%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET240-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:25:31 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 51 ~; 45 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 121 ( 111 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(restrict_type,type,
restrict: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,Xr: $i,X: $i] :
refl(( ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
tff(5,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
| ( intersection(cross_product(x,y),xr) = restrict(xr,x,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
intersection(cross_product(x,y),xr) = restrict(xr,x,y),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
<=> member(ordered_pair(u,v),restrict(xr,x,y)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( member(ordered_pair(u,v),restrict(xr,x,y))
<=> member(ordered_pair(u,v),intersection(cross_product(x,y),xr)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( member(ordered_pair(u,v),restrict(xr,x,y))
<=> member(ordered_pair(u,v),restrict(xr,x,y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
member(ordered_pair(u,v),restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn3_1) ).
tff(14,plain,
member(ordered_pair(u,v),restrict(xr,x,y)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
member(ordered_pair(u,v),intersection(cross_product(x,y),xr)),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
( ~ member(u,x)
<=> ~ member(u,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
~ member(u,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn3_2) ).
tff(18,plain,
~ member(u,x),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
tff(23,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(u,v),cross_product(x,y))
| member(u,x) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(u,v),cross_product(x,y))
| member(u,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(u,v),cross_product(x,y))
| member(u,x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(u,v),cross_product(x,y))
| member(u,x) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ member(ordered_pair(u,v),cross_product(x,y)),
inference(unit_resolution,[status(thm)],[28,25,18]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr)),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET240-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 04:37:55 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% See solution above
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------