TSTP Solution File: SET050-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET050-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:05:09 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 61 ( 17 unt; 10 typ; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 240 ( 113 ~; 105 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 139 ( 126 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(u_type,type,
u: $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
( ~ member(x,unordered_pair(x,y))
<=> ~ member(x,unordered_pair(x,y)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ member(x,unordered_pair(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_unordered_pair_2) ).
tff(3,plain,
~ member(x,unordered_pair(x,y)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,y)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,y)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,y)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ member(x,universal_class),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( member(ordered_pair(x,y),cross_product(u,v))
<=> member(ordered_pair(x,y),cross_product(u,v)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_unordered_pair_1) ).
tff(17,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(19,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)],[18]) ).
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(rewrite,[status(thm)],]) ).
tff(21,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(22,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)],[21,20]) ).
tff(23,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)],[22]) ).
tff(24,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)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(x,y),cross_product(u,v))
| member(x,u) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(x,y),cross_product(u,v))
| member(x,u) ) ),
inference(rewrite,[status(thm)],]) ).
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(x,y),cross_product(u,v))
| member(x,u) ),
inference(quant_inst,[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(x,y),cross_product(u,v))
| member(x,u) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
member(x,u),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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(33,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)],[32]) ).
tff(34,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(35,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,u)
| ~ subclass(u,universal_class) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,u)
| ~ subclass(u,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,u)
| ~ subclass(u,universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,u)
| ~ subclass(u,universal_class) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ subclass(u,universal_class),
inference(unit_resolution,[status(thm)],[41,38,28,14]) ).
tff(43,plain,
^ [X: $i] :
refl(
( subclass(X,universal_class)
<=> subclass(X,universal_class) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X: $i] : subclass(X,universal_class)
<=> ! [X: $i] : subclass(X,universal_class) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i] : subclass(X,universal_class)
<=> ! [X: $i] : subclass(X,universal_class) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [X: $i] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
tff(47,plain,
! [X: $i] : subclass(X,universal_class),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i] : subclass(X,universal_class),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] : subclass(X,universal_class),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [X: $i] : subclass(X,universal_class)
| subclass(u,universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,49,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SET050-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 01:52:25 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------