TSTP Solution File: PUZ131_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : PUZ131_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n013.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 14:11:32 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   45 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :  159 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  191 (  83   ~;  76   |;   0   &)
%                                         (  20 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   13 (  13 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   4 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :   95 (  87   !;   0   ?;  95   :)

% Comments : 
%------------------------------------------------------------------------------
tff(taughtby_type,type,
    taughtby: ( student * professor ) > $o ).

tff(michael_type,type,
    michael: student ).

tff(teaches_type,type,
    teaches: ( professor * course ) > $o ).

tff(csc410_type,type,
    csc410: course ).

tff(enrolled_type,type,
    enrolled: ( student * course ) > $o ).

tff(coordinatorof_type,type,
    coordinatorof: course > professor ).

tff(victor_type,type,
    victor: professor ).

tff(1,plain,
    ( enrolled(michael,csc410)
  <=> enrolled(michael,csc410) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    enrolled(michael,csc410),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',michael_enrolled_csc410_axiom) ).

tff(3,plain,
    enrolled(michael,csc410),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [X: student,Y: course] :
      refl(
        ( ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) )
      <=> ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) )
  <=> ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ^ [X: student,Y: course] :
      rewrite(
        ( ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) )
      <=> ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) ) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) )
  <=> ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) ) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ( ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) )
  <=> ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) ) ),
    inference(transitivity,[status(thm)],[7,5]) ).

tff(9,plain,
    ( ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) )
  <=> ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,plain,
    ^ [X: student,Y: course] :
      trans(
        monotonicity(
          quant_intro(
            proof_bind(
              ^ [Z: professor] :
                rewrite(
                  ( ( teaches(Z,Y)
                   => taughtby(X,Z) )
                <=> ( ~ teaches(Z,Y)
                    | taughtby(X,Z) ) ))),
            ( ! [Z: professor] :
                ( teaches(Z,Y)
               => taughtby(X,Z) )
          <=> ! [Z: professor] :
                ( ~ teaches(Z,Y)
                | taughtby(X,Z) ) )),
          ( ( enrolled(X,Y)
           => ! [Z: professor] :
                ( teaches(Z,Y)
               => taughtby(X,Z) ) )
        <=> ( enrolled(X,Y)
           => ! [Z: professor] :
                ( ~ teaches(Z,Y)
                | taughtby(X,Z) ) ) )),
        rewrite(
          ( ( enrolled(X,Y)
           => ! [Z: professor] :
                ( ~ teaches(Z,Y)
                | taughtby(X,Z) ) )
        <=> ( ~ enrolled(X,Y)
            | ! [Z: professor] :
                ( ~ teaches(Z,Y)
                | taughtby(X,Z) ) ) )),
        ( ( enrolled(X,Y)
         => ! [Z: professor] :
              ( teaches(Z,Y)
             => taughtby(X,Z) ) )
      <=> ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X: student,Y: course] :
        ( enrolled(X,Y)
       => ! [Z: professor] :
            ( teaches(Z,Y)
           => taughtby(X,Z) ) )
  <=> ! [X: student,Y: course] :
        ( ~ enrolled(X,Y)
        | ! [Z: professor] :
            ( ~ teaches(Z,Y)
            | taughtby(X,Z) ) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,axiom,
    ! [X: student,Y: course] :
      ( enrolled(X,Y)
     => ! [Z: professor] :
          ( teaches(Z,Y)
         => taughtby(X,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',student_enrolled_taught) ).

tff(13,plain,
    ! [X: student,Y: course] :
      ( ~ enrolled(X,Y)
      | ! [Z: professor] :
          ( ~ teaches(Z,Y)
          | taughtby(X,Z) ) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ! [X: student,Y: course] :
      ( ~ enrolled(X,Y)
      | ! [Z: professor] :
          ( ~ teaches(Z,Y)
          | taughtby(X,Z) ) ),
    inference(modus_ponens,[status(thm)],[13,9]) ).

tff(15,plain,
    ! [X: student,Y: course] :
      ( ~ enrolled(X,Y)
      | ! [Z: professor] :
          ( ~ teaches(Z,Y)
          | taughtby(X,Z) ) ),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [X: student,Y: course] :
      ( ~ enrolled(X,Y)
      | ! [Z: professor] :
          ( ~ teaches(Z,Y)
          | taughtby(X,Z) ) ),
    inference(modus_ponens,[status(thm)],[15,8]) ).

tff(17,plain,
    ( ( ~ ! [X: student,Y: course] :
            ( ~ enrolled(X,Y)
            | ! [Z: professor] :
                ( ~ teaches(Z,Y)
                | taughtby(X,Z) ) )
      | ~ enrolled(michael,csc410)
      | ! [Z: professor] :
          ( ~ teaches(Z,csc410)
          | taughtby(michael,Z) ) )
  <=> ( ~ ! [X: student,Y: course] :
            ( ~ enrolled(X,Y)
            | ! [Z: professor] :
                ( ~ teaches(Z,Y)
                | taughtby(X,Z) ) )
      | ~ enrolled(michael,csc410)
      | ! [Z: professor] :
          ( ~ teaches(Z,csc410)
          | taughtby(michael,Z) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [X: student,Y: course] :
          ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) )
    | ~ enrolled(michael,csc410)
    | ! [Z: professor] :
        ( ~ teaches(Z,csc410)
        | taughtby(michael,Z) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [X: student,Y: course] :
          ( ~ enrolled(X,Y)
          | ! [Z: professor] :
              ( ~ teaches(Z,Y)
              | taughtby(X,Z) ) )
    | ~ enrolled(michael,csc410)
    | ! [Z: professor] :
        ( ~ teaches(Z,csc410)
        | taughtby(michael,Z) ) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [Z: professor] :
      ( ~ teaches(Z,csc410)
      | taughtby(michael,Z) ),
    inference(unit_resolution,[status(thm)],[19,16,3]) ).

tff(21,plain,
    ^ [X: course] :
      refl(
        ( teaches(coordinatorof(X),X)
      <=> teaches(coordinatorof(X),X) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [X: course] : teaches(coordinatorof(X),X)
  <=> ! [X: course] : teaches(coordinatorof(X),X) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [X: course] : teaches(coordinatorof(X),X)
  <=> ! [X: course] : teaches(coordinatorof(X),X) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ! [X: course] : teaches(coordinatorof(X),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coordinator_teaches) ).

tff(25,plain,
    ! [X: course] : teaches(coordinatorof(X),X),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [X: course] : teaches(coordinatorof(X),X),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [X: course] : teaches(coordinatorof(X),X),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ( ~ ! [X: course] : teaches(coordinatorof(X),X)
    | teaches(coordinatorof(csc410),csc410) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    teaches(coordinatorof(csc410),csc410),
    inference(unit_resolution,[status(thm)],[28,27]) ).

tff(30,plain,
    ( ~ taughtby(michael,victor)
  <=> ~ taughtby(michael,coordinatorof(csc410)) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ~ taughtby(michael,victor)
  <=> ~ taughtby(michael,victor) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ~ taughtby(michael,victor),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',teaching_conjecture) ).

tff(33,plain,
    ~ taughtby(michael,victor),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ~ taughtby(michael,coordinatorof(csc410)),
    inference(modus_ponens,[status(thm)],[33,30]) ).

tff(35,plain,
    ( ( ~ ! [Z: professor] :
            ( ~ teaches(Z,csc410)
            | taughtby(michael,Z) )
      | ~ teaches(coordinatorof(csc410),csc410)
      | taughtby(michael,coordinatorof(csc410)) )
  <=> ( ~ ! [Z: professor] :
            ( ~ teaches(Z,csc410)
            | taughtby(michael,Z) )
      | ~ teaches(coordinatorof(csc410),csc410)
      | taughtby(michael,coordinatorof(csc410)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ~ ! [Z: professor] :
          ( ~ teaches(Z,csc410)
          | taughtby(michael,Z) )
    | ~ teaches(coordinatorof(csc410),csc410)
    | taughtby(michael,coordinatorof(csc410)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    ( ~ ! [Z: professor] :
          ( ~ teaches(Z,csc410)
          | taughtby(michael,Z) )
    | ~ teaches(coordinatorof(csc410),csc410)
    | taughtby(michael,coordinatorof(csc410)) ),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    $false,
    inference(unit_resolution,[status(thm)],[37,34,29,20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : PUZ131_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n013.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri Sep  2 19:00:02 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------