TSTP Solution File: SET240-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET240-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 05:06:17 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 51 ( 15 unt; 10 typ; 0 def)
% Number of atoms : 105 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 50 ~; 46 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 121 ( 111 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(restrict_type,type,
restrict: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,Xr: $i,X: $i] :
refl(
( ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
tff(5,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
| ( intersection(cross_product(x,y),xr) = restrict(xr,x,y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
intersection(cross_product(x,y),xr) = restrict(xr,x,y),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
<=> member(ordered_pair(u,v),restrict(xr,x,y)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( member(ordered_pair(u,v),restrict(xr,x,y))
<=> member(ordered_pair(u,v),intersection(cross_product(x,y),xr)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( member(ordered_pair(u,v),restrict(xr,x,y))
<=> member(ordered_pair(u,v),restrict(xr,x,y)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
member(ordered_pair(u,v),restrict(xr,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn3_1) ).
tff(14,plain,
member(ordered_pair(u,v),restrict(xr,x,y)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
member(ordered_pair(u,v),intersection(cross_product(x,y),xr)),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,X) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ member(ordered_pair(u,v),intersection(cross_product(x,y),xr))
| member(ordered_pair(u,v),cross_product(x,y)) ),
inference(unit_resolution,[status(thm)],[25,22]) ).
tff(27,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(unit_resolution,[status(thm)],[26,15]) ).
tff(28,plain,
( ~ member(u,x)
<=> ~ member(u,x) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
~ member(u,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn3_2) ).
tff(30,plain,
~ member(u,x),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
tff(35,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)],[34,33]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,32]) ).
tff(38,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ 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) )
| ~ member(ordered_pair(u,v),cross_product(x,y))
| member(u,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ 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(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ 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(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37,30,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET240-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.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 03:30:57 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.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------