TSTP Solution File: ARI607_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI607_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 0.14s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of formulae : 71 ( 20 unt; 1 typ; 0 def)
% Number of atoms : 188 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 202 ( 87 ~; 70 |; 0 &)
% ( 41 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number arithmetic : 1014 ( 160 atm; 300 fun; 480 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 : 12 ( 1 usr; 9 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)) )
=> $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) )
<=> ~ ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
| $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ ( ! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> $lesseq(f(X),f(Y)) )
=> $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_mon_implies_f2plusf5_gt_f7plusf3) ).
tff(10,plain,
~ ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq(X,Y)
| $lesseq(f(X),f(Y)) )
| $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
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(3))),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(3))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( $false
| $lesseq($sum(f(2),$product(-1,f(3))),0) )
<=> $lesseq($sum(f(2),$product(-1,f(3))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( $greatereq($sum($product(-1,f(2)),f(3)),0)
<=> $lesseq($sum(f(2),$product(-1,f(3))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
$sum(f(3),$product(-1,f(2))) = $sum($product(-1,f(2)),f(3)),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( $greatereq($sum(f(3),$product(-1,f(2))),0)
<=> $greatereq($sum($product(-1,f(2)),f(3)),0) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( $greatereq($sum(f(3),$product(-1,f(2))),0)
<=> $lesseq($sum(f(2),$product(-1,f(3))),0) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( $lesseq(-1,0)
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
$sum(2,-3) = -1,
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
$product(-1,3) = -3,
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
$sum(2,$product(-1,3)) = $sum(2,-3),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
$sum(2,$product(-1,3)) = -1,
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( $lesseq($sum(2,$product(-1,3)),0)
<=> $lesseq(-1,0) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( $lesseq($sum(2,$product(-1,3)),0)
<=> $true ),
inference(transitivity,[status(thm)],[29,24]) ).
tff(31,plain,
( ~ $lesseq($sum(2,$product(-1,3)),0)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ~ $lesseq($sum(2,$product(-1,3)),0)
<=> $false ),
inference(transitivity,[status(thm)],[31,23]) ).
tff(33,plain,
( ( ~ $lesseq($sum(2,$product(-1,3)),0)
| $greatereq($sum(f(3),$product(-1,f(2))),0) )
<=> ( $false
| $lesseq($sum(f(2),$product(-1,f(3))),0) ) ),
inference(monotonicity,[status(thm)],[32,22]) ).
tff(34,plain,
( ( ~ $lesseq($sum(2,$product(-1,3)),0)
| $greatereq($sum(f(3),$product(-1,f(2))),0) )
<=> $lesseq($sum(f(2),$product(-1,f(3))),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(-1,3)),0)
| $greatereq($sum(f(3),$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(3))),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(-1,3)),0)
| $greatereq($sum(f(3),$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(3))),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(-1,3)),0)
| $greatereq($sum(f(3),$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(3))),0) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$lesseq($sum(f(2),$product(-1,f(3))),0),
inference(unit_resolution,[status(thm)],[38,16]) ).
tff(40,plain,
( ~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3)))
<=> ~ $lesseq($sum(f(2),$sum(f(5),$sum($product(-1,f(7)),$product(-1,f(3))))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( $lesseq($sum(f(2),f(5)),$sum(f(7),f(3)))
<=> $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3)))
<=> ~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3)))
<=> ~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))),
inference(or_elim,[status(thm)],[10]) ).
tff(45,plain,
~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
~ $lesseq($sum(f(2),$sum(f(5),$sum($product(-1,f(7)),$product(-1,f(3))))),0),
inference(modus_ponens,[status(thm)],[46,40]) ).
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(5),$product(-1,f(7))),0) )
<=> ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(5),$product(-1,f(7))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( $false
| $lesseq($sum(f(5),$product(-1,f(7))),0) )
<=> $lesseq($sum(f(5),$product(-1,f(7))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( $greatereq($sum($product(-1,f(5)),f(7)),0)
<=> $lesseq($sum(f(5),$product(-1,f(7))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
$sum(f(7),$product(-1,f(5))) = $sum($product(-1,f(5)),f(7)),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( $greatereq($sum(f(7),$product(-1,f(5))),0)
<=> $greatereq($sum($product(-1,f(5)),f(7)),0) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( $greatereq($sum(f(7),$product(-1,f(5))),0)
<=> $lesseq($sum(f(5),$product(-1,f(7))),0) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( $lesseq(-2,0)
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
$sum(5,-7) = -2,
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
$product(-1,7) = -7,
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
$sum(5,$product(-1,7)) = $sum(5,-7),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
$sum(5,$product(-1,7)) = -2,
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( $lesseq($sum(5,$product(-1,7)),0)
<=> $lesseq(-2,0) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( $lesseq($sum(5,$product(-1,7)),0)
<=> $true ),
inference(transitivity,[status(thm)],[59,54]) ).
tff(61,plain,
( ~ $lesseq($sum(5,$product(-1,7)),0)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ~ $lesseq($sum(5,$product(-1,7)),0)
<=> $false ),
inference(transitivity,[status(thm)],[61,23]) ).
tff(63,plain,
( ( ~ $lesseq($sum(5,$product(-1,7)),0)
| $greatereq($sum(f(7),$product(-1,f(5))),0) )
<=> ( $false
| $lesseq($sum(f(5),$product(-1,f(7))),0) ) ),
inference(monotonicity,[status(thm)],[62,53]) ).
tff(64,plain,
( ( ~ $lesseq($sum(5,$product(-1,7)),0)
| $greatereq($sum(f(7),$product(-1,f(5))),0) )
<=> $lesseq($sum(f(5),$product(-1,f(7))),0) ),
inference(transitivity,[status(thm)],[63,49]) ).
tff(65,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(5,$product(-1,7)),0)
| $greatereq($sum(f(7),$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(5),$product(-1,f(7))),0) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(5,$product(-1,7)),0)
| $greatereq($sum(f(7),$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(5),$product(-1,f(7))),0) ) ),
inference(transitivity,[status(thm)],[65,48]) ).
tff(67,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| ~ $lesseq($sum(5,$product(-1,7)),0)
| $greatereq($sum(f(7),$product(-1,f(5))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X: $int,Y: $int] :
( ~ $lesseq($sum(X,$product(-1,Y)),0)
| $greatereq($sum(f(Y),$product(-1,f(X))),0) )
| $lesseq($sum(f(5),$product(-1,f(7))),0) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
$lesseq($sum(f(5),$product(-1,f(7))),0),
inference(unit_resolution,[status(thm)],[68,16]) ).
tff(70,plain,
$false,
inference(theory_lemma,[status(thm)],[69,47,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : ARI607_1 : TPTP v8.1.0. Released v5.1.0.
% 0.09/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 00:50:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------