TSTP Solution File: ARI655_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI655_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 17:02:28 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of formulae : 25 ( 12 unt; 4 typ; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 2 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 182 ( 30 atm; 102 fun; 50 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $int ).
tff(b_type,type,
b: $int ).
tff(d_type,type,
d: $int ).
tff(a_type,type,
a: $int ).
tff(1,plain,
( ~ $lesseq(0,$sum($product(a,c),$sum($product(-1,$product(b,c)),$sum($product(-1,$product(a,d)),$product(b,d)))))
<=> ~ $greatereq($sum($product(a,c),$sum($product(b,d),$sum($product(-1,$product(a,d)),$product(-1,$product(b,c))))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $lesseq(0,$product($sum(a,$product(-1,b)),$sum(c,$product(-1,d))))
<=> ~ $lesseq(0,$sum($product(a,c),$sum($product(-1,$product(b,c)),$sum($product(-1,$product(a,d)),$product(b,d))))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ $lesseq(0,$product($sum(a,$product(-1,b)),$sum(c,$product(-1,d))))
<=> ~ $lesseq(0,$product($sum(a,$product(-1,b)),$sum(c,$product(-1,d)))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ $lesseq(0,$product($difference(a,b),$difference(c,d)))
<=> ~ $lesseq(0,$product($sum(a,$product(-1,b)),$sum(c,$product(-1,d)))) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ $lesseq(0,$product($difference(a,b),$difference(c,d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(6,plain,
~ $lesseq(0,$product($sum(a,$product(-1,b)),$sum(c,$product(-1,d)))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
~ $lesseq(0,$product($sum(a,$product(-1,b)),$sum(c,$product(-1,d)))),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
~ $lesseq(0,$sum($product(a,c),$sum($product(-1,$product(b,c)),$sum($product(-1,$product(a,d)),$product(b,d))))),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
~ $greatereq($sum($product(a,c),$sum($product(b,d),$sum($product(-1,$product(a,d)),$product(-1,$product(b,c))))),0),
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
( $lesseq(d,c)
<=> $lesseq($sum(d,$product(-1,c)),0) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( $lesseq(d,c)
<=> $lesseq(d,c) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
$lesseq(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(13,plain,
$lesseq(d,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
$lesseq($sum(d,$product(-1,c)),0),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
( $lesseq(b,a)
<=> $lesseq($sum(b,$product(-1,a)),0) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( $lesseq(b,a)
<=> $lesseq(b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
$lesseq(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(18,plain,
$lesseq(b,a),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
$lesseq($sum(b,$product(-1,a)),0),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( ~ $lesseq($sum(b,$product(-1,a)),0)
| ~ $lesseq($sum(d,$product(-1,c)),0)
| $greatereq($sum($product(a,c),$sum($product(b,d),$sum($product(-1,$product(a,d)),$product(-1,$product(b,c))))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(21,plain,
$false,
inference(unit_resolution,[status(thm)],[20,19,14,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ARI655_1 : TPTP v8.1.0. Released v6.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 : Tue Aug 30 01:20:10 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------