TSTP Solution File: ARI189_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI189_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.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 17:00:53 EDT 2022

% Result   : Theorem 0.12s 0.40s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   21 (   8 unt;   1 typ;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   39 (  18   ~;  10   |;   0   &)
%                                         (   9 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :   91 (   0 atm;  26 fun;  44 num;  21 var)
%            Number of types       :    2 (   0 usr;   1 ari)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   0 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (  20   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p_type,type,
    p: $int > $o ).

tff(1,plain,
    ^ [U: $int] :
      refl(
        ( p($product(2,U))
      <=> p($product(2,U)) )),
    inference(bind,[status(th)],]) ).

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

tff(3,plain,
    ( ! [U: $int] : p($product(2,U))
  <=> ! [U: $int] : p($product(2,U)) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ~ ( ! [U: $int] : p($product(2,U))
       => p(10) )
  <=> ~ ( p(10)
        | ~ ! [U: $int] : p($product(2,U)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    ~ ( ! [U: $int] : p($product(2,U))
     => p(10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(6,plain,
    ~ ( p(10)
      | ~ ! [U: $int] : p($product(2,U)) ),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ! [U: $int] : p($product(2,U)),
    inference(or_elim,[status(thm)],[6]) ).

tff(8,plain,
    ! [U: $int] : p($product(2,U)),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [U: $int] : p($product(2,U)),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [U: $int] : p($product(2,U)),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ p(10)
  <=> ~ p(10) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ~ p(10),
    inference(or_elim,[status(thm)],[6]) ).

tff(13,plain,
    ~ p(10),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ( ~ ! [U: $int] : p($product(2,U))
      | p(10) )
  <=> ( ~ ! [U: $int] : p($product(2,U))
      | p(10) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( p($product(2,5))
  <=> p(10) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    ( ( ~ ! [U: $int] : p($product(2,U))
      | p($product(2,5)) )
  <=> ( ~ ! [U: $int] : p($product(2,U))
      | p(10) ) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( ( ~ ! [U: $int] : p($product(2,U))
      | p($product(2,5)) )
  <=> ( ~ ! [U: $int] : p($product(2,U))
      | p(10) ) ),
    inference(transitivity,[status(thm)],[16,14]) ).

tff(18,plain,
    ( ~ ! [U: $int] : p($product(2,U))
    | p($product(2,5)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [U: $int] : p($product(2,U))
    | p(10) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    $false,
    inference(unit_resolution,[status(thm)],[19,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : ARI189_1 : TPTP v8.1.0. Released v5.0.0.
% 0.10/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n015.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 : Mon Aug 29 22:32:20 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.12/0.40  % SZS status Theorem
% 0.12/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------