TSTP Solution File: ARI680_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI680_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 17:02:34 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 38 ( 17 unt; 3 typ; 0 def)
% Number of atoms : 54 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 30 ~; 2 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 212 ( 52 atm; 71 fun; 89 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 : 11 ( 3 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(y_type,type,
y: $int ).
tff(x_type,type,
x: $int ).
tff(a_type,type,
a: $int ).
tff(1,plain,
( ~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a)))
<=> ~ $greatereq($sum($product(7,a),$product(3,$product(x,y))),4) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a)))
<=> ~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( $greater(4,$sum($product(3,$product(x,y)),$product(7,a)))
<=> ~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
$sum($product($product(3,x),y),$product(7,a)) = $sum($product(3,$product(x,y)),$product(7,a)),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( $greater(4,$sum($product($product(3,x),y),$product(7,a)))
<=> $greater(4,$sum($product(3,$product(x,y)),$product(7,a))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( $greater(4,$sum($product($product(3,x),y),$product(7,a)))
<=> ~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a))) ),
inference(transitivity,[status(thm)],[5,3]) ).
tff(7,axiom,
$greater(4,$sum($product($product(3,x),y),$product(7,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(8,plain,
~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a))),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
~ $lesseq(4,$sum($product(3,$product(x,y)),$product(7,a))),
inference(modus_ponens,[status(thm)],[8,2]) ).
tff(10,plain,
~ $greatereq($sum($product(7,a),$product(3,$product(x,y))),4),
inference(modus_ponens,[status(thm)],[9,1]) ).
tff(11,plain,
( $lesseq(0,a)
<=> $greatereq(a,0) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( $lesseq(0,a)
<=> $lesseq(0,a) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ ~ $lesseq(0,a)
<=> $lesseq(0,a) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( $greater(0,a)
<=> ~ $lesseq(0,a) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ $greater(0,a)
<=> ~ ~ $lesseq(0,a) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ $greater(0,a)
<=> $lesseq(0,a) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,axiom,
~ $greater(0,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_003) ).
tff(18,plain,
$lesseq(0,a),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
$lesseq(0,a),
inference(modus_ponens,[status(thm)],[18,12]) ).
tff(20,plain,
$greatereq(a,0),
inference(modus_ponens,[status(thm)],[19,11]) ).
tff(21,plain,
( ~ $lesseq(y,1)
<=> ~ $lesseq(y,1) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( $less(1,y)
<=> ~ $lesseq(y,1) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
$less(1,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(24,plain,
~ $lesseq(y,1),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ $lesseq(y,1),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
( ~ $lesseq(x,1)
<=> ~ $lesseq(x,1) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ $lesseq($product(2,x),3)
<=> ~ $lesseq(x,1) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( $less(3,$product(2,x))
<=> ~ $lesseq($product(2,x),3) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( $less(3,$product(2,x))
<=> ~ $lesseq(x,1) ),
inference(transitivity,[status(thm)],[28,27]) ).
tff(30,axiom,
$less(3,$product(2,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(31,plain,
~ $lesseq(x,1),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ $lesseq(x,1),
inference(modus_ponens,[status(thm)],[31,26]) ).
tff(33,plain,
( $greatereq($product(x,y),4)
| $lesseq(x,1)
| $lesseq(y,1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(34,plain,
$greatereq($product(x,y),4),
inference(unit_resolution,[status(thm)],[33,32,25]) ).
tff(35,plain,
$false,
inference(theory_lemma,[status(thm)],[34,20,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI680_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 01:57:15 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.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------