TSTP Solution File: PUZ131_1 by Z3---4.8.9.0
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- 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
%------------------------------------------------------------------------------