%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ003-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:23:07 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 31
% Syntax : Number of formulae : 63 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 393 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 602 ( 288 ~; 279 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 108 ( 100 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
tff(shaved_type,type,
shaved: ( $i * $i ) > $o ).
tff(guido_type,type,
guido: $i ).
tff(lorenzo_type,type,
lorenzo: $i ).
tff(members_type,type,
members: $i ).
tff(cesare_type,type,
cesare: $i ).
tff(member_type,type,
member: $i > $o ).
tff(petruchio_type,type,
petruchio: $i ).
tff(1,plain,
( shaved(guido,cesare)
<=> shaved(guido,cesare) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
shaved(guido,cesare),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',guido_has_shaved_cesare) ).
tff(3,plain,
shaved(guido,cesare),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( member(cesare)
<=> member(cesare) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
member(cesare),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cesare) ).
tff(6,plain,
member(cesare),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( member(guido)
<=> member(guido) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
member(guido),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',guido) ).
tff(9,plain,
member(guido),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
<=> ( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
<=> ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
<=> ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ member(X)
| ~ member(Y)
| ~ shaved(X,Y) )
<=> ( ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) )),
( ( ~ member(X)
| ~ member(Y)
| ~ shaved(X,Y)
| shaved(members,X) )
<=> ( ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X)
| shaved(members,X) ) )),
rewrite(( ( ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X)
| shaved(members,X) )
<=> ( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) )),
( ( ~ member(X)
| ~ member(Y)
| ~ shaved(X,Y)
| shaved(members,X) )
<=> ( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i,X: $i] :
( ~ member(X)
| ~ member(Y)
| ~ shaved(X,Y)
| shaved(members,X) )
<=> ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [Y: $i,X: $i] :
( ~ member(X)
| ~ member(Y)
| ~ shaved(X,Y)
| shaved(members,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_shaved_then_all_shaved) ).
tff(16,plain,
! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,guido)
| ~ shaved(guido,cesare)
| ~ member(cesare)
| ~ member(guido) )
<=> ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,guido)
| ~ shaved(guido,cesare)
| ~ member(cesare)
| ~ member(guido) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,guido)
| ~ shaved(guido,cesare)
| ~ member(cesare)
| ~ member(guido) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,guido)
| ~ shaved(guido,cesare)
| ~ member(cesare)
| ~ member(guido) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
shaved(members,guido),
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
tff(24,plain,
( member(lorenzo)
<=> member(lorenzo) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
member(lorenzo),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lorenzo) ).
tff(26,plain,
member(lorenzo),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
<=> ( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
<=> ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
<=> ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ shaved(members,X)
| ~ member(Y) )
<=> ( ~ shaved(members,X)
| ~ member(Y) ) )),
( ( ~ shaved(members,X)
| ~ member(Y)
| shaved(Y,X) )
<=> ( ~ shaved(members,X)
| ~ member(Y)
| shaved(Y,X) ) )),
rewrite(( ( ~ shaved(members,X)
| ~ member(Y)
| shaved(Y,X) )
<=> ( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ) )),
( ( ~ shaved(members,X)
| ~ member(Y)
| shaved(Y,X) )
<=> ( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| ~ member(Y)
| shaved(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [Y: $i,X: $i] :
( ~ shaved(members,X)
| ~ member(Y)
| shaved(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_shaved_then_one_shaved) ).
tff(33,plain,
! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| ~ member(lorenzo)
| shaved(lorenzo,guido) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| ~ member(lorenzo)
| shaved(lorenzo,guido) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ shaved(members,guido)
| shaved(lorenzo,guido)
| ~ member(lorenzo) )
<=> ( ~ shaved(members,guido)
| ~ member(lorenzo)
| shaved(lorenzo,guido) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| shaved(lorenzo,guido)
| ~ member(lorenzo) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| ~ member(lorenzo)
| shaved(lorenzo,guido) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| shaved(lorenzo,guido)
| ~ member(lorenzo) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| ~ member(lorenzo)
| shaved(lorenzo,guido) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| shaved(lorenzo,guido)
| ~ member(lorenzo) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,guido)
| ~ member(lorenzo)
| shaved(lorenzo,guido) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
shaved(lorenzo,guido),
inference(unit_resolution,[status(thm)],[42,36,26,23]) ).
tff(44,plain,
( ~ shaved(petruchio,lorenzo)
<=> ~ shaved(petruchio,lorenzo) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
~ shaved(petruchio,lorenzo),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_petruchio_has_shaved_lorenzo) ).
tff(46,plain,
~ shaved(petruchio,lorenzo),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( member(petruchio)
<=> member(petruchio) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
member(petruchio),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',petruchio) ).
tff(49,plain,
member(petruchio),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| shaved(petruchio,lorenzo)
| ~ shaved(members,lorenzo)
| ~ member(petruchio) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| shaved(petruchio,lorenzo)
| ~ shaved(members,lorenzo)
| ~ member(petruchio) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ shaved(members,lorenzo)
| shaved(petruchio,lorenzo)
| ~ member(petruchio) )
<=> ( shaved(petruchio,lorenzo)
| ~ shaved(members,lorenzo)
| ~ member(petruchio) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,lorenzo)
| shaved(petruchio,lorenzo)
| ~ member(petruchio) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| shaved(petruchio,lorenzo)
| ~ shaved(members,lorenzo)
| ~ member(petruchio) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,lorenzo)
| shaved(petruchio,lorenzo)
| ~ member(petruchio) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| shaved(petruchio,lorenzo)
| ~ shaved(members,lorenzo)
| ~ member(petruchio) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| ~ shaved(members,lorenzo)
| shaved(petruchio,lorenzo)
| ~ member(petruchio) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( ~ shaved(members,X)
| shaved(Y,X)
| ~ member(Y) )
| shaved(petruchio,lorenzo)
| ~ shaved(members,lorenzo)
| ~ member(petruchio) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ shaved(members,lorenzo),
inference(unit_resolution,[status(thm)],[55,36,49,46]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| ~ member(guido)
| shaved(members,lorenzo)
| ~ member(lorenzo)
| ~ shaved(lorenzo,guido) )
<=> ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| ~ member(guido)
| shaved(members,lorenzo)
| ~ member(lorenzo)
| ~ shaved(lorenzo,guido) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( shaved(members,lorenzo)
| ~ shaved(lorenzo,guido)
| ~ member(guido)
| ~ member(lorenzo) )
<=> ( ~ member(guido)
| shaved(members,lorenzo)
| ~ member(lorenzo)
| ~ shaved(lorenzo,guido) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,lorenzo)
| ~ shaved(lorenzo,guido)
| ~ member(guido)
| ~ member(lorenzo) )
<=> ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| ~ member(guido)
| shaved(members,lorenzo)
| ~ member(lorenzo)
| ~ shaved(lorenzo,guido) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,lorenzo)
| ~ shaved(lorenzo,guido)
| ~ member(guido)
| ~ member(lorenzo) )
<=> ( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| ~ member(guido)
| shaved(members,lorenzo)
| ~ member(lorenzo)
| ~ shaved(lorenzo,guido) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| shaved(members,lorenzo)
| ~ shaved(lorenzo,guido)
| ~ member(guido)
| ~ member(lorenzo) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( shaved(members,X)
| ~ shaved(X,Y)
| ~ member(Y)
| ~ member(X) )
| ~ member(guido)
| shaved(members,lorenzo)
| ~ member(lorenzo)
| ~ shaved(lorenzo,guido) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,19,9,26,56,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.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 Jun 20 02:43:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------