%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI185_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : Tue Sep  6 17:00:52 EDT 2022

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   16 (   8 unt;   1 typ;   0 def)
%            Number of atoms       :   26 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   33 (  23   ~;   3   |;   0   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :   79 (  24 atm;   4 fun;  37 num;  14 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   1 usr;   5 con; 0-2 aty)
%            Number of variables   :   14 (  13   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f_type,type,
    f: $int > $int ).

tff(1,plain,
    ^ [U: $int] :
      refl(
        ( ~ $lesseq(f(U),1)
      <=> ~ $lesseq(f(U),1) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [U: $int] : ~ $lesseq(f(U),1)
  <=> ! [U: $int] : ~ $lesseq(f(U),1) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [U: $int] : ~ $lesseq(f(U),1)
  <=> ! [U: $int] : ~ $lesseq(f(U),1) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ~ ( ! [U: $int] : $greater(f(U),1)
       => $less($difference(7,$product(2,f(3))),4) )
  <=> ~ ( ~ $lesseq(f(3),1)
        | ~ ! [U: $int] : ~ $lesseq(f(U),1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    ~ ( ! [U: $int] : $greater(f(U),1)
     => $less($difference(7,$product(2,f(3))),4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(6,plain,
    ~ ( ~ $lesseq(f(3),1)
      | ~ ! [U: $int] : ~ $lesseq(f(U),1) ),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ! [U: $int] : ~ $lesseq(f(U),1),
    inference(or_elim,[status(thm)],[6]) ).

tff(8,plain,
    ! [U: $int] : ~ $lesseq(f(U),1),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [U: $int] : ~ $lesseq(f(U),1),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [U: $int] : ~ $lesseq(f(U),1),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( $lesseq(f(3),1)
  <=> $lesseq(f(3),1) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    $lesseq(f(3),1),
    inference(or_elim,[status(thm)],[6]) ).

tff(13,plain,
    $lesseq(f(3),1),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ~ ! [U: $int] : ~ $lesseq(f(U),1)
    | ~ $lesseq(f(3),1) ),
    inference(quant_inst,[status(thm)],]) ).

tff(15,plain,
    $false,
    inference(unit_resolution,[status(thm)],[14,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ARI185_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13  % 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 : Mon Aug 29 22:19:41 EDT 2022
% 0.13/0.34  % 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.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------