%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI647_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n021.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 17:02:26 EDT 2022

% Result   : Theorem 0.20s 0.38s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   15 (   6 unt;   1 typ;   0 def)
%            Number of atoms       :   22 (   6 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   3   ~;   1   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   65 (  13 atm;  16 fun;  36 num;   0 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   1 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(a_type,type,
    a: $int ).

tff(1,plain,
    ( $lesseq(1,0)
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( $product(3,a) = 3 )
  <=> ( a = 1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ ( ~ $lesseq(-1,$product(-1,$product(2,a)))
      | ( $product(3,a) != 3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

tff(4,plain,
    $product(3,a) = 3,
    inference(or_elim,[status(thm)],[3]) ).

tff(5,plain,
    a = 1,
    inference(modus_ponens,[status(thm)],[4,2]) ).

tff(6,plain,
    ( $lesseq(a,0)
  <=> $lesseq(1,0) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( $lesseq(a,0)
  <=> $false ),
    inference(transitivity,[status(thm)],[6,1]) ).

tff(8,plain,
    ( $lesseq(-1,$product(-2,a))
  <=> $lesseq(a,0) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    $product(-1,$product(2,a)) = $product(-2,a),
    inference(rewrite,[status(thm)],]) ).

tff(10,plain,
    ( $lesseq(-1,$product(-1,$product(2,a)))
  <=> $lesseq(-1,$product(-2,a)) ),
    inference(monotonicity,[status(thm)],[9]) ).

tff(11,plain,
    ( $lesseq(-1,$product(-1,$product(2,a)))
  <=> $lesseq(a,0) ),
    inference(transitivity,[status(thm)],[10,8]) ).

tff(12,plain,
    $lesseq(-1,$product(-1,$product(2,a))),
    inference(or_elim,[status(thm)],[3]) ).

tff(13,plain,
    $lesseq(a,0),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    $false,
    inference(modus_ponens,[status(thm)],[13,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ARI647_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 30 01:09:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.20/0.38  % SZS status Theorem
% 0.20/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------