%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM180-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:18:52 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 46 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 143 ( 54 ~; 71 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 90 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(ordinal_numbers_type,type,
ordinal_numbers: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(kind_1_ordinals_type,type,
kind_1_ordinals: $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(limit_ordinals_type,type,
limit_ordinals: $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(1,plain,
( ( intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals )
<=> ( intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',limit_ordinals) ).
tff(3,plain,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers))
<=> member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals)
<=> member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers)) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ~ subclass(limit_ordinals,ordinal_numbers)
<=> ~ subclass(limit_ordinals,ordinal_numbers) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
~ subclass(limit_ordinals,ordinal_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_limit_ordinals_are_ordinals_1) ).
tff(8,plain,
~ subclass(limit_ordinals,ordinal_numbers),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
^ [Y: $i,X: $i] :
refl(( ( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
<=> ( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
<=> ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
<=> ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
^ [Y: $i,X: $i] :
rewrite(( ( member(not_subclass_element(X,Y),X)
| subclass(X,Y) )
<=> ( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [Y: $i,X: $i] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [Y: $i,X: $i] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
tff(15,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(limit_ordinals,ordinal_numbers)
| member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(limit_ordinals,ordinal_numbers)
| member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(limit_ordinals,ordinal_numbers)
| member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(limit_ordinals,ordinal_numbers)
| member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals),
inference(unit_resolution,[status(thm)],[21,18,8]) ).
tff(23,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(modus_ponens,[status(thm)],[22,5]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
<=> ( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
tff(28,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers)
| subclass(limit_ordinals,ordinal_numbers) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers)
| subclass(limit_ordinals,ordinal_numbers) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers)
| subclass(limit_ordinals,ordinal_numbers) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers)
| subclass(limit_ordinals,ordinal_numbers) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers),
inference(unit_resolution,[status(thm)],[33,30,8]) ).
tff(35,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers))
| member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers))
| member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers))
| member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers))
| member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(unit_resolution,[status(thm)],[44,41,34]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM180-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.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 00:24:47 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% See solution above
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------