TSTP Solution File: NUM924_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM924_1 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 13:12:37 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   61 (  30 unt;  14 typ;   0 def)
%            Number of atoms       :   70 (  42 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   33 (  13   ~;   3   |;   0   &)
%                                         (  17 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    8 (   3 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   12 (   8   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :   40 (  36   !;   0   ?;  40   :)

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

tff(times_times_int_type,type,
    times_times_int: ( int * int ) > int ).

tff(number_number_of_int_type,type,
    number_number_of_int: int > int ).

tff(pls_type,type,
    pls: int ).

tff(plus_plus_int_type,type,
    plus_plus_int: ( int * int ) > int ).

tff(one_one_int_type,type,
    one_one_int: int ).

tff(m_type,type,
    m: int ).

tff(bit0_type,type,
    bit0: int > int ).

tff(bit1_type,type,
    bit1: int > int ).

tff(power_power_int_type,type,
    power_power_int: ( int * nat ) > int ).

tff(number_number_of_nat_type,type,
    number_number_of_nat: int > nat ).

tff(s_type,type,
    s: int ).

tff(zero_zero_int_type,type,
    zero_zero_int: int ).

tff(t_type,type,
    t: int ).

tff(1,plain,
    ^ [K_1: int] :
      refl(
        ( ( number_number_of_int(K_1) = K_1 )
      <=> ( number_number_of_int(K_1) = K_1 ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [K_1: int] : ( number_number_of_int(K_1) = K_1 )
  <=> ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [K_1: int] : ( number_number_of_int(K_1) = K_1 )
  <=> ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).

tff(5,plain,
    ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [K_1: int] : ( number_number_of_int(K_1) = K_1 )
    | ( number_number_of_int(pls) = pls ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    number_number_of_int(pls) = pls,
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    pls = number_number_of_int(pls),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ^ [W: int] :
      refl(
        ( ( times_times_int(pls,W) = pls )
      <=> ( times_times_int(pls,W) = pls ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [W: int] : ( times_times_int(pls,W) = pls )
  <=> ! [W: int] : ( times_times_int(pls,W) = pls ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [W: int] : ( times_times_int(pls,W) = pls )
  <=> ! [W: int] : ( times_times_int(pls,W) = pls ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    ! [W: int] : ( times_times_int(pls,W) = pls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).

tff(15,plain,
    ! [W: int] : ( times_times_int(pls,W) = pls ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ! [W: int] : ( times_times_int(pls,W) = pls ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [W: int] : ( times_times_int(pls,W) = pls ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ( ~ ! [W: int] : ( times_times_int(pls,W) = pls )
    | ( times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls,
    inference(unit_resolution,[status(thm)],[18,17]) ).

tff(20,plain,
    times_times_int(number_number_of_int(pls),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
    inference(monotonicity,[status(thm)],[9]) ).

tff(21,plain,
    ^ [Z: int,W: int] :
      refl(
        ( ( times_times_int(Z,W) = times_times_int(W,Z) )
      <=> ( times_times_int(Z,W) = times_times_int(W,Z) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) )
  <=> ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) )
  <=> ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).

tff(25,plain,
    ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ( ~ ! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) )
    | ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls)) = times_times_int(number_number_of_int(pls),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls)) = times_times_int(number_number_of_int(pls),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
    inference(unit_resolution,[status(thm)],[28,27]) ).

tff(30,plain,
    times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls)) = number_number_of_int(pls),
    inference(transitivity,[status(thm)],[29,20,19,10]) ).

tff(31,plain,
    ( ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls)))
  <=> ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),number_number_of_int(pls)) ),
    inference(monotonicity,[status(thm)],[30]) ).

tff(32,plain,
    ( ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),number_number_of_int(pls))
  <=> ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))) ),
    inference(symmetry,[status(thm)],[31]) ).

tff(33,plain,
    ( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),number_number_of_int(pls))
  <=> ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))) ),
    inference(monotonicity,[status(thm)],[32]) ).

tff(34,plain,
    ( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int)
  <=> ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),number_number_of_int(pls)) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int)
  <=> ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,axiom,
    ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(37,plain,
    ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),number_number_of_int(pls)),
    inference(modus_ponens,[status(thm)],[37,34]) ).

tff(39,plain,
    ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))),
    inference(modus_ponens,[status(thm)],[38,33]) ).

tff(40,plain,
    ( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls)))
  <=> ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,plain,
    ( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
  <=> ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
  <=> ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,axiom,
    ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).

tff(44,plain,
    ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
    inference(modus_ponens,[status(thm)],[43,42]) ).

tff(45,plain,
    ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))),
    inference(modus_ponens,[status(thm)],[44,41]) ).

tff(46,plain,
    ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(pls))),
    inference(modus_ponens,[status(thm)],[45,40]) ).

tff(47,plain,
    $false,
    inference(unit_resolution,[status(thm)],[46,39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM924_1 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Sep  2 15:42:16 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35  Usage: tptp [options] [-file:]file
% 0.12/0.35    -h, -?       prints this message.
% 0.12/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.35    -m, -model   generate model.
% 0.12/0.35    -p, -proof   generate proof.
% 0.12/0.35    -c, -core    generate unsat core of named formulas.
% 0.12/0.35    -st, -statistics display statistics.
% 0.12/0.35    -t:timeout   set timeout (in second).
% 0.12/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35    -<param>:<value> configuration parameter and value.
% 0.12/0.35    -o:<output-file> file to place output in.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------