%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ131_1 : TPTP v9.0.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:23:28 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 167 ( 5 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 191 ( 81 ~; 76 |; 0 &)
% ( 22 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 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(teaches_type,type,
teaches: ( professor * course ) > $o ).
tff(csc410_type,type,
csc410: course ).
tff(victor_type,type,
victor: professor ).
tff(coordinatorof_type,type,
coordinatorof: course > professor ).
tff(taughtby_type,type,
taughtby: ( student * professor ) > $o ).
tff(michael_type,type,
michael: student ).
tff(enrolled_type,type,
enrolled: ( student * course ) > $o ).
tff(1,plain,
( ( coordinatorof(csc410) = victor )
<=> ( coordinatorof(csc410) = victor ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
coordinatorof(csc410) = victor,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',victor_coordinator_csc410) ).
tff(3,plain,
coordinatorof(csc410) = victor,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
victor = coordinatorof(csc410),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( teaches(victor,csc410)
<=> teaches(coordinatorof(csc410),csc410) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( teaches(coordinatorof(csc410),csc410)
<=> teaches(victor,csc410) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [X: course] :
refl(( teaches(coordinatorof(X),X)
<=> teaches(coordinatorof(X),X) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: course] : teaches(coordinatorof(X),X)
<=> ! [X: course] : teaches(coordinatorof(X),X) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: course] : teaches(coordinatorof(X),X)
<=> ! [X: course] : teaches(coordinatorof(X),X) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [X: course] : teaches(coordinatorof(X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coordinator_teaches) ).
tff(11,plain,
! [X: course] : teaches(coordinatorof(X),X),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X: course] : teaches(coordinatorof(X),X),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: course] : teaches(coordinatorof(X),X),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [X: course] : teaches(coordinatorof(X),X)
| teaches(coordinatorof(csc410),csc410) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
teaches(coordinatorof(csc410),csc410),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
teaches(victor,csc410),
inference(modus_ponens,[status(thm)],[15,6]) ).
tff(17,plain,
( enrolled(michael,csc410)
<=> enrolled(michael,csc410) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
enrolled(michael,csc410),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',michael_enrolled_csc410) ).
tff(19,plain,
enrolled(michael,csc410),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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)],[23,21]) ).
tff(25,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(26,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(27,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)],[26]) ).
tff(28,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(29,plain,
! [X: student,Y: course] :
( ~ enrolled(X,Y)
| ! [Z: professor] :
( ~ teaches(Z,Y)
| taughtby(X,Z) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [X: student,Y: course] :
( ~ enrolled(X,Y)
| ! [Z: professor] :
( ~ teaches(Z,Y)
| taughtby(X,Z) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [X: student,Y: course] :
( ~ enrolled(X,Y)
| ! [Z: professor] :
( ~ teaches(Z,Y)
| taughtby(X,Z) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: student,Y: course] :
( ~ enrolled(X,Y)
| ! [Z: professor] :
( ~ teaches(Z,Y)
| taughtby(X,Z) ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,plain,
! [Z: professor] :
( ~ teaches(Z,csc410)
| taughtby(michael,Z) ),
inference(unit_resolution,[status(thm)],[35,32,19]) ).
tff(37,plain,
( ~ taughtby(michael,victor)
<=> ~ taughtby(michael,victor) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
~ taughtby(michael,victor),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',teaching_conjecture) ).
tff(39,plain,
~ taughtby(michael,victor),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [Z: professor] :
( ~ teaches(Z,csc410)
| taughtby(michael,Z) )
| ~ teaches(victor,csc410)
| taughtby(michael,victor) )
<=> ( ~ ! [Z: professor] :
( ~ teaches(Z,csc410)
| taughtby(michael,Z) )
| ~ teaches(victor,csc410)
| taughtby(michael,victor) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Z: professor] :
( ~ teaches(Z,csc410)
| taughtby(michael,Z) )
| ~ teaches(victor,csc410)
| taughtby(michael,victor) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Z: professor] :
( ~ teaches(Z,csc410)
| taughtby(michael,Z) )
| ~ teaches(victor,csc410)
| taughtby(michael,victor) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ teaches(victor,csc410),
inference(unit_resolution,[status(thm)],[42,39,36]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : PUZ131_1 : TPTP v9.0.0. Released v5.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:47:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------