TSTP Solution File: SET122-7 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET122-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 05:05:48 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of formulae : 55 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 156 ( 79 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 147 ( 42 ~; 85 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 79 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(second_type,type,
second: $i > $i ).
tff(first_type,type,
first: $i > $i ).
tff(1,plain,
( ( second(ordered_pair(x,y)) != ordered_pair(x,y) )
<=> ( second(ordered_pair(x,y)) != ordered_pair(x,y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components2_2) ).
tff(3,plain,
second(ordered_pair(x,y)) != ordered_pair(x,y),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
<=> ( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
<=> ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
<=> ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X: $i] :
rewrite(
( ( ( ordered_pair(first(X),second(X)) = X )
| ( second(X) = X ) )
<=> ( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( ( ordered_pair(first(X),second(X)) = X )
| ( second(X) = X ) )
<=> ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( ( ordered_pair(first(X),second(X)) = X )
| ( second(X) = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
tff(10,plain,
! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| ( ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y) ) )
<=> ( ~ ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| ( ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| ( ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ( second(X) = X )
| ( ordered_pair(first(X),second(X)) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| ( ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
<=> member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
^ [X: $i] :
refl(
( ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
<=> ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
<=> ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
<=> ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
tff(23,plain,
! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) )
<=> ( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) ) )
<=> ( ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) ) )
<=> ( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) ) )
<=> ( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( second(X) = X ) )
| ( second(ordered_pair(x,y)) = ordered_pair(x,y) )
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)),
inference(unit_resolution,[status(thm)],[31,25,3]) ).
tff(33,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[32,18]) ).
tff(34,plain,
( ~ member(y,universal_class)
<=> ~ member(y,universal_class) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components2_1) ).
tff(36,plain,
~ member(y,universal_class),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
tff(41,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43,36,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET122-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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 02:06:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------