TSTP Solution File: ARI602_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI602_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 17:02:14 EDT 2022
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% 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 : 162 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 237 ( 139 ~; 40 |; 27 &)
% ( 29 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number arithmetic : 614 ( 149 atm; 126 fun; 276 num; 63 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 38 !; 20 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $int > $int ).
tff(1,plain,
^ [Y: $int] :
trans(
monotonicity(
rewrite(
( ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) )
<=> ~ ( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) ) )),
( ~ ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) )
<=> ~ ~ ( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) ) )),
rewrite(
( ~ ~ ( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
<=> ( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) ) )),
( ~ ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) )
<=> ( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $int] :
~ ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) )
<=> ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) )
<=> ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq($sum(f(5),$product(-1,Y)),0) )
<=> ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) )
<=> ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq($sum(f(5),$product(-1,Y)),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) )
<=> ~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ~ ( ! [X: $int] : $greater(f(X),X)
=> ? [Y: $int] :
( $less(4,Y)
& $less(Y,f(5)) ) )
<=> ~ ( ~ ! [X: $int] : ~ $lesseq(f(X),X)
| ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
~ ( ! [X: $int] : $greater(f(X),X)
=> ? [Y: $int] :
( $less(4,Y)
& $less(Y,f(5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_exist_ineq) ).
tff(9,plain,
~ ( ~ ! [X: $int] : ~ $lesseq(f(X),X)
| ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ),
inference(or_elim,[status(thm)],[9]) ).
tff(11,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq(f(5),Y) ),
inference(modus_ponens,[status(thm)],[12,6]) ).
tff(14,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $lesseq($sum(f(5),$product(-1,Y)),0) ),
inference(modus_ponens,[status(thm)],[13,5]) ).
tff(15,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ),
inference(modus_ponens,[status(thm)],[15,3]) ).
tff(17,plain,
~ ? [Y: $int] :
( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ),
inference(modus_ponens,[status(thm)],[16,3]) ).
tff(18,plain,
^ [Y: $int] :
refl(
$oeq(
~ ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ),
~ ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ))),
inference(bind,[status(th)],]) ).
tff(19,plain,
! [Y: $int] :
~ ( ~ $lesseq(Y,4)
& ~ $greatereq($sum(Y,$product(-1,f(5))),0) ),
inference(nnf-neg,[status(sab)],[17,18]) ).
tff(20,plain,
! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) ),
inference(modus_ponens,[status(thm)],[19,2]) ).
tff(21,plain,
( ( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(f(5),5) )
<=> ( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(f(5),5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( $false
| $lesseq(f(5),5) )
<=> $lesseq(f(5),5) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( $greatereq($sum(5,$product(-1,f(5))),0)
<=> $lesseq(f(5),5) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( $lesseq(5,4)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( $lesseq(5,4)
| $greatereq($sum(5,$product(-1,f(5))),0) )
<=> ( $false
| $lesseq(f(5),5) ) ),
inference(monotonicity,[status(thm)],[24,23]) ).
tff(26,plain,
( ( $lesseq(5,4)
| $greatereq($sum(5,$product(-1,f(5))),0) )
<=> $lesseq(f(5),5) ),
inference(transitivity,[status(thm)],[25,22]) ).
tff(27,plain,
( ( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(5,4)
| $greatereq($sum(5,$product(-1,f(5))),0) )
<=> ( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(f(5),5) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(5,4)
| $greatereq($sum(5,$product(-1,f(5))),0) )
<=> ( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(f(5),5) ) ),
inference(transitivity,[status(thm)],[27,21]) ).
tff(29,plain,
( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(5,4)
| $greatereq($sum(5,$product(-1,f(5))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Y: $int] :
( $lesseq(Y,4)
| $greatereq($sum(Y,$product(-1,f(5))),0) )
| $lesseq(f(5),5) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$lesseq(f(5),5),
inference(unit_resolution,[status(thm)],[30,20]) ).
tff(32,plain,
^ [X: $int] :
refl(
( ~ $greatereq($sum(X,$product(-1,f(X))),0)
<=> ~ $greatereq($sum(X,$product(-1,f(X))),0) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
<=> ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [X: $int] :
rewrite(
( ~ $lesseq($sum(f(X),$product(-1,X)),0)
<=> ~ $greatereq($sum(X,$product(-1,f(X))),0) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X: $int] : ~ $lesseq($sum(f(X),$product(-1,X)),0)
<=> ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [X: $int] :
rewrite(
( ~ $lesseq(f(X),X)
<=> ~ $lesseq($sum(f(X),$product(-1,X)),0) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X: $int] : ~ $lesseq(f(X),X)
<=> ! [X: $int] : ~ $lesseq($sum(f(X),$product(-1,X)),0) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $int] : ~ $lesseq(f(X),X)
<=> ! [X: $int] : ~ $lesseq(f(X),X) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
! [X: $int] : ~ $lesseq(f(X),X),
inference(or_elim,[status(thm)],[9]) ).
tff(40,plain,
! [X: $int] : ~ $lesseq(f(X),X),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X: $int] : ~ $lesseq($sum(f(X),$product(-1,X)),0),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0),
inference(modus_ponens,[status(thm)],[41,35]) ).
tff(43,plain,
! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0),
inference(modus_ponens,[status(thm)],[43,33]) ).
tff(45,plain,
( ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $lesseq(f(5),5) )
<=> ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $lesseq(f(5),5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ $greatereq($sum(5,$product(-1,f(5))),0)
<=> ~ $lesseq(f(5),5) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(5,$product(-1,f(5))),0) )
<=> ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $lesseq(f(5),5) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(5,$product(-1,f(5))),0) )
<=> ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $lesseq(f(5),5) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(5,$product(-1,f(5))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $lesseq(f(5),5) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,44,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ARI602_1 : TPTP v8.1.0. Released v5.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 00:56:28 EDT 2022
% 0.14/0.34 % 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.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------