TSTP Solution File: ARI675_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI675_1 : TPTP v8.1.0. Released v6.3.0.
% 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 6 17:02:33 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 11 ( 7 unt; 1 typ; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 10 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 82 ( 12 atm; 56 fun; 14 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 : 6 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $int ).
tff(1,plain,
( ~ $lesseq(-10,$sum($product(a,$product(a,$product(a,a))),$product(a,a)))
<=> ~ $greatereq($sum($product(a,a),$product(a,$product(a,$product(a,a)))),-10) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $lesseq(-10,$sum($product(a,$product(a,$product(a,a))),$product(a,a)))
<=> ~ $lesseq(-10,$sum($product(a,$product(a,$product(a,a))),$product(a,a))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ $lesseq(0,$sum($sum($product($product($product(a,a),a),a),$product(a,a)),10))
<=> ~ $lesseq(-10,$sum($product(a,$product(a,$product(a,a))),$product(a,a))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
~ $lesseq(0,$sum($sum($product($product($product(a,a),a),a),$product(a,a)),10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(5,plain,
~ $lesseq(-10,$sum($product(a,$product(a,$product(a,a))),$product(a,a))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
~ $lesseq(-10,$sum($product(a,$product(a,$product(a,a))),$product(a,a))),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
~ $greatereq($sum($product(a,a),$product(a,$product(a,$product(a,a)))),-10),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
$greatereq($product(a,a),0),
inference(theory_lemma,[status(thm)],]) ).
tff(9,plain,
$greatereq($product(a,$product(a,$product(a,a))),0),
inference(theory_lemma,[status(thm)],]) ).
tff(10,plain,
$false,
inference(theory_lemma,[status(thm)],[9,8,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI675_1 : TPTP v8.1.0. Released v6.3.0.
% 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 : Tue Aug 30 01:31:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------