TSTP Solution File: ARI609_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI609_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 17:02:16 EDT 2022
% Result : Theorem 0.15s 0.34s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 41 ( 12 unt; 3 typ; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 143 ( 65 ~; 51 |; 5 &)
% ( 18 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number arithmetic : 543 ( 115 atm; 186 fun; 182 num; 60 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $int > $int ).
tff(b_type,type,
b: $int ).
tff(a_type,type,
a: $int ).
tff(1,plain,
( ~ $lesseq(0,$sum(f(a),$product(-1,f(b))))
<=> ~ $greatereq($sum(f(a),$product(-1,f(b))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( $lesseq(0,$sum(f(a),$product(-1,f(b))))
<=> $lesseq(0,$sum(f(a),$product(-1,f(b)))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ $lesseq(0,$sum(f(a),$product(-1,f(b))))
<=> ~ $lesseq(0,$sum(f(a),$product(-1,f(b)))) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ~ $lesseq(0,$sum(f(a),$product(-1,f(b))))
<=> ~ $lesseq(0,$sum(f(a),$product(-1,f(b)))) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ~ ( ( ! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> $lesseq(f(X),f(Y)) )
& $lesseq(0,$sum(a,$uminus(b))) )
=> $lesseq(0,$sum(f(a),$uminus(f(b)))) )
<=> ~ ( ~ ( ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
& $lesseq(0,$sum(a,$product(-1,b))) )
| $lesseq(0,$sum(f(a),$product(-1,f(b)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ ( ( ! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> $lesseq(f(X),f(Y)) )
& $lesseq(0,$sum(a,$uminus(b))) )
=> $lesseq(0,$sum(f(a),$uminus(f(b)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_f_a_b_1) ).
tff(7,plain,
~ ( ~ ( ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
& $lesseq(0,$sum(a,$product(-1,b))) )
| $lesseq(0,$sum(f(a),$product(-1,f(b)))) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
~ $lesseq(0,$sum(f(a),$product(-1,f(b)))),
inference(or_elim,[status(thm)],[7]) ).
tff(9,plain,
~ $lesseq(0,$sum(f(a),$product(-1,f(b)))),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
~ $lesseq(0,$sum(f(a),$product(-1,f(b)))),
inference(modus_ponens,[status(thm)],[9,3]) ).
tff(11,plain,
~ $greatereq($sum(f(a),$product(-1,f(b))),0),
inference(modus_ponens,[status(thm)],[10,1]) ).
tff(12,plain,
( $lesseq(0,$sum(a,$product(-1,b)))
<=> $greatereq($sum(a,$product(-1,b)),0) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( $lesseq(0,$sum(a,$product(-1,b)))
<=> $lesseq(0,$sum(a,$product(-1,b))) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
& $lesseq(0,$sum(a,$product(-1,b))) ),
inference(or_elim,[status(thm)],[7]) ).
tff(15,plain,
$lesseq(0,$sum(a,$product(-1,b))),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
$lesseq(0,$sum(a,$product(-1,b))),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
$lesseq(0,$sum(a,$product(-1,b))),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
$greatereq($sum(a,$product(-1,b)),0),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
^ [X: $int,Y: $int] :
refl(
( ( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
<=> ( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
<=> ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [X: $int,Y: $int] :
rewrite(
( ( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $lesseq($sum(f(X),$product(-1,f(Y))),0) )
<=> ( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $lesseq($sum(f(X),$product(-1,f(Y))),0) )
<=> ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
^ [X: $int,Y: $int] :
rewrite(
( ( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
<=> ( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $lesseq($sum(f(X),$product(-1,f(Y))),0) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
<=> ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $lesseq($sum(f(X),$product(-1,f(Y))),0) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
<=> ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) ),
inference(and_elim,[status(thm)],[14]) ).
tff(27,plain,
! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $lesseq($sum(f(X),$product(-1,f(Y))),0) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ),
inference(modus_ponens,[status(thm)],[28,22]) ).
tff(30,plain,
! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $greatereq($sum(a,$product(-1,b)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $greatereq($sum(a,$product(-1,b)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ $lesseq($sum(b,$product(-1,a)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) )
<=> ( ~ $greatereq($sum(a,$product(-1,b)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(b,$product(-1,a)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $greatereq($sum(a,$product(-1,b)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(b,$product(-1,a)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $greatereq($sum(a,$product(-1,b)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(b,$product(-1,a)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $greatereq($sum(a,$product(-1,b)),0)
| $greatereq($sum(f(a),$product(-1,f(b))),0) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,31,18,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : ARI609_1 : TPTP v8.1.0. Released v5.1.0.
% 0.04/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 30 00:52:10 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.15/0.34 % SZS status Theorem
% 0.15/0.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------