TSTP Solution File: ARI606_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI606_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 17:02:15 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 52 ( 13 unt; 1 typ; 0 def)
% Number of atoms : 160 ( 5 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 192 ( 86 ~; 73 |; 0 &)
% ( 29 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number arithmetic : 823 ( 143 atm; 235 fun; 371 num; 74 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 1 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 68 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $int > $int ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[3]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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(8,plain,
( ~ ( ! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> $lesseq(f(X),f(Y)) )
=> $lesseq(f(f(2)),f(f(5))) )
<=> ~ ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
| $lesseq(f(f(2)),f(f(5))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ ( ! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> $lesseq(f(X),f(Y)) )
=> $lesseq(f(f(2)),f(f(5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_ff2_gt_ff5) ).
tff(10,plain,
~ ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
| $lesseq(f(f(2)),f(f(5))) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) ),
inference(or_elim,[status(thm)],[10]) ).
tff(12,plain,
! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,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)],[12,6]) ).
tff(14,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)],[13,4]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,2]) ).
tff(17,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(2),$product(-1,f(5))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(2),$product(-1,f(5))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( $false
| $lesseq($sum(f(2),$product(-1,f(5))),0) )
<=> $lesseq($sum(f(2),$product(-1,f(5))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( $greatereq($sum($product(-1,f(2)),f(5)),0)
<=> $lesseq($sum(f(2),$product(-1,f(5))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
$sum(f(5),$product(-1,f(2))) = $sum($product(-1,f(2)),f(5)),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( $greatereq($sum(f(5),$product(-1,f(2))),0)
<=> $greatereq($sum($product(-1,f(2)),f(5)),0) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( $greatereq($sum(f(5),$product(-1,f(2))),0)
<=> $lesseq($sum(f(2),$product(-1,f(5))),0) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( $lesseq(-3,0)
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
$sum(2,-5) = -3,
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
$product(-1,5) = -5,
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
$sum(2,$product(-1,5)) = $sum(2,-5),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
$sum(2,$product(-1,5)) = -3,
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( $lesseq($sum(2,$product(-1,5)),0)
<=> $lesseq(-3,0) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( $lesseq($sum(2,$product(-1,5)),0)
<=> $true ),
inference(transitivity,[status(thm)],[29,24]) ).
tff(31,plain,
( ~ $lesseq($sum(2,$product(-1,5)),0)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ~ $lesseq($sum(2,$product(-1,5)),0)
<=> $false ),
inference(transitivity,[status(thm)],[31,23]) ).
tff(33,plain,
( ( ~ $lesseq($sum(2,$product(-1,5)),0)
| $greatereq($sum(f(5),$product(-1,f(2))),0) )
<=> ( $false
| $lesseq($sum(f(2),$product(-1,f(5))),0) ) ),
inference(monotonicity,[status(thm)],[32,22]) ).
tff(34,plain,
( ( ~ $lesseq($sum(2,$product(-1,5)),0)
| $greatereq($sum(f(5),$product(-1,f(2))),0) )
<=> $lesseq($sum(f(2),$product(-1,f(5))),0) ),
inference(transitivity,[status(thm)],[33,18]) ).
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(2,$product(-1,5)),0)
| $greatereq($sum(f(5),$product(-1,f(2))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(2),$product(-1,f(5))),0) ) ),
inference(monotonicity,[status(thm)],[34]) ).
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(2,$product(-1,5)),0)
| $greatereq($sum(f(5),$product(-1,f(2))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(2),$product(-1,f(5))),0) ) ),
inference(transitivity,[status(thm)],[35,17]) ).
tff(37,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(2,$product(-1,5)),0)
| $greatereq($sum(f(5),$product(-1,f(2))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(2),$product(-1,f(5))),0) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$lesseq($sum(f(2),$product(-1,f(5))),0),
inference(unit_resolution,[status(thm)],[38,16]) ).
tff(40,plain,
( ~ $lesseq(f(f(2)),f(f(5)))
<=> ~ $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ $lesseq(f(f(2)),f(f(5)))
<=> ~ $lesseq(f(f(2)),f(f(5))) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
~ $lesseq(f(f(2)),f(f(5))),
inference(or_elim,[status(thm)],[10]) ).
tff(43,plain,
~ $lesseq(f(f(2)),f(f(5))),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0),
inference(modus_ponens,[status(thm)],[43,40]) ).
tff(45,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $greatereq($sum(f(f(5)),$product(-1,f(f(2)))),0) )
<=> ( ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $greatereq($sum(f(f(5)),$product(-1,f(f(2)))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $greatereq($sum(f(f(5)),$product(-1,f(f(2)))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $greatereq($sum(f(f(5)),$product(-1,f(f(2)))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(f(2),$product(-1,f(5))),0)
| $lesseq($sum(f(f(2)),$product(-1,f(f(5)))),0) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,16,44,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI606_1 : TPTP v8.1.0. Released v5.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 01:08:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------