%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP161-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n029.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 : Fri Sep 16 22:26:26 EDT 2022

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   14 (   8 unt;   2 typ;   0 def)
%            Number of atoms       :   18 (  16 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   5   ~;   1   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   10 (   9   !;   0   ?;  10   :)

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

tff(greatest_lower_bound_type,type,
    greatest_lower_bound: ( $i * $i ) > $i ).

tff(1,plain,
    ( ( greatest_lower_bound(a,a) != a )
  <=> ( greatest_lower_bound(a,a) != a ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    greatest_lower_bound(a,a) != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_reflb) ).

tff(3,plain,
    greatest_lower_bound(a,a) != a,
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [X: $i] :
      refl(
        ( ( greatest_lower_bound(X,X) = X )
      <=> ( greatest_lower_bound(X,X) = X ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X: $i] : ( greatest_lower_bound(X,X) = X )
  <=> ! [X: $i] : ( greatest_lower_bound(X,X) = X ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [X: $i] : ( greatest_lower_bound(X,X) = X )
  <=> ! [X: $i] : ( greatest_lower_bound(X,X) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [X: $i] : ( greatest_lower_bound(X,X) = X ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).

tff(8,plain,
    ! [X: $i] : ( greatest_lower_bound(X,X) = X ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [X: $i] : ( greatest_lower_bound(X,X) = X ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [X: $i] : ( greatest_lower_bound(X,X) = X ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ~ ! [X: $i] : ( greatest_lower_bound(X,X) = X )
    | ( greatest_lower_bound(a,a) = a ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    $false,
    inference(unit_resolution,[status(thm)],[11,10,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP161-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 31 15:24:43 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.14/0.39  % SZS status Unsatisfiable
% 0.14/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------