TSTP Solution File: ARI648_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI648_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 6 17:02:26 EDT 2022
% Result : Theorem 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 14 unt; 2 typ; 0 def)
% Number of atoms : 105 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 131 ( 76 ~; 30 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 511 ( 99 atm; 188 fun; 224 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 2 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $int ).
tff(b_type,type,
b: $int ).
tff(1,plain,
( ~ $lesseq(1,a)
<=> ~ $greatereq(a,1) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $lesseq(1,a)
<=> ~ $lesseq(1,a) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( $sum($product(20,a),$product(-1,$product(30,b))) = 7 )
| $greatereq(3,$sum(a,$product(-1,$product(2,b))))
| $lesseq(1,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(4,plain,
~ $lesseq(1,a),
inference(or_elim,[status(thm)],[3]) ).
tff(5,plain,
~ $lesseq(1,a),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
~ $greatereq(a,1),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( $lesseq(a,0)
| $greatereq(a,1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(8,plain,
$lesseq(a,0),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( ~ $greatereq(3,$sum(a,$product(-2,b)))
<=> ~ $lesseq($sum(a,$product(-2,b)),3) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( $greatereq(3,$sum(a,$product(-2,b)))
<=> $greatereq(3,$sum(a,$product(-2,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ~ $greatereq(3,$sum(a,$product(-2,b)))
<=> ~ $greatereq(3,$sum(a,$product(-2,b))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ $greatereq(3,$sum(a,$product(-2,b)))
<=> ~ $greatereq(3,$sum(a,$product(-2,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ $greatereq(3,$sum(a,$product(-1,$product(2,b))))
<=> ~ $greatereq(3,$sum(a,$product(-2,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
~ ( ( $sum($product(20,a),$product(-1,$product(30,b))) = 7 )
| $greatereq(3,$sum(a,$product(-1,$product(2,b)))) ),
inference(or_elim,[status(thm)],[3]) ).
tff(15,plain,
~ $greatereq(3,$sum(a,$product(-1,$product(2,b)))),
inference(or_elim,[status(thm)],[14]) ).
tff(16,plain,
~ $greatereq(3,$sum(a,$product(-2,b))),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
~ $greatereq(3,$sum(a,$product(-2,b))),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
~ $greatereq(3,$sum(a,$product(-2,b))),
inference(modus_ponens,[status(thm)],[17,11]) ).
tff(19,plain,
~ $lesseq($sum(a,$product(-2,b)),3),
inference(modus_ponens,[status(thm)],[18,9]) ).
tff(20,plain,
( $lesseq($sum(a,$product(-2,b)),3)
| $greatereq($sum(a,$product(-2,b)),4) ),
inference(theory_lemma,[status(thm)],]) ).
tff(21,plain,
$greatereq($sum(a,$product(-2,b)),4),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ $lesseq(a,0)
| ~ $greatereq($sum($product(2,a),$product(-4,b)),8) )
<=> ( ~ $lesseq(a,0)
| ~ $greatereq($sum(a,$product(-2,b)),4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ~ $greatereq($sum($product(2,a),$product(-4,b)),8)
| ~ $lesseq(a,0) )
<=> ( ~ $lesseq(a,0)
| ~ $greatereq($sum($product(2,a),$product(-4,b)),8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
<=> ~ $greatereq($sum($product(2,a),$product(-4,b)),8) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) )
<=> ( ~ $greatereq($sum($product(2,a),$product(-4,b)),8)
| ~ $lesseq(a,0) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) )
<=> ( ~ $lesseq(a,0)
| ~ $greatereq($sum($product(2,a),$product(-4,b)),8) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) )
<=> ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( $lesseq(8,$sum($product(2,a),$product(-4,b)))
<=> $lesseq(8,$sum($product(2,a),$product(-4,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
<=> ~ $lesseq(8,$sum($product(2,a),$product(-4,b))) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) )
<=> ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) )
<=> ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ) ),
inference(transitivity,[status(thm)],[30,27]) ).
tff(32,plain,
( ~ $lesseq($product(2,a),0)
<=> ~ $lesseq(a,0) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( $less(0,$product(2,a))
<=> ~ $lesseq($product(2,a),0) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( $less(0,$product(2,a))
<=> ~ $lesseq(a,0) ),
inference(transitivity,[status(thm)],[33,32]) ).
tff(35,plain,
( $greater(8,$sum($product(2,a),$product(-4,b)))
<=> ~ $lesseq(8,$sum($product(2,a),$product(-4,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
$sum($product(2,a),$product(-1,$product(4,b))) = $sum($product(2,a),$product(-4,b)),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
$difference($product(2,a),$product(4,b)) = $sum($product(2,a),$product(-1,$product(4,b))),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
$difference($product(2,a),$product(4,b)) = $sum($product(2,a),$product(-4,b)),
inference(transitivity,[status(thm)],[37,36]) ).
tff(39,plain,
( $greater(8,$difference($product(2,a),$product(4,b)))
<=> $greater(8,$sum($product(2,a),$product(-4,b))) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( $greater(8,$difference($product(2,a),$product(4,b)))
<=> ~ $lesseq(8,$sum($product(2,a),$product(-4,b))) ),
inference(transitivity,[status(thm)],[39,35]) ).
tff(41,plain,
( ( $greater(8,$difference($product(2,a),$product(4,b)))
| $less(0,$product(2,a)) )
<=> ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ) ),
inference(monotonicity,[status(thm)],[40,34]) ).
tff(42,plain,
( ( $greater(8,$difference($product(2,a),$product(4,b)))
| $less(0,$product(2,a)) )
<=> ( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ) ),
inference(transitivity,[status(thm)],[41,27]) ).
tff(43,axiom,
( $greater(8,$difference($product(2,a),$product(4,b)))
| $less(0,$product(2,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(44,plain,
( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ),
inference(modus_ponens,[status(thm)],[44,27]) ).
tff(46,plain,
( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ),
inference(modus_ponens,[status(thm)],[45,27]) ).
tff(47,plain,
( ~ $lesseq(8,$sum($product(2,a),$product(-4,b)))
| ~ $lesseq(a,0) ),
inference(modus_ponens,[status(thm)],[46,31]) ).
tff(48,plain,
( ~ $lesseq(a,0)
| ~ $greatereq($sum($product(2,a),$product(-4,b)),8) ),
inference(modus_ponens,[status(thm)],[47,26]) ).
tff(49,plain,
( ~ $lesseq(a,0)
| ~ $greatereq($sum(a,$product(-2,b)),4) ),
inference(modus_ponens,[status(thm)],[48,22]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,21,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI648_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 01:24:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.22/0.39 % SZS status Theorem
% 0.22/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------