%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ131-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 82 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 104 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 11 ~; 7 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 82 ( 75 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(taughtby_type,type,
taughtby: ( $i * $i ) > $i ).
tff(victor_type,type,
victor: $i ).
tff(michael_type,type,
michael: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(student_type,type,
student: $i > $i ).
tff(professor_type,type,
professor: $i > $i ).
tff(course_type,type,
course: $i > $i ).
tff(csc410_type,type,
csc410: $i ).
tff(enrolled_type,type,
enrolled: ( $i * $i ) > $i ).
tff(teaches_type,type,
teaches: ( $i * $i ) > $i ).
tff(sK5_course_type_A_type,type,
sK5_course_type_A: $i ).
tff(coordinatorof_type,type,
coordinatorof: $i > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true )
<=> ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true )
<=> ! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true )
<=> ! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',student_enrolled_taught) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( ifeq(teaches(Z,Y),true,ifeq(enrolled(X,Y),true,ifeq(course(Y),true,ifeq(professor(Z),true,ifeq(student(X),true,taughtby(X,Z),true),true),true),true),true) = true )
| ( ifeq(teaches(victor,csc410),true,ifeq(enrolled(michael,csc410),true,ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(teaches(victor,csc410),true,ifeq(enrolled(michael,csc410),true,ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( course(sK5_course_type_A) = true )
<=> ( course(sK5_course_type_A) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
course(sK5_course_type_A) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',course_type) ).
tff(12,plain,
course(sK5_course_type_A) = true,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
true = course(sK5_course_type_A),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ( course(csc410) = true )
<=> ( course(csc410) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
course(csc410) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',csc410_type) ).
tff(16,plain,
course(csc410) = true,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
course(csc410) = course(sK5_course_type_A),
inference(transitivity,[status(thm)],[16,13]) ).
tff(18,plain,
ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( enrolled(michael,csc410) = true )
<=> ( enrolled(michael,csc410) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
enrolled(michael,csc410) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',michael_enrolled_csc410_axiom) ).
tff(22,plain,
enrolled(michael,csc410) = true,
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
true = enrolled(michael,csc410),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
ifeq(true,true,ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true) = ifeq(enrolled(michael,csc410),true,ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true),
inference(monotonicity,[status(thm)],[23,19]) ).
tff(25,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true) = ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
ifeq(true,true,ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true) = ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(true,true,ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(enrolled(michael,csc410),true,ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true),
inference(transitivity,[status(thm)],[18,34,24]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,teaches(victor,csc410),true) = teaches(victor,csc410) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
ifeq(true,true,teaches(victor,csc410),true) = teaches(victor,csc410),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ( coordinatorof(csc410) = victor )
<=> ( coordinatorof(csc410) = victor ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
coordinatorof(csc410) = victor,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',victor_coordinator_csc410_axiom) ).
tff(40,plain,
coordinatorof(csc410) = victor,
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
teaches(coordinatorof(csc410),csc410) = teaches(victor,csc410),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
teaches(victor,csc410) = teaches(coordinatorof(csc410),csc410),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
true = course(csc410),
inference(symmetry,[status(thm)],[16]) ).
tff(44,plain,
ifeq(true,true,teaches(victor,csc410),true) = ifeq(course(csc410),true,teaches(coordinatorof(csc410),csc410),true),
inference(monotonicity,[status(thm)],[43,42]) ).
tff(45,plain,
ifeq(course(csc410),true,teaches(coordinatorof(csc410),csc410),true) = ifeq(true,true,teaches(victor,csc410),true),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
^ [X: $i] :
refl(( ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true )
<=> ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true )
<=> ! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true )
<=> ! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coordinator_teaches) ).
tff(50,plain,
! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [X: $i] : ( ifeq(course(X),true,teaches(coordinatorof(X),X),true) = true )
| ( ifeq(course(csc410),true,teaches(coordinatorof(csc410),csc410),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
ifeq(course(csc410),true,teaches(coordinatorof(csc410),csc410),true) = true,
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
true = ifeq(course(csc410),true,teaches(coordinatorof(csc410),csc410),true),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
enrolled(michael,csc410) = teaches(victor,csc410),
inference(transitivity,[status(thm)],[22,55,45,37]) ).
tff(57,plain,
ifeq(enrolled(michael,csc410),true,ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true) = ifeq(teaches(victor,csc410),true,ifeq(enrolled(michael,csc410),true,ifeq(course(csc410),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),true),true),
inference(monotonicity,[status(thm)],[56,35]) ).
tff(58,plain,
ifeq(true,true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(course(sK5_course_type_A),true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),
inference(monotonicity,[status(thm)],[13]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
ifeq(true,true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true) = ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),
inference(unit_resolution,[status(thm)],[59,31]) ).
tff(61,plain,
ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true) = ifeq(true,true,ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),true),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ( professor(victor) = true )
<=> ( professor(victor) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
professor(victor) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',victor_type) ).
tff(64,plain,
professor(victor) = true,
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
true = professor(victor),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
ifeq(true,true,ifeq(student(michael),true,taughtby(michael,victor),true),true) = ifeq(professor(victor),true,ifeq(student(michael),true,taughtby(michael,victor),true),true),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(student(michael),true,taughtby(michael,victor),true),true) = ifeq(student(michael),true,taughtby(michael,victor),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
ifeq(true,true,ifeq(student(michael),true,taughtby(michael,victor),true),true) = ifeq(student(michael),true,taughtby(michael,victor),true),
inference(unit_resolution,[status(thm)],[67,31]) ).
tff(69,plain,
ifeq(student(michael),true,taughtby(michael,victor),true) = ifeq(true,true,ifeq(student(michael),true,taughtby(michael,victor),true),true),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ( student(michael) = true )
<=> ( student(michael) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
student(michael) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',michael_type) ).
tff(72,plain,
student(michael) = true,
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
true = student(michael),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
ifeq(true,true,taughtby(michael,victor),true) = ifeq(student(michael),true,taughtby(michael,victor),true),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,taughtby(michael,victor),true) = taughtby(michael,victor) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
ifeq(true,true,taughtby(michael,victor),true) = taughtby(michael,victor),
inference(unit_resolution,[status(thm)],[75,31]) ).
tff(77,plain,
taughtby(michael,victor) = ifeq(true,true,taughtby(michael,victor),true),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
taughtby(michael,victor) = true,
inference(transitivity,[status(thm)],[77,74,69,66,61,58,34,24,57,9]) ).
tff(79,plain,
( ( taughtby(michael,victor) != true )
<=> ( taughtby(michael,victor) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
taughtby(michael,victor) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',teaching_conjecture) ).
tff(81,plain,
taughtby(michael,victor) != true,
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ131-10 : TPTP v9.0.0. Released v7.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:47:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------