TSTP Solution File: ARI629_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI629_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 17:02:22 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 12 ( 6 unt; 2 typ; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 1 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 77 ( 13 atm; 43 fun; 21 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(y_type,type,
y: $real ).
tff(x_type,type,
x: $real ).
tff(1,plain,
( ~ $greatereq($product(x,$sum(1,$product(y,y))),$sum(1,$product(y,y)))
<=> ~ $greatereq($sum(x,$sum($product(-1,$product(y,y)),$product(x,$product(y,y)))),1) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $greatereq($product($sum(1,$product(y,y)),x),$sum(1,$product(y,y)))
<=> ~ $greatereq($product(x,$sum(1,$product(y,y))),$sum(1,$product(y,y))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ $greatereq($product($sum(1,$product(y,y)),x),$sum(1,$product(y,y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(4,plain,
~ $greatereq($product(x,$sum(1,$product(y,y))),$sum(1,$product(y,y))),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ $greatereq($sum(x,$sum($product(-1,$product(y,y)),$product(x,$product(y,y)))),1),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( $greater(x,1)
<=> ~ $lesseq(x,1) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
$greater(x,1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(8,plain,
~ $lesseq(x,1),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
( $lesseq(x,1)
| $greatereq($sum(x,$sum($product(-1,$product(y,y)),$product(x,$product(y,y)))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(10,plain,
$false,
inference(unit_resolution,[status(thm)],[9,8,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI629_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 : n010.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 00:55:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -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
%------------------------------------------------------------------------------