TSTP Solution File: DAT055_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT055_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 16 14:36:33 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 23 unt; 5 typ; 0 def)
% Number of atoms : 102 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 69 ( 23 ~; 10 |; 10 &)
% ( 24 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number arithmetic : 354 ( 92 atm; 140 fun; 122 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(min_type,type,
min: list > $int ).
tff(a_type,type,
a: list ).
tff(l_type,type,
l: $int ).
tff(k_type,type,
k: $int ).
tff(max_type,type,
max: list > $int ).
tff(1,plain,
( $lesseq(l,min(a))
<=> $lesseq($sum(l,$product(-1,min(a))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( $lesseq(l,min(a))
<=> $lesseq(l,min(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ ( ( ! [X: list] : $lesseq(min(X),max(X))
& $lesseq(l,min(a))
& $less(0,k) )
=> $less(l,$sum(max(a),k)) )
<=> ~ ( ~ $lesseq($sum(max(a),k),l)
| ~ ( ! [X: list] : $lesseq(min(X),max(X))
& $lesseq(l,min(a))
& ~ $lesseq(k,0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
~ ( ( ! [X: list] : $lesseq(min(X),max(X))
& $lesseq(l,min(a))
& $less(0,k) )
=> $less(l,$sum(max(a),k)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boyer_moore_max_min) ).
tff(5,plain,
~ ( ~ $lesseq($sum(max(a),k),l)
| ~ ( ! [X: list] : $lesseq(min(X),max(X))
& $lesseq(l,min(a))
& ~ $lesseq(k,0) ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
( ! [X: list] : $lesseq(min(X),max(X))
& $lesseq(l,min(a))
& ~ $lesseq(k,0) ),
inference(or_elim,[status(thm)],[5]) ).
tff(7,plain,
$lesseq(l,min(a)),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
$lesseq(l,min(a)),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
$lesseq($sum(l,$product(-1,min(a))),0),
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
( $lesseq($sum($product(-1,l),$sum(k,max(a))),0)
<=> $greatereq($sum(l,$sum($product(-1,k),$product(-1,max(a)))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
$sum(max(a),$sum(k,$product(-1,l))) = $sum($product(-1,l),$sum(k,max(a))),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( $lesseq($sum(max(a),$sum(k,$product(-1,l))),0)
<=> $lesseq($sum($product(-1,l),$sum(k,max(a))),0) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( $lesseq($sum(max(a),$sum(k,$product(-1,l))),0)
<=> $greatereq($sum(l,$sum($product(-1,k),$product(-1,max(a)))),0) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
( $lesseq($sum(max(a),k),l)
<=> $lesseq($sum(max(a),$sum(k,$product(-1,l))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( $lesseq($sum(max(a),k),l)
<=> $lesseq($sum(max(a),k),l) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
$lesseq($sum(max(a),k),l),
inference(or_elim,[status(thm)],[5]) ).
tff(17,plain,
$lesseq($sum(max(a),k),l),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
$lesseq($sum(max(a),k),l),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,plain,
$lesseq($sum(max(a),$sum(k,$product(-1,l))),0),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
$greatereq($sum(l,$sum($product(-1,k),$product(-1,max(a)))),0),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
( ~ $lesseq(k,0)
<=> ~ $lesseq(k,0) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
~ $lesseq(k,0),
inference(and_elim,[status(thm)],[6]) ).
tff(23,plain,
~ $lesseq(k,0),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [X: list] :
refl(
( $greatereq($sum(max(X),$product(-1,min(X))),0)
<=> $greatereq($sum(max(X),$product(-1,min(X))),0) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
<=> ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [X: list] :
trans(
monotonicity(rewrite($sum(min(X),$product(-1,max(X))) = $sum($product(-1,max(X)),min(X))),
( $lesseq($sum(min(X),$product(-1,max(X))),0)
<=> $lesseq($sum($product(-1,max(X)),min(X)),0) )),
rewrite(
( $lesseq($sum($product(-1,max(X)),min(X)),0)
<=> $greatereq($sum(max(X),$product(-1,min(X))),0) )),
( $lesseq($sum(min(X),$product(-1,max(X))),0)
<=> $greatereq($sum(max(X),$product(-1,min(X))),0) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [X: list] : $lesseq($sum(min(X),$product(-1,max(X))),0)
<=> ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [X: list] :
rewrite(
( $lesseq(min(X),max(X))
<=> $lesseq($sum(min(X),$product(-1,max(X))),0) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X: list] : $lesseq(min(X),max(X))
<=> ! [X: list] : $lesseq($sum(min(X),$product(-1,max(X))),0) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: list] : $lesseq(min(X),max(X))
<=> ! [X: list] : $lesseq(min(X),max(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
! [X: list] : $lesseq(min(X),max(X)),
inference(and_elim,[status(thm)],[6]) ).
tff(32,plain,
! [X: list] : $lesseq(min(X),max(X)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: list] : $lesseq($sum(min(X),$product(-1,max(X))),0),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0),
inference(modus_ponens,[status(thm)],[33,27]) ).
tff(35,plain,
! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
( ( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $lesseq($sum(min(a),$product(-1,max(a))),0) )
<=> ( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $lesseq($sum(min(a),$product(-1,max(a))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( $greatereq($sum($product(-1,min(a)),max(a)),0)
<=> $lesseq($sum(min(a),$product(-1,max(a))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
$sum(max(a),$product(-1,min(a))) = $sum($product(-1,min(a)),max(a)),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( $greatereq($sum(max(a),$product(-1,min(a))),0)
<=> $greatereq($sum($product(-1,min(a)),max(a)),0) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( $greatereq($sum(max(a),$product(-1,min(a))),0)
<=> $lesseq($sum(min(a),$product(-1,max(a))),0) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $greatereq($sum(max(a),$product(-1,min(a))),0) )
<=> ( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $lesseq($sum(min(a),$product(-1,max(a))),0) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $greatereq($sum(max(a),$product(-1,min(a))),0) )
<=> ( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $lesseq($sum(min(a),$product(-1,max(a))),0) ) ),
inference(transitivity,[status(thm)],[42,37]) ).
tff(44,plain,
( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $greatereq($sum(max(a),$product(-1,min(a))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X: list] : $greatereq($sum(max(X),$product(-1,min(X))),0)
| $lesseq($sum(min(a),$product(-1,max(a))),0) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$lesseq($sum(min(a),$product(-1,max(a))),0),
inference(unit_resolution,[status(thm)],[45,36]) ).
tff(47,plain,
$false,
inference(theory_lemma,[status(thm)],[46,23,20,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT055_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n013.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 : Wed Aug 31 01:42:47 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------