TSTP Solution File: ARI639_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI639_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 17:02:24 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 66 ( 34 unt; 5 typ; 0 def)
% Number of atoms : 98 ( 18 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 79 ( 42 ~; 20 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 788 ( 79 atm; 402 fun; 307 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 : 16 ( 5 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(n_type,type,
n: $real ).
tff(c_type,type,
c: $real ).
tff(eps_type,type,
eps: $real ).
tff(x_type,type,
x: $real ).
tff(k_type,type,
k: $real ).
tff(1,axiom,
$greatereq(n,0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(2,plain,
( $lesseq($product(k,x),$sum(n,$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c)))))))
<=> $greatereq($sum(n,$sum($product(-1,$product(k,x)),$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c))))))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
$sum($product(n,1),$product(n,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))) = $sum(n,$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c)))))),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))) = $sum($product(n,1),$product(n,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))) = $sum(n,$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c)))))),
inference(transitivity,[status(thm)],[4,3]) ).
tff(6,plain,
( $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))))
<=> $lesseq($product(k,x),$sum(n,$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c))))))) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))))
<=> $greatereq($sum(n,$sum($product(-1,$product(k,x)),$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c))))))),0) ),
inference(transitivity,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ~ $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))))
<=> $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( $less($product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))),$product(k,x))
<=> ~ $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
$product($sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))),n) = $product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
$sum($product(1/3,$product(eps,$quotient(1,$sum(3,c)))),1) = $sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
$product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)) = $product(1/3,$product(eps,$quotient(1,$sum(3,c)))),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
$sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1) = $sum($product(1/3,$product(eps,$quotient(1,$sum(3,c)))),1),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
$sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1) = $sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
$product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n) = $product($sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))),n),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
$product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n) = $product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))),
inference(transitivity,[status(thm)],[15,10]) ).
tff(17,plain,
( $less($product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n),$product(k,x))
<=> $less($product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c)))))),$product(k,x)) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( $less($product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n),$product(k,x))
<=> ~ $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))))) ),
inference(transitivity,[status(thm)],[17,9]) ).
tff(19,plain,
( ~ $less($product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n),$product(k,x))
<=> ~ ~ $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))))) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ $less($product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n),$product(k,x))
<=> $lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))))) ),
inference(transitivity,[status(thm)],[19,8]) ).
tff(21,axiom,
~ $less($product($sum($product($quotient(1,3),$product($quotient(1,$sum(3,c)),eps)),1),n),$product(k,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(22,plain,
$lesseq($product(k,x),$product(n,$sum(1,$product(1/3,$product(eps,$quotient(1,$sum(3,c))))))),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$greatereq($sum(n,$sum($product(-1,$product(k,x)),$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c))))))),0),
inference(modus_ponens,[status(thm)],[22,7]) ).
tff(24,plain,
( ~ $lesseq($product(1/2,$product(k,x)),n)
<=> ~ $greatereq($sum(n,$product(-1/2,$product(k,x))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( $less(n,$product(1/2,$product(k,x)))
<=> ~ $lesseq($product(1/2,$product(k,x)),n) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
$product($quotient(1,2),$product(k,x)) = $product(1/2,$product(k,x)),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( $less(n,$product($quotient(1,2),$product(k,x)))
<=> $less(n,$product(1/2,$product(k,x))) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( $less(n,$product($quotient(1,2),$product(k,x)))
<=> ~ $lesseq($product(1/2,$product(k,x)),n) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,axiom,
$less(n,$product($quotient(1,2),$product(k,x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).
tff(30,plain,
~ $lesseq($product(1/2,$product(k,x)),n),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ $greatereq($sum(n,$product(-1/2,$product(k,x))),0),
inference(modus_ponens,[status(thm)],[30,24]) ).
tff(32,plain,
( ~ $greatereq(n,0)
| ~ $greatereq($sum(n,$sum($product(-1,$product(k,x)),$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c))))))),0)
| $greatereq($sum(n,$product(-1/2,$product(k,x))),0)
| ~ $lesseq($product(n,$product(eps,$quotient(1,$sum(3,c)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(33,plain,
~ $lesseq($product(n,$product(eps,$quotient(1,$sum(3,c)))),0),
inference(unit_resolution,[status(thm)],[32,31,23,1]) ).
tff(34,plain,
( $greater(c,0)
<=> ~ $lesseq(c,0) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
$greater(c,0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_02) ).
tff(36,plain,
~ $lesseq(c,0),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( $lesseq(c,0)
| ~ $lesseq($sum(3,c),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(38,plain,
~ $lesseq($sum(3,c),0),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
( ( 0 != $sum(3,c) )
| $lesseq($sum(3,c),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(40,plain,
0 != $sum(3,c),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ( 0 = $sum(3,c) )
| ( 1 = $product($sum(3,c),$quotient(1,$sum(3,c))) ) ),
inference(theory_lemma,[status(thm)],]) ).
tff(42,plain,
1 = $product($sum(3,c),$quotient(1,$sum(3,c))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ( 1 != $product($sum(3,c),$quotient(1,$sum(3,c))) )
| $greatereq($product($sum(3,c),$quotient(1,$sum(3,c))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(44,plain,
$greatereq($product($sum(3,c),$quotient(1,$sum(3,c))),1),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ $lesseq($quotient(1,$sum(3,c)),0)
| ~ $greatereq($product($sum(3,c),$quotient(1,$sum(3,c))),1)
| $lesseq($sum(3,c),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(46,plain,
~ $lesseq($quotient(1,$sum(3,c)),0),
inference(unit_resolution,[status(thm)],[45,38,44]) ).
tff(47,plain,
( $greater(eps,0)
<=> ~ $lesseq(eps,0) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
$greater(eps,0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_03) ).
tff(49,plain,
~ $lesseq(eps,0),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ $lesseq(n,0)
| $lesseq(eps,0)
| $lesseq($quotient(1,$sum(3,c)),0)
| $lesseq($product(n,$product(eps,$quotient(1,$sum(3,c)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(51,plain,
( ~ $lesseq(n,0)
| $lesseq($product(n,$product(eps,$quotient(1,$sum(3,c)))),0) ),
inference(unit_resolution,[status(thm)],[50,49,46]) ).
tff(52,plain,
~ $lesseq(n,0),
inference(unit_resolution,[status(thm)],[51,33]) ).
tff(53,plain,
( ( 1 != $product($sum(3,c),$quotient(1,$sum(3,c))) )
| $lesseq($product($sum(3,c),$quotient(1,$sum(3,c))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(54,plain,
$lesseq($product($sum(3,c),$quotient(1,$sum(3,c))),1),
inference(unit_resolution,[status(thm)],[53,42]) ).
tff(55,plain,
( ~ $lesseq(1,eps)
<=> ~ $greatereq(eps,1) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( $less(eps,1)
<=> ~ $lesseq(1,eps) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
$less(eps,1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_04) ).
tff(58,plain,
~ $lesseq(1,eps),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ $greatereq(eps,1),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
( $lesseq($quotient(1,$sum(3,c)),0)
| $greatereq(eps,1)
| ~ $lesseq($product($sum(3,c),$quotient(1,$sum(3,c))),1)
| $lesseq(n,0)
| $greatereq($sum(n,$product(-1/2,$product(k,x))),0)
| $lesseq(c,0)
| ~ $greatereq($sum(n,$sum($product(-1,$product(k,x)),$product(1/3,$product(n,$product(eps,$quotient(1,$sum(3,c))))))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,31,36,59,23,54,46,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI639_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 01:11:05 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.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------