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
%------------------------------------------------------------------------------