%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV123+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 15:10:03 EDT 2022

% Result   : Theorem 0.19s 0.41s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   3 unt;   9 typ;   0 def)
%            Number of atoms       :   37 (   0 equ)
%            Maximal formula atoms :   17 (   6 avg)
%            Number of connectives :   44 (  13   ~;   8   |;   8   &)
%                                         (   1 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 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 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(true_type,type,
    true: $o ).

tff(geq_type,type,
    geq: ( $i * $i ) > $o ).

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

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

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

tff(n3_type,type,
    n3: $i ).

tff(n999_type,type,
    n999: $i ).

tff(n2_type,type,
    n2: $i ).

tff(n6_type,type,
    n6: $i ).

tff(1,plain,
    ( ~ ( geq(minus(n3,n1),n0)
       => ( geq(minus(n6,n1),n0)
         => ( ( geq(n2,n0)
              & geq(minus(n999,n1),n0) )
           => ( geq(minus(n6,n1),n0)
             => ( geq(minus(n6,n1),n0)
               => ( geq(minus(n6,n1),n0)
                 => ( ( geq(minus(n3,n1),n0)
                      & geq(minus(n999,n1),n0) )
                   => true ) ) ) ) ) ) )
  <=> ~ ( true
        | ~ ( geq(minus(n3,n1),n0)
            & geq(minus(n999,n1),n0) )
        | ~ geq(minus(n6,n1),n0)
        | ~ ( geq(n2,n0)
            & geq(minus(n999,n1),n0) )
        | ~ geq(minus(n3,n1),n0) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ ( geq(minus(n3,n1),n0)
     => ( geq(minus(n6,n1),n0)
       => ( ( geq(n2,n0)
            & geq(minus(n999,n1),n0) )
         => ( geq(minus(n6,n1),n0)
           => ( geq(minus(n6,n1),n0)
             => ( geq(minus(n6,n1),n0)
               => ( ( geq(minus(n3,n1),n0)
                    & geq(minus(n999,n1),n0) )
                 => true ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0016) ).

tff(3,plain,
    ~ ( true
      | ~ ( geq(minus(n3,n1),n0)
          & geq(minus(n999,n1),n0) )
      | ~ geq(minus(n6,n1),n0)
      | ~ ( geq(n2,n0)
          & geq(minus(n999,n1),n0) )
      | ~ geq(minus(n3,n1),n0) ),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ~ true,
    inference(or_elim,[status(thm)],[3]) ).

tff(5,axiom,
    true,
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',ttrue) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWV123+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Sep  4 01:31:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------