%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET479-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:25:47 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 48 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 286 ( 135 ~; 128 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 10 ( 10 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 128 ( 117 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(x_type,type,
x: $i ).
tff(domain_relation_type,type,
domain_relation: $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(1,plain,
( ~ member(domain_of(x),universal_class)
<=> ~ member(domain_of(x),universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ member(domain_of(x),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_replacement_property1_2) ).
tff(3,plain,
~ member(domain_of(x),universal_class),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
tff(8,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| member(domain_of(x),universal_class) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| member(domain_of(x),universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| member(domain_of(x),universal_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| member(domain_of(x),universal_class) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( member(x,universal_class)
<=> member(x,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_replacement_property1_1) ).
tff(17,plain,
member(x,universal_class),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [X: $i] :
refl(( ( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
<=> ( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
<=> ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
<=> ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',definition_of_domain_relation3) ).
tff(22,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
| ~ member(x,universal_class)
| member(ordered_pair(x,domain_of(x)),domain_relation) )
<=> ( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
| ~ member(x,universal_class)
| member(ordered_pair(x,domain_of(x)),domain_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
| ~ member(x,universal_class)
| member(ordered_pair(x,domain_of(x)),domain_relation) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(ordered_pair(X,domain_of(X)),domain_relation) )
| ~ member(x,universal_class)
| member(ordered_pair(x,domain_of(x)),domain_relation) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
member(ordered_pair(x,domain_of(x)),domain_relation),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',definition_of_domain_relation1) ).
tff(31,plain,
subclass(domain_relation,cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [Y: $i,U: $i,X: $i] :
refl(( ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ subclass(X,Y)
| ~ member(U,X) )
<=> ( ~ member(U,X)
| ~ subclass(X,Y) ) )),
( ( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ( ~ member(U,X)
| ~ subclass(X,Y)
| member(U,Y) ) )),
rewrite(( ( ~ member(U,X)
| ~ subclass(X,Y)
| member(U,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
( ( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Y: $i,U: $i,X: $i] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Y: $i,U: $i,X: $i] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
tff(38,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation)
| ~ subclass(domain_relation,cross_product(universal_class,universal_class)) )
<=> ( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation)
| ~ subclass(domain_relation,cross_product(universal_class,universal_class)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation)
| ~ subclass(domain_relation,cross_product(universal_class,universal_class)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation)
| ~ subclass(domain_relation,cross_product(universal_class,universal_class)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(x,domain_of(x)),domain_relation) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,41,31,28,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET479-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:15:26 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------