TSTP Solution File: ARI529_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI529_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 : Tue Sep  6 17:01:56 EDT 2022

% Result   : Theorem 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   33 (  22 unt;   0 typ;   0 def)
%            Number of atoms       :   44 (  20 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   22 (  11   ~;   0   |;   0   &)
%                                         (  11 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number arithmetic     :  195 (  13 atm;  85 fun;  97 num;   0 var)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   0 usr;   2 prp; 0-2 aty)
%            Number of functors    :   14 (   0 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(1,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ $false
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( $lesseq(10,9)
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ~ $lesseq(10,9)
  <=> ~ $false ),
    inference(monotonicity,[status(thm)],[3]) ).

tff(5,plain,
    ( ~ $lesseq(10,9)
  <=> $true ),
    inference(transitivity,[status(thm)],[4,2]) ).

tff(6,plain,
    ( $less(9,10)
  <=> ~ $lesseq(10,9) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    $product(5,2) = 10,
    inference(rewrite,[status(thm)],]) ).

tff(8,plain,
    $to_real(2) = 2,
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    $to_real(5) = 5,
    inference(rewrite,[status(thm)],]) ).

tff(10,plain,
    $to_int(11/2) = 5,
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    $to_real($to_int(11/2)) = $to_real(5),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    $to_real($to_int(11/2)) = 5,
    inference(transitivity,[status(thm)],[11,9]) ).

tff(13,plain,
    $product($to_real($to_int(11/2)),$to_real(2)) = $product(5,2),
    inference(monotonicity,[status(thm)],[12,8]) ).

tff(14,plain,
    $product($to_real($to_int(11/2)),$to_real(2)) = 10,
    inference(transitivity,[status(thm)],[13,7]) ).

tff(15,plain,
    $to_real(9) = 9,
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    $to_int(99999/10000) = 9,
    inference(rewrite,[status(thm)],]) ).

tff(17,plain,
    $sum(10,-1/10000) = 99999/10000,
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    $product(-1,1/10000) = -1/10000,
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    $sum(10,$product(-1,1/10000)) = $sum(10,-1/10000),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    $sum(10,$product(-1,1/10000)) = 99999/10000,
    inference(transitivity,[status(thm)],[19,17]) ).

tff(21,plain,
    $difference(10,1/10000) = $sum(10,$product(-1,1/10000)),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    $difference(10,1/10000) = 99999/10000,
    inference(transitivity,[status(thm)],[21,20]) ).

tff(23,plain,
    $to_int($difference(10,1/10000)) = $to_int(99999/10000),
    inference(monotonicity,[status(thm)],[22]) ).

tff(24,plain,
    $to_int($difference(10,1/10000)) = 9,
    inference(transitivity,[status(thm)],[23,16]) ).

tff(25,plain,
    $to_real($to_int($difference(10,1/10000))) = $to_real(9),
    inference(monotonicity,[status(thm)],[24]) ).

tff(26,plain,
    $to_real($to_int($difference(10,1/10000))) = 9,
    inference(transitivity,[status(thm)],[25,15]) ).

tff(27,plain,
    ( $less($to_real($to_int($difference(10,1/10000))),$product($to_real($to_int(11/2)),$to_real(2)))
  <=> $less(9,10) ),
    inference(monotonicity,[status(thm)],[26,14]) ).

tff(28,plain,
    ( $less($to_real($to_int($difference(10,1/10000))),$product($to_real($to_int(11/2)),$to_real(2)))
  <=> ~ $lesseq(10,9) ),
    inference(transitivity,[status(thm)],[27,6]) ).

tff(29,plain,
    ( $less($to_real($to_int($difference(10,1/10000))),$product($to_real($to_int(11/2)),$to_real(2)))
  <=> $true ),
    inference(transitivity,[status(thm)],[28,5]) ).

tff(30,plain,
    ( ~ $less($to_real($to_int($difference(10,1/10000))),$product($to_real($to_int(11/2)),$to_real(2)))
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[29]) ).

tff(31,plain,
    ( ~ $less($to_real($to_int($difference(10,1/10000))),$product($to_real($to_int(11/2)),$to_real(2)))
  <=> $false ),
    inference(transitivity,[status(thm)],[30,1]) ).

tff(32,axiom,
    ~ $less($to_real($to_int($difference(10,1/10000))),$product($to_real($to_int(11/2)),$to_real(2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mixed_types_problem_34) ).

tff(33,plain,
    $false,
    inference(modus_ponens,[status(thm)],[32,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ARI529_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n007.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 : Mon Aug 29 23:59:30 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.13/0.39  % SZS status Theorem
% 0.13/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------