TSTP Solution File: NUM180-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Sun Sep 18 13:03:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 53 ( 10 unt; 12 typ; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 143 ( 56 ~; 71 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 90 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(ordinal_numbers_type,type,
ordinal_numbers: $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(union_type,type,
union: ( $i * $i ) > $i ).
tff(image_type,type,
image: ( $i * $i ) > $i ).
tff(successor_relation_type,type,
successor_relation: $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(null_class_type,type,
null_class: $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(limit_ordinals_type,type,
limit_ordinals: $i ).
tff(1,plain,
( ~ subclass(limit_ordinals,ordinal_numbers)
<=> ~ subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ subclass(limit_ordinals,ordinal_numbers)
<=> ~ subclass(limit_ordinals,ordinal_numbers) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ subclass(limit_ordinals,ordinal_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_limit_ordinals_are_ordinals_1) ).
tff(4,plain,
~ subclass(limit_ordinals,ordinal_numbers),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,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(7,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)],[6]) ).
tff(8,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(9,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(10,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers)
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers)
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers)
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers)
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers),
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,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(21,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)],[20]) ).
tff(22,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(23,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers)
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers)) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers)
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers)
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers)) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers)
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers)),
inference(unit_resolution,[status(thm)],[29,26,5]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers))
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers))
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers))
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers))
| member(not_subclass_element(intersection(complement(union(singleton(null_class),image(successor_relation,ordinal_numbers))),ordinal_numbers),ordinal_numbers),ordinal_numbers) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37,30,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 Sep 2 08:07:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------