TSTP Solution File: SET020-7 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET020-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:04:53 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 64 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 243 ( 99 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 333 ( 157 ~; 150 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 11 ( 11 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 184 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(first_type,type,
first: $i > $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(second_type,type,
second: $i > $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(1,plain,
( member(ordered_pair(u,v),cross_product(universal_class,universal_class))
<=> member(ordered_pair(u,v),cross_product(universal_class,universal_class)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
tff(3,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
tff(8,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)],[7,6]) ).
tff(9,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,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)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ( first(ordered_pair(u,v)) != u )
<=> ( first(ordered_pair(u,v)) != u ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
tff(17,plain,
first(ordered_pair(u,v)) != u,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
<=> ( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(W,universal_class) )
<=> ( ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
( ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(W,universal_class)
| ( W = Y ) )
<=> ( ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ( W = Y ) ) )),
rewrite(
( ( ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ( W = Y ) )
<=> ( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
( ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(W,universal_class)
| ( W = Y ) )
<=> ( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(W,universal_class)
| ( W = Y ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(W,universal_class)
| ( W = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
tff(24,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) )
| ~ member(first(ordered_pair(u,v)),universal_class) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) )
| ~ member(first(ordered_pair(u,v)),universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ( first(ordered_pair(u,v)) = u )
| ~ member(first(ordered_pair(u,v)),universal_class)
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) ) )
<=> ( ( first(ordered_pair(u,v)) = u )
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) )
| ~ member(first(ordered_pair(u,v)),universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ~ member(first(ordered_pair(u,v)),universal_class)
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) )
| ~ member(first(ordered_pair(u,v)),universal_class) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ~ member(first(ordered_pair(u,v)),universal_class)
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) )
| ~ member(first(ordered_pair(u,v)),universal_class) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ~ member(first(ordered_pair(u,v)),universal_class)
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( W = Y )
| ~ member(W,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( first(ordered_pair(u,v)) = u )
| ( ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) != ordered_pair(u,v) )
| ~ member(first(ordered_pair(u,v)),universal_class) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ member(first(ordered_pair(u,v)),universal_class),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
^ [Z: $i,Y: $i] :
refl(
( ( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
<=> ( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
<=> ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
<=> ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_1) ).
tff(39,plain,
! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) )
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)),
inference(unit_resolution,[status(thm)],[44,41,3]) ).
tff(46,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
tff(50,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class))
| member(first(ordered_pair(u,v)),universal_class) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class))
| member(first(ordered_pair(u,v)),universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class))
| member(first(ordered_pair(u,v)),universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class))
| member(first(ordered_pair(u,v)),universal_class) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,52,45,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET020-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 01:17:40 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------