TSTP Solution File: SET025-8 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n016.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 20 05:04:57 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   38 (  15 unt;   6 typ;   0 def)
%            Number of atoms       :   69 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   65 (  30   ~;  23   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   5   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   33 (  30   !;   0   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
tff(little_set_type,type,
    little_set: $i > $o ).

tff(ordered_pair_type,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(f3_type,type,
    f3: $i > $i ).

tff(a_type,type,
    a: $i ).

tff(f2_type,type,
    f2: $i > $i ).

tff(ordered_pair_predicate_type,type,
    ordered_pair_predicate: $i > $o ).

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

tff(2,axiom,
    ordered_pair_predicate(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).

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

tff(4,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ ordered_pair_predicate(X)
          | ( X = ordered_pair(f2(X),f3(X)) ) )
      <=> ( ~ ordered_pair_predicate(X)
          | ( X = ordered_pair(f2(X),f3(X)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X: $i] :
        ( ~ ordered_pair_predicate(X)
        | ( X = ordered_pair(f2(X),f3(X)) ) )
  <=> ! [X: $i] :
        ( ~ ordered_pair_predicate(X)
        | ( X = ordered_pair(f2(X),f3(X)) ) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [X: $i] :
        ( ~ ordered_pair_predicate(X)
        | ( X = ordered_pair(f2(X),f3(X)) ) )
  <=> ! [X: $i] :
        ( ~ ordered_pair_predicate(X)
        | ( X = ordered_pair(f2(X),f3(X)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [X: $i] :
      ( ~ ordered_pair_predicate(X)
      | ( X = ordered_pair(f2(X),f3(X)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).

tff(8,plain,
    ! [X: $i] :
      ( ~ ordered_pair_predicate(X)
      | ( X = ordered_pair(f2(X),f3(X)) ) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [X: $i] :
      ( ~ ordered_pair_predicate(X)
      | ( X = ordered_pair(f2(X),f3(X)) ) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [X: $i] :
      ( ~ ordered_pair_predicate(X)
      | ( X = ordered_pair(f2(X),f3(X)) ) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [X: $i] :
            ( ~ ordered_pair_predicate(X)
            | ( X = ordered_pair(f2(X),f3(X)) ) )
      | ~ ordered_pair_predicate(a)
      | ( a = ordered_pair(f2(a),f3(a)) ) )
  <=> ( ~ ! [X: $i] :
            ( ~ ordered_pair_predicate(X)
            | ( X = ordered_pair(f2(X),f3(X)) ) )
      | ~ ordered_pair_predicate(a)
      | ( a = ordered_pair(f2(a),f3(a)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [X: $i] :
          ( ~ ordered_pair_predicate(X)
          | ( X = ordered_pair(f2(X),f3(X)) ) )
    | ~ ordered_pair_predicate(a)
    | ( a = ordered_pair(f2(a),f3(a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [X: $i] :
          ( ~ ordered_pair_predicate(X)
          | ( X = ordered_pair(f2(X),f3(X)) ) )
    | ~ ordered_pair_predicate(a)
    | ( a = ordered_pair(f2(a),f3(a)) ) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    a = ordered_pair(f2(a),f3(a)),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ordered_pair(f2(a),f3(a)) = a,
    inference(symmetry,[status(thm)],[14]) ).

tff(16,plain,
    ( little_set(ordered_pair(f2(a),f3(a)))
  <=> little_set(a) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( little_set(a)
  <=> little_set(ordered_pair(f2(a),f3(a))) ),
    inference(symmetry,[status(thm)],[16]) ).

tff(18,plain,
    ( ~ little_set(a)
  <=> ~ little_set(ordered_pair(f2(a),f3(a))) ),
    inference(monotonicity,[status(thm)],[17]) ).

tff(19,plain,
    ( ~ little_set(a)
  <=> ~ little_set(a) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,axiom,
    ~ little_set(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_predicate_is_small) ).

tff(21,plain,
    ~ little_set(a),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ~ little_set(ordered_pair(f2(a),f3(a))),
    inference(modus_ponens,[status(thm)],[21,18]) ).

tff(23,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( little_set(ordered_pair(X,Y))
      <=> little_set(ordered_pair(X,Y)) )),
    inference(bind,[status(th)],]) ).

tff(24,plain,
    ( ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y))
  <=> ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y)) ),
    inference(quant_intro,[status(thm)],[23]) ).

tff(25,plain,
    ( ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y))
  <=> ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y)) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,axiom,
    ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pairs_are_small1) ).

tff(27,plain,
    ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y)),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y)),
    inference(skolemize,[status(sab)],[27]) ).

tff(29,plain,
    ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y)),
    inference(modus_ponens,[status(thm)],[28,24]) ).

tff(30,plain,
    ( ~ ! [Y: $i,X: $i] : little_set(ordered_pair(X,Y))
    | little_set(ordered_pair(f2(a),f3(a))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    little_set(ordered_pair(f2(a),f3(a))),
    inference(unit_resolution,[status(thm)],[30,29]) ).

tff(32,plain,
    $false,
    inference(unit_resolution,[status(thm)],[31,22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n016.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 : Sat Sep  3 01:45:06 EDT 2022
% 0.12/0.33  % 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.
% 0.20/0.43  % SZS status Unsatisfiable
% 0.20/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------