%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV082+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n011.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 : Thu Sep 29 15:09:54 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   12 (   1 unt;   6 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   21 (   5   ~;   0   |;   8   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   2 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(leq_type,type,
    leq: ( $i * $i ) > $o ).

tff(minus_type,type,
    minus: ( $i * $i ) > $i ).

tff(n1_type,type,
    n1: $i ).

tff(n5_type,type,
    n5: $i ).

tff(pv58_type,type,
    pv58: $i ).

tff(n0_type,type,
    n0: $i ).

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

tff(2,plain,
    ( ( ( leq(n0,pv58)
        & leq(pv58,minus(n5,n1)) )
     => ( leq(n0,pv58)
        & leq(pv58,minus(n5,n1)) ) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ~ ( ( leq(n0,pv58)
          & leq(pv58,minus(n5,n1)) )
       => ( leq(n0,pv58)
          & leq(pv58,minus(n5,n1)) ) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[2]) ).

tff(4,plain,
    ( ~ ( ( leq(n0,pv58)
          & leq(pv58,minus(n5,n1)) )
       => ( leq(n0,pv58)
          & leq(pv58,minus(n5,n1)) ) )
  <=> $false ),
    inference(transitivity,[status(thm)],[3,1]) ).

tff(5,axiom,
    ~ ( ( leq(n0,pv58)
        & leq(pv58,minus(n5,n1)) )
     => ( leq(n0,pv58)
        & leq(pv58,minus(n5,n1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0023) ).

tff(6,plain,
    $false,
    inference(modus_ponens,[status(thm)],[5,4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWV082+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.00/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n011.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 : Sun Sep  4 01:16:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.19/0.38  % SZS status Theorem
% 0.19/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------