TSTP Solution File: SET098-7 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 20 05:05:38 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 41 ( 11 unt; 7 typ; 0 def)
% Number of atoms : 141 ( 64 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 136 ( 38 ~; 82 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 51 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(null_class_type,type,
null_class: $i ).
tff(1,plain,
( ( x != null_class )
<=> ( x != null_class ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
tff(3,plain,
x != null_class,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( singleton(not_subclass_element(x,null_class)) != x )
<=> ( singleton(not_subclass_element(x,null_class)) != x ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
tff(6,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(
( ( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
<=> ( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
<=> ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
<=> ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X ) )
<=> ( ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) )),
( ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X )
| ( X = null_class ) )
<=> ( ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( X = null_class ) ) )),
rewrite(
( ( ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( X = null_class ) )
<=> ( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) )),
( ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X )
| ( X = null_class ) )
<=> ( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X )
| ( X = null_class ) )
<=> ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X )
| ( X = null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_of_elements_in_class) ).
tff(13,plain,
! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
| ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) )
<=> ( ~ ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
| ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
| ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ( X = null_class )
| ( singleton(not_subclass_element(X,null_class)) = X )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) )
| ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x)
<=> ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
tff(23,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x))
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x))
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x))
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x))
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.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 : Sat Sep 3 02:19:13 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.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------