TSTP Solution File: SET238-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 20 05:06:16 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 58 ( 18 unt; 11 typ; 0 def)
% Number of atoms : 114 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 53 ~; 46 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 99 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(restrict_type,type,
restrict: ( $i * $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(xr_type,type,
xr: $i ).
tff(z_type,type,
z: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(second_type,type,
second: $i > $i ).
tff(first_type,type,
first: $i > $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(intersection_type,type,
intersection: ( $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/sandbox/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(z,intersection(cross_product(x,y),xr))
<=> member(z,restrict(xr,x,y)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( member(z,restrict(xr,x,y))
<=> member(z,intersection(cross_product(x,y),xr)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( member(z,restrict(xr,x,y))
<=> member(z,restrict(xr,x,y)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_1) ).
tff(14,plain,
member(z,restrict(xr,x,y)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
member(z,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/sandbox/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(z,intersection(cross_product(x,y),xr))
| member(z,cross_product(x,y)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(z,intersection(cross_product(x,y),xr))
| member(z,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(z,intersection(cross_product(x,y),xr))
| member(z,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(z,intersection(cross_product(x,y),xr))
| member(z,cross_product(x,y)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ member(z,intersection(cross_product(x,y),xr))
| member(z,cross_product(x,y)) ),
inference(unit_resolution,[status(thm)],[25,22]) ).
tff(27,plain,
member(z,cross_product(x,y)),
inference(unit_resolution,[status(thm)],[26,15]) ).
tff(28,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
<=> ( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(z,cross_product(x,y))
| ( ordered_pair(first(z),second(z)) = z ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(z,cross_product(x,y))
| ( ordered_pair(first(z),second(z)) = z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(z,cross_product(x,y))
| ( ordered_pair(first(z),second(z)) = z ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(z,cross_product(x,y))
| ( ordered_pair(first(z),second(z)) = z ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
ordered_pair(first(z),second(z)) = z,
inference(unit_resolution,[status(thm)],[37,34,27]) ).
tff(39,plain,
z = ordered_pair(first(z),second(z)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( member(z,restrict(xr,x,y))
<=> member(ordered_pair(first(z),second(z)),restrict(xr,x,y)) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( member(ordered_pair(first(z),second(z)),restrict(xr,x,y))
<=> member(z,restrict(xr,x,y)) ),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y))
<=> ~ member(z,restrict(xr,x,y)) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y))
<=> ~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_2) ).
tff(45,plain,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ member(z,restrict(xr,x,y)),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[14,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 04:00:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------