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 v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.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 0.12s 0.39s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   80 (  22 unt;  10 typ;   0 def)
%            Number of atoms       :  602 (   0 equ)
%            Maximal formula atoms :   24 (   8 avg)
%            Number of connectives :  890 ( 399   ~; 380   |;  20   &)
%                                         (  53 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   41 (  41 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   7   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :  167 ( 153   !;   0   ?; 167   :)

% Comments : 
%------------------------------------------------------------------------------
tff(teaches_type,type,
    teaches: ( $i * $i ) > $o ).

tff(csc410_type,type,
    csc410: $i ).

tff(taughtby_type,type,
    taughtby: ( $i * $i ) > $o ).

tff(michael_type,type,
    michael: $i ).

tff(professor_type,type,
    professor: $i > $o ).

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

tff(student_type,type,
    student: $i > $o ).

tff(course_type,type,
    course: $i > $o ).

tff(coordinatorof_type,type,
    coordinatorof: $i > $i ).

tff(victor_type,type,
    victor: $i ).

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

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

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

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

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

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

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

tff(8,plain,
    ^ [X: $i,Y: $i] :
      rewrite(
        ( ( ~ course(Y)
          | ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) )
          | ~ enrolled(X,Y)
          | ~ student(X) )
      <=> ( ~ course(Y)
          | ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) )
          | ~ enrolled(X,Y)
          | ~ student(X) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ course(Y)
        | ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ student(X) )
  <=> ! [X: $i,Y: $i] :
        ( ~ course(Y)
        | ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ student(X) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ course(Y)
        | ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ student(X) )
  <=> ! [X: $i,Y: $i] :
        ( ~ course(Y)
        | ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ student(X) ) ),
    inference(transitivity,[status(thm)],[9,7]) ).

tff(11,plain,
    ^ [X: $i,Y: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( student(X)
                  & course(Y) )
              <=> ~ ( ~ course(Y)
                    | ~ student(X) ) )),
              ( ~ ( student(X)
                  & course(Y) )
            <=> ~ ~ ( ~ course(Y)
                    | ~ student(X) ) )),
            rewrite(
              ( ~ ~ ( ~ course(Y)
                    | ~ student(X) )
            <=> ( ~ course(Y)
                | ~ student(X) ) )),
            ( ~ ( student(X)
                & course(Y) )
          <=> ( ~ course(Y)
              | ~ student(X) ) )),
          ( ( ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) )
            | ~ enrolled(X,Y)
            | ~ ( student(X)
                & course(Y) ) )
        <=> ( ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) )
            | ~ enrolled(X,Y)
            | ~ course(Y)
            | ~ student(X) ) )),
        rewrite(
          ( ( ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) )
            | ~ enrolled(X,Y)
            | ~ course(Y)
            | ~ student(X) )
        <=> ( ~ course(Y)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) )
            | ~ enrolled(X,Y)
            | ~ student(X) ) )),
        ( ( ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) )
          | ~ enrolled(X,Y)
          | ~ ( student(X)
              & course(Y) ) )
      <=> ( ~ course(Y)
          | ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) )
          | ~ enrolled(X,Y)
          | ~ student(X) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [X: $i,Y: $i] :
        ( ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ ( student(X)
            & course(Y) ) )
  <=> ! [X: $i,Y: $i] :
        ( ~ course(Y)
        | ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ student(X) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [X: $i,Y: $i] :
        ( ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ ( student(X)
            & course(Y) ) )
  <=> ! [X: $i,Y: $i] :
        ( ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ ( student(X)
            & course(Y) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ^ [X: $i,Y: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              quant_intro(
                proof_bind(
                  ^ [Z: $i] :
                    trans(
                      monotonicity(
                        rewrite(
                          ( ( teaches(Z,Y)
                           => taughtby(X,Z) )
                        <=> ( ~ teaches(Z,Y)
                            | taughtby(X,Z) ) )),
                        ( ( professor(Z)
                         => ( teaches(Z,Y)
                           => taughtby(X,Z) ) )
                      <=> ( professor(Z)
                         => ( ~ teaches(Z,Y)
                            | taughtby(X,Z) ) ) )),
                      rewrite(
                        ( ( professor(Z)
                         => ( ~ teaches(Z,Y)
                            | taughtby(X,Z) ) )
                      <=> ( taughtby(X,Z)
                          | ~ professor(Z)
                          | ~ teaches(Z,Y) ) )),
                      ( ( professor(Z)
                       => ( teaches(Z,Y)
                         => taughtby(X,Z) ) )
                    <=> ( taughtby(X,Z)
                        | ~ professor(Z)
                        | ~ teaches(Z,Y) ) ))),
                ( ! [Z: $i] :
                    ( professor(Z)
                   => ( teaches(Z,Y)
                     => taughtby(X,Z) ) )
              <=> ! [Z: $i] :
                    ( taughtby(X,Z)
                    | ~ professor(Z)
                    | ~ teaches(Z,Y) ) )),
              ( ( enrolled(X,Y)
               => ! [Z: $i] :
                    ( professor(Z)
                   => ( teaches(Z,Y)
                     => taughtby(X,Z) ) ) )
            <=> ( enrolled(X,Y)
               => ! [Z: $i] :
                    ( taughtby(X,Z)
                    | ~ professor(Z)
                    | ~ teaches(Z,Y) ) ) )),
            rewrite(
              ( ( enrolled(X,Y)
               => ! [Z: $i] :
                    ( taughtby(X,Z)
                    | ~ professor(Z)
                    | ~ teaches(Z,Y) ) )
            <=> ( ~ enrolled(X,Y)
                | ! [Z: $i] :
                    ( taughtby(X,Z)
                    | ~ professor(Z)
                    | ~ teaches(Z,Y) ) ) )),
            ( ( enrolled(X,Y)
             => ! [Z: $i] :
                  ( professor(Z)
                 => ( teaches(Z,Y)
                   => taughtby(X,Z) ) ) )
          <=> ( ~ enrolled(X,Y)
              | ! [Z: $i] :
                  ( taughtby(X,Z)
                  | ~ professor(Z)
                  | ~ teaches(Z,Y) ) ) )),
          ( ( ( student(X)
              & course(Y) )
           => ( enrolled(X,Y)
             => ! [Z: $i] :
                  ( professor(Z)
                 => ( teaches(Z,Y)
                   => taughtby(X,Z) ) ) ) )
        <=> ( ( student(X)
              & course(Y) )
           => ( ~ enrolled(X,Y)
              | ! [Z: $i] :
                  ( taughtby(X,Z)
                  | ~ professor(Z)
                  | ~ teaches(Z,Y) ) ) ) )),
        rewrite(
          ( ( ( student(X)
              & course(Y) )
           => ( ~ enrolled(X,Y)
              | ! [Z: $i] :
                  ( taughtby(X,Z)
                  | ~ professor(Z)
                  | ~ teaches(Z,Y) ) ) )
        <=> ( ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) )
            | ~ enrolled(X,Y)
            | ~ ( student(X)
                & course(Y) ) ) )),
        ( ( ( student(X)
            & course(Y) )
         => ( enrolled(X,Y)
           => ! [Z: $i] :
                ( professor(Z)
               => ( teaches(Z,Y)
                 => taughtby(X,Z) ) ) ) )
      <=> ( ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) )
          | ~ enrolled(X,Y)
          | ~ ( student(X)
              & course(Y) ) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [X: $i,Y: $i] :
        ( ( student(X)
          & course(Y) )
       => ( enrolled(X,Y)
         => ! [Z: $i] :
              ( professor(Z)
             => ( teaches(Z,Y)
               => taughtby(X,Z) ) ) ) )
  <=> ! [X: $i,Y: $i] :
        ( ! [Z: $i] :
            ( taughtby(X,Z)
            | ~ professor(Z)
            | ~ teaches(Z,Y) )
        | ~ enrolled(X,Y)
        | ~ ( student(X)
            & course(Y) ) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,axiom,
    ! [X: $i,Y: $i] :
      ( ( student(X)
        & course(Y) )
     => ( enrolled(X,Y)
       => ! [Z: $i] :
            ( professor(Z)
           => ( teaches(Z,Y)
             => taughtby(X,Z) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',student_enrolled_taught) ).

tff(17,plain,
    ! [X: $i,Y: $i] :
      ( ! [Z: $i] :
          ( taughtby(X,Z)
          | ~ professor(Z)
          | ~ teaches(Z,Y) )
      | ~ enrolled(X,Y)
      | ~ ( student(X)
          & course(Y) ) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [X: $i,Y: $i] :
      ( ! [Z: $i] :
          ( taughtby(X,Z)
          | ~ professor(Z)
          | ~ teaches(Z,Y) )
      | ~ enrolled(X,Y)
      | ~ ( student(X)
          & course(Y) ) ),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    ! [X: $i,Y: $i] :
      ( ! [Z: $i] :
          ( taughtby(X,Z)
          | ~ professor(Z)
          | ~ teaches(Z,Y) )
      | ~ enrolled(X,Y)
      | ~ ( student(X)
          & course(Y) ) ),
    inference(skolemize,[status(sab)],[18]) ).

tff(20,plain,
    ! [X: $i,Y: $i] :
      ( ~ course(Y)
      | ! [Z: $i] :
          ( taughtby(X,Z)
          | ~ professor(Z)
          | ~ teaches(Z,Y) )
      | ~ enrolled(X,Y)
      | ~ student(X) ),
    inference(modus_ponens,[status(thm)],[19,12]) ).

tff(21,plain,
    ! [X: $i,Y: $i] :
      ( ~ course(Y)
      | ! [Z: $i] :
          ( taughtby(X,Z)
          | ~ professor(Z)
          | ~ teaches(Z,Y) )
      | ~ enrolled(X,Y)
      | ~ student(X) ),
    inference(modus_ponens,[status(thm)],[20,10]) ).

tff(22,plain,
    ! [X: $i,Y: $i] :
      ( ~ course(Y)
      | ~ enrolled(X,Y)
      | ~ student(X)
      | ! [Z: $i] :
          ( taughtby(X,Z)
          | ~ professor(Z)
          | ~ teaches(Z,Y) ) ),
    inference(modus_ponens,[status(thm)],[21,5]) ).

tff(23,plain,
    ( course(csc410)
  <=> course(csc410) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    course(csc410),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',csc410_type) ).

tff(25,plain,
    course(csc410),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ( student(michael)
  <=> student(michael) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    student(michael),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',michael_type) ).

tff(28,plain,
    student(michael),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ course(Y)
            | ~ enrolled(X,Y)
            | ~ student(X)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) ) )
      | ~ course(csc410)
      | ~ student(michael)
      | ~ enrolled(michael,csc410)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ course(Y)
            | ~ enrolled(X,Y)
            | ~ student(X)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) ) )
      | ~ course(csc410)
      | ~ student(michael)
      | ~ enrolled(michael,csc410)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( ~ course(csc410)
      | ~ enrolled(michael,csc410)
      | ~ student(michael)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) )
  <=> ( ~ course(csc410)
      | ~ student(michael)
      | ~ enrolled(michael,csc410)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ^ [Z: $i] :
      rewrite(
        ( ( taughtby(michael,Z)
          | ~ professor(Z)
          | ~ teaches(Z,csc410) )
      <=> ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [Z: $i] :
        ( taughtby(michael,Z)
        | ~ professor(Z)
        | ~ teaches(Z,csc410) )
  <=> ! [Z: $i] :
        ( ~ professor(Z)
        | taughtby(michael,Z)
        | ~ teaches(Z,csc410) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ( ( ~ course(csc410)
      | ~ enrolled(michael,csc410)
      | ~ student(michael)
      | ! [Z: $i] :
          ( taughtby(michael,Z)
          | ~ professor(Z)
          | ~ teaches(Z,csc410) ) )
  <=> ( ~ course(csc410)
      | ~ enrolled(michael,csc410)
      | ~ student(michael)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) ) ),
    inference(monotonicity,[status(thm)],[32]) ).

tff(34,plain,
    ( ( ~ course(csc410)
      | ~ enrolled(michael,csc410)
      | ~ student(michael)
      | ! [Z: $i] :
          ( taughtby(michael,Z)
          | ~ professor(Z)
          | ~ teaches(Z,csc410) ) )
  <=> ( ~ course(csc410)
      | ~ student(michael)
      | ~ enrolled(michael,csc410)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) ) ),
    inference(transitivity,[status(thm)],[33,30]) ).

tff(35,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ course(Y)
            | ~ enrolled(X,Y)
            | ~ student(X)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) ) )
      | ~ course(csc410)
      | ~ enrolled(michael,csc410)
      | ~ student(michael)
      | ! [Z: $i] :
          ( taughtby(michael,Z)
          | ~ professor(Z)
          | ~ teaches(Z,csc410) ) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ course(Y)
            | ~ enrolled(X,Y)
            | ~ student(X)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) ) )
      | ~ course(csc410)
      | ~ student(michael)
      | ~ enrolled(michael,csc410)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) ) ),
    inference(monotonicity,[status(thm)],[34]) ).

tff(36,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ course(Y)
            | ~ enrolled(X,Y)
            | ~ student(X)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) ) )
      | ~ course(csc410)
      | ~ enrolled(michael,csc410)
      | ~ student(michael)
      | ! [Z: $i] :
          ( taughtby(michael,Z)
          | ~ professor(Z)
          | ~ teaches(Z,csc410) ) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ course(Y)
            | ~ enrolled(X,Y)
            | ~ student(X)
            | ! [Z: $i] :
                ( taughtby(X,Z)
                | ~ professor(Z)
                | ~ teaches(Z,Y) ) )
      | ~ course(csc410)
      | ~ student(michael)
      | ~ enrolled(michael,csc410)
      | ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) ) ) ),
    inference(transitivity,[status(thm)],[35,29]) ).

tff(37,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ course(Y)
          | ~ enrolled(X,Y)
          | ~ student(X)
          | ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) ) )
    | ~ course(csc410)
    | ~ enrolled(michael,csc410)
    | ~ student(michael)
    | ! [Z: $i] :
        ( taughtby(michael,Z)
        | ~ professor(Z)
        | ~ teaches(Z,csc410) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ course(Y)
          | ~ enrolled(X,Y)
          | ~ student(X)
          | ! [Z: $i] :
              ( taughtby(X,Z)
              | ~ professor(Z)
              | ~ teaches(Z,Y) ) )
    | ~ course(csc410)
    | ~ student(michael)
    | ~ enrolled(michael,csc410)
    | ! [Z: $i] :
        ( ~ professor(Z)
        | taughtby(michael,Z)
        | ~ teaches(Z,csc410) ) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    ! [Z: $i] :
      ( ~ professor(Z)
      | taughtby(michael,Z)
      | ~ teaches(Z,csc410) ),
    inference(unit_resolution,[status(thm)],[38,28,25,22,3]) ).

tff(40,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ course(X)
          | teaches(coordinatorof(X),X) )
      <=> ( ~ course(X)
          | teaches(coordinatorof(X),X) ) )),
    inference(bind,[status(th)],]) ).

tff(41,plain,
    ( ! [X: $i] :
        ( ~ course(X)
        | teaches(coordinatorof(X),X) )
  <=> ! [X: $i] :
        ( ~ course(X)
        | teaches(coordinatorof(X),X) ) ),
    inference(quant_intro,[status(thm)],[40]) ).

tff(42,plain,
    ( ! [X: $i] :
        ( ~ course(X)
        | teaches(coordinatorof(X),X) )
  <=> ! [X: $i] :
        ( ~ course(X)
        | teaches(coordinatorof(X),X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ^ [X: $i] :
      rewrite(
        ( ( course(X)
         => teaches(coordinatorof(X),X) )
      <=> ( ~ course(X)
          | teaches(coordinatorof(X),X) ) )),
    inference(bind,[status(th)],]) ).

tff(44,plain,
    ( ! [X: $i] :
        ( course(X)
       => teaches(coordinatorof(X),X) )
  <=> ! [X: $i] :
        ( ~ course(X)
        | teaches(coordinatorof(X),X) ) ),
    inference(quant_intro,[status(thm)],[43]) ).

tff(45,axiom,
    ! [X: $i] :
      ( course(X)
     => teaches(coordinatorof(X),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',coordinator_teaches) ).

tff(46,plain,
    ! [X: $i] :
      ( ~ course(X)
      | teaches(coordinatorof(X),X) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ! [X: $i] :
      ( ~ course(X)
      | teaches(coordinatorof(X),X) ),
    inference(modus_ponens,[status(thm)],[46,42]) ).

tff(48,plain,
    ! [X: $i] :
      ( ~ course(X)
      | teaches(coordinatorof(X),X) ),
    inference(skolemize,[status(sab)],[47]) ).

tff(49,plain,
    ! [X: $i] :
      ( ~ course(X)
      | teaches(coordinatorof(X),X) ),
    inference(modus_ponens,[status(thm)],[48,41]) ).

tff(50,plain,
    ( ( ~ ! [X: $i] :
            ( ~ course(X)
            | teaches(coordinatorof(X),X) )
      | ~ course(csc410)
      | teaches(coordinatorof(csc410),csc410) )
  <=> ( ~ ! [X: $i] :
            ( ~ course(X)
            | teaches(coordinatorof(X),X) )
      | ~ course(csc410)
      | teaches(coordinatorof(csc410),csc410) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ( ~ ! [X: $i] :
          ( ~ course(X)
          | teaches(coordinatorof(X),X) )
    | ~ course(csc410)
    | teaches(coordinatorof(csc410),csc410) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [X: $i] :
          ( ~ course(X)
          | teaches(coordinatorof(X),X) )
    | ~ course(csc410)
    | teaches(coordinatorof(csc410),csc410) ),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    teaches(coordinatorof(csc410),csc410),
    inference(unit_resolution,[status(thm)],[52,25,49]) ).

tff(54,plain,
    ( ~ taughtby(michael,victor)
  <=> ~ taughtby(michael,coordinatorof(csc410)) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ~ taughtby(michael,victor)
  <=> ~ taughtby(michael,victor) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,axiom,
    ~ taughtby(michael,victor),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',teaching_conjecture) ).

tff(57,plain,
    ~ taughtby(michael,victor),
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ~ taughtby(michael,coordinatorof(csc410)),
    inference(modus_ponens,[status(thm)],[57,54]) ).

tff(59,plain,
    ( professor(victor)
  <=> professor(coordinatorof(csc410)) ),
    inference(rewrite,[status(thm)],]) ).

tff(60,plain,
    ( professor(victor)
  <=> professor(victor) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,axiom,
    professor(victor),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',victor_type) ).

tff(62,plain,
    professor(victor),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    professor(coordinatorof(csc410)),
    inference(modus_ponens,[status(thm)],[62,59]) ).

tff(64,plain,
    ( ( ~ ! [Z: $i] :
            ( ~ professor(Z)
            | taughtby(michael,Z)
            | ~ teaches(Z,csc410) )
      | taughtby(michael,coordinatorof(csc410))
      | ~ professor(coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) )
  <=> ( ~ ! [Z: $i] :
            ( ~ professor(Z)
            | taughtby(michael,Z)
            | ~ teaches(Z,csc410) )
      | taughtby(michael,coordinatorof(csc410))
      | ~ professor(coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ( ( ~ professor(coordinatorof(csc410))
      | taughtby(michael,coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) )
  <=> ( taughtby(michael,coordinatorof(csc410))
      | ~ professor(coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(66,plain,
    ( ( ~ ! [Z: $i] :
            ( ~ professor(Z)
            | taughtby(michael,Z)
            | ~ teaches(Z,csc410) )
      | ~ professor(coordinatorof(csc410))
      | taughtby(michael,coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) )
  <=> ( ~ ! [Z: $i] :
            ( ~ professor(Z)
            | taughtby(michael,Z)
            | ~ teaches(Z,csc410) )
      | taughtby(michael,coordinatorof(csc410))
      | ~ professor(coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) ) ),
    inference(monotonicity,[status(thm)],[65]) ).

tff(67,plain,
    ( ( ~ ! [Z: $i] :
            ( ~ professor(Z)
            | taughtby(michael,Z)
            | ~ teaches(Z,csc410) )
      | ~ professor(coordinatorof(csc410))
      | taughtby(michael,coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) )
  <=> ( ~ ! [Z: $i] :
            ( ~ professor(Z)
            | taughtby(michael,Z)
            | ~ teaches(Z,csc410) )
      | taughtby(michael,coordinatorof(csc410))
      | ~ professor(coordinatorof(csc410))
      | ~ teaches(coordinatorof(csc410),csc410) ) ),
    inference(transitivity,[status(thm)],[66,64]) ).

tff(68,plain,
    ( ~ ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) )
    | ~ professor(coordinatorof(csc410))
    | taughtby(michael,coordinatorof(csc410))
    | ~ teaches(coordinatorof(csc410),csc410) ),
    inference(quant_inst,[status(thm)],]) ).

tff(69,plain,
    ( ~ ! [Z: $i] :
          ( ~ professor(Z)
          | taughtby(michael,Z)
          | ~ teaches(Z,csc410) )
    | taughtby(michael,coordinatorof(csc410))
    | ~ professor(coordinatorof(csc410))
    | ~ teaches(coordinatorof(csc410),csc410) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    $false,
    inference(unit_resolution,[status(thm)],[69,63,58,53,39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ131+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Sep  2 19:03:04 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35  Usage: tptp [options] [-file:]file
% 0.12/0.35    -h, -?       prints this message.
% 0.12/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.35    -m, -model   generate model.
% 0.12/0.35    -p, -proof   generate proof.
% 0.12/0.35    -c, -core    generate unsat core of named formulas.
% 0.12/0.35    -st, -statistics display statistics.
% 0.12/0.35    -t:timeout   set timeout (in second).
% 0.12/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35    -<param>:<value> configuration parameter and value.
% 0.12/0.35    -o:<output-file> file to place output in.
% 0.12/0.39  % SZS status Theorem
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------