    the_nat: option_nat > nat ).

tff(vEBT_vebt_maxt_type,type,
    vEBT_vebt_maxt: vEBT_VEBT > option_nat ).

tff(nth_VEBT_VEBT_type,type,
    nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).

tff(na_type,type,
    na: nat ).

tff(lx_type,type,
    lx: nat ).

tff(summin_type,type,
    summin: nat ).

tff(times_times_nat_type,type,
    times_times_nat: fun_nat_fun_nat_nat ).

tff(plus_plus_nat_type,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

tff(vEBT_VEBT_high_type,type,
    vEBT_VEBT_high: fun_nat_fun_nat_nat ).

tff(list_u1324408373059187874T_VEBT_type,type,
    list_u1324408373059187874T_VEBT: ( list_VEBT_VEBT * nat * vEBT_VEBT ) > list_VEBT_VEBT ).

tff(vEBT_vebt_delete_type,type,
    vEBT_vebt_delete: ( vEBT_VEBT * nat ) > vEBT_VEBT ).

tff(vEBT_VEBT_low_type,type,
    vEBT_VEBT_low: fun_nat_fun_nat_nat ).

tff(treeList_type,type,
    treeList: list_VEBT_VEBT ).

tff(divide_divide_nat_type,type,
    divide_divide_nat: fun_nat_fun_nat_nat ).

tff(if_nat_type,type,
    if_nat: bool > fun_nat_fun_nat_nat ).

tff(fequal_nat_type,type,
    fequal_nat: fun_nat_fun_nat_bool ).

tff(ord_less_nat_type,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

tff(ord_less_eq_nat_type,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

tff(1,axiom,
    ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(2,axiom,
    ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
    & pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__C114_C) ).

tff(3,plain,
    pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
    inference(and_elim,[status(thm)],[2]) ).

tff(4,plain,
    $false,
    inference(unit_resolution,[status(thm)],[3,1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP269_1 : TPTP v8.1.0. Released v8.0.0.
% 0.07/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Sep  1 06:48:04 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36  Usage: tptp [options] [-file:]file
% 0.13/0.36    -h, -?       prints this message.
% 0.13/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.36    -m, -model   generate model.
% 0.13/0.36    -p, -proof   generate proof.
% 0.13/0.36    -c, -core    generate unsat core of named formulas.
% 0.13/0.36    -st, -statistics display statistics.
% 0.13/0.36    -t:timeout   set timeout (in second).
% 0.13/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36    -<param>:<value> configuration parameter and value.
% 0.13/0.36    -o:<output-file> file to place output in.
% 2.37/2.55  % SZS status Theorem
% 2.37/2.55  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------