%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM925+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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 : Sun Sep 18 13:12:42 EDT 2022

% Result   : Theorem 0.16s 0.39s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   58 (  19 unt;  12 typ;   0 def)
%            Number of atoms       :   98 (  67 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   70 (  21   ~;   4   |;   0   &)
%                                         (  45 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   8   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (  15   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
tff(ord_less_int_type,type,
    ord_less_int: ( $i * $i ) > $o ).

tff(plus_plus_int_type,type,
    plus_plus_int: ( $i * $i ) > $i ).

tff(semiri1621563631at_int_type,type,
    semiri1621563631at_int: $i > $i ).

tff(n_type,type,
    n: $i ).

tff(number_number_of_int_type,type,
    number_number_of_int: $i > $i ).

tff(bit1_type,type,
    bit1: $i > $i ).

tff(pls_type,type,
    pls: $i ).

tff(power_power_int_type,type,
    power_power_int: ( $i * $i ) > $i ).

tff(number_number_of_nat_type,type,
    number_number_of_nat: $i > $i ).

tff(bit0_type,type,
    bit0: $i > $i ).

tff(zero_zero_int_type,type,
    zero_zero_int: $i ).

tff(one_one_int_type,type,
    one_one_int: $i ).

tff(1,plain,
    ^ [A_1: $i] :
      refl(
        ( ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
        <=> ( A_1 = pls ) )
      <=> ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
        <=> ( A_1 = pls ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
      <=> ( A_1 = pls ) )
  <=> ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
      <=> ( A_1 = pls ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [A_1: $i] :
      rewrite(
        ( ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
        <=> ( A_1 = number_number_of_int(pls) ) )
      <=> ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
        <=> ( A_1 = pls ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
      <=> ( A_1 = number_number_of_int(pls) ) )
  <=> ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
      <=> ( A_1 = pls ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ^ [A_1: $i] :
      rewrite(
        ( ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
        <=> ( A_1 = zero_zero_int ) )
      <=> ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
        <=> ( A_1 = number_number_of_int(pls) ) ) )),
    inference(bind,[status(th)],]) ).

tff(6,plain,
    ( ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) )
  <=> ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
      <=> ( A_1 = number_number_of_int(pls) ) ) ),
    inference(quant_intro,[status(thm)],[5]) ).

tff(7,plain,
    ( ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) )
  <=> ! [A_1: $i] :
        ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,axiom,
    ! [A_1: $i] :
      ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
    <=> ( A_1 = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zero__eq__power2) ).

tff(9,plain,
    ! [A_1: $i] :
      ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
    <=> ( A_1 = zero_zero_int ) ),
    inference(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    ! [A_1: $i] :
      ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
    <=> ( A_1 = number_number_of_int(pls) ) ),
    inference(modus_ponens,[status(thm)],[9,6]) ).

tff(11,plain,
    ! [A_1: $i] :
      ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
    <=> ( A_1 = pls ) ),
    inference(modus_ponens,[status(thm)],[10,4]) ).

tff(12,plain,
    ! [A_1: $i] :
      ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
    <=> ( A_1 = pls ) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [A_1: $i] :
      ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
    <=> ( A_1 = pls ) ),
    inference(modus_ponens,[status(thm)],[12,2]) ).

tff(14,plain,
    ( ~ ! [A_1: $i] :
          ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = pls )
        <=> ( A_1 = pls ) )
    | ( ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = pls )
    <=> ( plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(15,plain,
    ( ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = pls )
  <=> ( plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls ) ),
    inference(unit_resolution,[status(thm)],[14,13]) ).

tff(16,plain,
    ( ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
  <=> ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = pls ) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,plain,
    ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
  <=> ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
  <=> ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
  <=> ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,axiom,
    ~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(21,plain,
    power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(modus_ponens,[status(thm)],[21,18]) ).

tff(23,plain,
    power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls),
    inference(modus_ponens,[status(thm)],[22,17]) ).

tff(24,plain,
    power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = pls,
    inference(modus_ponens,[status(thm)],[23,16]) ).

tff(25,plain,
    ( ~ ( ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = pls )
      <=> ( plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls ) )
    | ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != pls )
    | ( plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls ) ),
    inference(tautology,[status(thm)],]) ).

tff(26,plain,
    ( ~ ( ( power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = pls )
      <=> ( plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls ) )
    | ( plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls ) ),
    inference(unit_resolution,[status(thm)],[25,24]) ).

tff(27,plain,
    plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)) = pls,
    inference(unit_resolution,[status(thm)],[26,15]) ).

tff(28,plain,
    ( ord_less_int(pls,plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)))
  <=> ord_less_int(pls,pls) ),
    inference(monotonicity,[status(thm)],[27]) ).

tff(29,plain,
    ( ord_less_int(pls,pls)
  <=> ord_less_int(pls,plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))) ),
    inference(symmetry,[status(thm)],[28]) ).

tff(30,plain,
    ( ~ ord_less_int(pls,pls)
  <=> ~ ord_less_int(pls,plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))) ),
    inference(monotonicity,[status(thm)],[29]) ).

tff(31,plain,
    ( ~ ord_less_int(pls,number_number_of_int(pls))
  <=> ~ ord_less_int(pls,pls) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ord_less_int(pls,zero_zero_int)
  <=> ~ ord_less_int(pls,number_number_of_int(pls)) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ ord_less_int(pls,zero_zero_int)
  <=> ~ ord_less_int(pls,zero_zero_int) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,axiom,
    ~ ord_less_int(pls,zero_zero_int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).

tff(35,plain,
    ~ ord_less_int(pls,zero_zero_int),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ~ ord_less_int(pls,number_number_of_int(pls)),
    inference(modus_ponens,[status(thm)],[35,32]) ).

tff(37,plain,
    ~ ord_less_int(pls,pls),
    inference(modus_ponens,[status(thm)],[36,31]) ).

tff(38,plain,
    ~ ord_less_int(pls,plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))),
    inference(modus_ponens,[status(thm)],[37,30]) ).

tff(39,plain,
    ( ord_less_int(number_number_of_int(pls),plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n)))
  <=> ord_less_int(pls,plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,plain,
    ( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n)))
  <=> ord_less_int(number_number_of_int(pls),plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,plain,
    ( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n)))
  <=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).

tff(43,plain,
    ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ord_less_int(number_number_of_int(pls),plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))),
    inference(modus_ponens,[status(thm)],[43,40]) ).

tff(45,plain,
    ord_less_int(pls,plus_plus_int(number_number_of_int(bit1(pls)),semiri1621563631at_int(n))),
    inference(modus_ponens,[status(thm)],[44,39]) ).

tff(46,plain,
    $false,
    inference(unit_resolution,[status(thm)],[45,38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : NUM925+1 : TPTP v8.1.0. Released v5.3.0.
% 0.02/0.11  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31  % Computer : n002.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Fri Sep  2 15:59:01 EDT 2022
% 0.10/0.31  % CPUTime  : 
% 0.10/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32  Usage: tptp [options] [-file:]file
% 0.10/0.32    -h, -?       prints this message.
% 0.10/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.10/0.32    -m, -model   generate model.
% 0.10/0.32    -p, -proof   generate proof.
% 0.10/0.32    -c, -core    generate unsat core of named formulas.
% 0.10/0.32    -st, -statistics display statistics.
% 0.10/0.32    -t:timeout   set timeout (in second).
% 0.10/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.10/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32    -<param>:<value> configuration parameter and value.
% 0.10/0.32    -o:<output-file> file to place output in.
% 0.16/0.39  % SZS status Theorem
% 0.16/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------