TSTP Solution File: TOP004-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Fri Sep 30 01:55:48 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of formulae : 23 ( 12 unt; 5 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 2 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(element_of_collection_type,type,
element_of_collection: ( $i * $i ) > $o ).
tff(top_of_basis_type,type,
top_of_basis: $i > $i ).
tff(f_type,type,
f: $i ).
tff(intersection_of_sets_type,type,
intersection_of_sets: ( $i * $i ) > $i ).
tff(cx_type,type,
cx: $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(
( ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
<=> ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
<=> ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
<=> ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_4) ).
tff(5,plain,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
| ~ element_of_collection(intersection_of_sets(cx,cx),top_of_basis(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
~ element_of_collection(intersection_of_sets(cx,cx),top_of_basis(f)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [U: $i] :
refl(
( element_of_collection(U,top_of_basis(f))
<=> element_of_collection(U,top_of_basis(f)) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [U: $i] : element_of_collection(U,top_of_basis(f))
<=> ! [U: $i] : element_of_collection(U,top_of_basis(f)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [U: $i] : element_of_collection(U,top_of_basis(f))
<=> ! [U: $i] : element_of_collection(U,top_of_basis(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_2) ).
tff(14,plain,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [U: $i] : element_of_collection(U,top_of_basis(f))
| element_of_collection(intersection_of_sets(cx,cx),top_of_basis(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
$false,
inference(unit_resolution,[status(thm)],[17,16,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : TOP004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 09:23:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------