%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM489+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 13:10:01 EDT 2022

% Result   : Theorem 0.21s 0.42s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (   7 unt;   6 typ;   0 def)
%            Number of atoms       :   32 (  23 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  11   ~;   0   |;   3   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   1 usr;   2 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(sdtmndt0_type,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(xp_type,type,
    xp: $i ).

tff(xn_type,type,
    xn: $i ).

tff(xr_type,type,
    xr: $i ).

tff(aNaturalNumber0_type,type,
    aNaturalNumber0: $i > $o ).

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

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

tff(3,plain,
    ( ( sdtpldt0(xp,xr) = xn )
  <=> ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ( sdtpldt0(xp,xr) = xn )
  <=> ( sdtpldt0(xp,xr) = xn ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    ( aNaturalNumber0(xr)
    & ( sdtpldt0(xp,xr) = xn )
    & ( xr = sdtmndt0(xn,xp) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).

tff(6,plain,
    ( aNaturalNumber0(xr)
    & ( sdtpldt0(xp,xr) = xn ) ),
    inference(and_elim,[status(thm)],[5]) ).

tff(7,plain,
    sdtpldt0(xp,xr) = xn,
    inference(and_elim,[status(thm)],[6]) ).

tff(8,plain,
    sdtpldt0(xp,xr) = xn,
    inference(modus_ponens,[status(thm)],[7,4]) ).

tff(9,plain,
    sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
    inference(modus_ponens,[status(thm)],[8,3]) ).

tff(10,plain,
    ( ( xn = sdtpldt0(xp,sdtmndt0(xn,xp)) )
  <=> ( xn = xn ) ),
    inference(monotonicity,[status(thm)],[9]) ).

tff(11,plain,
    ( ( xn = sdtpldt0(xp,sdtmndt0(xn,xp)) )
  <=> $true ),
    inference(transitivity,[status(thm)],[10,2]) ).

tff(12,plain,
    ( ( xn != sdtpldt0(xp,sdtmndt0(xn,xp)) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[11]) ).

tff(13,plain,
    ( ( xn != sdtpldt0(xp,sdtmndt0(xn,xp)) )
  <=> $false ),
    inference(transitivity,[status(thm)],[12,1]) ).

tff(14,plain,
    ( ( xn != sdtpldt0(xp,xr) )
  <=> ( xn != sdtpldt0(xp,sdtmndt0(xn,xp)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ( xn != sdtpldt0(xp,xr) )
  <=> ( xn != sdtpldt0(xp,xr) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    xn != sdtpldt0(xp,xr),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(17,plain,
    xn != sdtpldt0(xp,xr),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    xn != sdtpldt0(xp,sdtmndt0(xn,xp)),
    inference(modus_ponens,[status(thm)],[17,14]) ).

tff(19,plain,
    $false,
    inference(modus_ponens,[status(thm)],[18,13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : NUM489+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Sep  2 10:59:49 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 0.21/0.42  % SZS status Theorem
% 0.21/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------