TSTP Solution File: SET117-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET117-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 05:05:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 38 ( 19 unt; 8 typ; 0 def)
% Number of atoms : 45 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 2 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(second_type,type,
second: $i > $i ).
tff(x_type,type,
x: $i ).
tff(first_type,type,
first: $i > $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
( ( ordered_pair(first(x),second(x)) = x )
<=> ( ordered_pair(first(x),second(x)) = x ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ordered_pair(first(x),second(x)) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_1) ).
tff(3,plain,
ordered_pair(first(x),second(x)) = x,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
tff(8,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
| ( unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))) = ordered_pair(first(x),second(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))) = ordered_pair(first(x),second(x)),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))) = x,
inference(transitivity,[status(thm)],[12,3]) ).
tff(14,plain,
( member(unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))),universal_class)
<=> member(x,universal_class) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( member(x,universal_class)
<=> member(unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))),universal_class) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ~ member(x,universal_class)
<=> ~ member(unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))),universal_class) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ member(x,universal_class)
<=> ~ member(x,universal_class) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_2) ).
tff(19,plain,
~ member(x,universal_class),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ member(unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))),universal_class),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(
( member(unordered_pair(X,Y),universal_class)
<=> member(unordered_pair(X,Y),universal_class) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class)
<=> ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class)
<=> ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
tff(25,plain,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class)
| member(unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))),universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
member(unordered_pair(singleton(first(x)),unordered_pair(first(x),singleton(second(x)))),universal_class),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET117-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 02:36:19 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.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------