TSTP Solution File: ARI601_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI601_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 17:02:14 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 35 ( 17 unt; 2 typ; 0 def)
% Number of atoms : 67 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 61 ~; 12 |; 0 &)
% ( 15 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number arithmetic : 298 ( 62 atm; 94 fun; 113 num; 29 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 26 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $int > $int ).
tff(a_type,type,
a: $int ).
tff(1,plain,
f($sum(1,a)) = f($sum(1,a)),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( $lesseq(f($sum(1,a)),4)
<=> $lesseq(f($sum(1,a)),4) ),
inference(monotonicity,[status(thm)],[1]) ).
tff(3,plain,
( $lesseq(f($sum(1,a)),4)
<=> $lesseq(f($sum(1,a)),4) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ! [X: $int] : $greater(f(X),X)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) )
<=> ~ ( $lesseq(a,3)
| ~ $lesseq(f($sum(1,a)),4)
| ~ ! [X: $int] : ~ $lesseq(f(X),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ( ! [X: $int] : $greater(f(X),X)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fX_gt_X_implies_ineq) ).
tff(6,plain,
~ ( $lesseq(a,3)
| ~ $lesseq(f($sum(1,a)),4)
| ~ ! [X: $int] : ~ $lesseq(f(X),X) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
$lesseq(f($sum(1,a)),4),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
$lesseq(f($sum(1,a)),4),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
$lesseq(f($sum(1,a)),4),
inference(modus_ponens,[status(thm)],[8,2]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,plain,
^ [X: $int] :
rewrite(
( ~ $lesseq(f(X),X)
<=> ~ $lesseq($sum(f(X),$product(-1,X)),0) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X: $int] : ~ $lesseq(f(X),X)
<=> ! [X: $int] : ~ $lesseq($sum(f(X),$product(-1,X)),0) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $int] : ~ $lesseq(f(X),X)
<=> ! [X: $int] : ~ $lesseq(f(X),X) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
! [X: $int] : ~ $lesseq(f(X),X),
inference(or_elim,[status(thm)],[6]) ).
tff(18,plain,
! [X: $int] : ~ $lesseq(f(X),X),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X: $int] : ~ $lesseq($sum(f(X),$product(-1,X)),0),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1) )
<=> ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ $greatereq($sum($sum(1,a),$product(-1,f($sum(1,a)))),0)
<=> ~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum($sum(1,a),$product(-1,f($sum(1,a)))),0) )
<=> ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum($sum(1,a),$product(-1,f($sum(1,a)))),0) )
<=> ( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum($sum(1,a),$product(-1,f($sum(1,a)))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X: $int] : ~ $greatereq($sum(X,$product(-1,f(X))),0)
| ~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ $greatereq($sum(a,$product(-1,f($sum(1,a)))),-1),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ $lesseq(a,3)
<=> ~ $lesseq(a,3) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
~ $lesseq(a,3),
inference(or_elim,[status(thm)],[6]) ).
tff(32,plain,
~ $lesseq(a,3),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
$false,
inference(theory_lemma,[status(thm)],[32,29,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : ARI601_1 : TPTP v8.1.0. Released v5.1.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.32 % Computer : n016.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Tue Aug 30 01:07:00 EDT 2022
% 0.09/0.32 % CPUTime :
% 0.09/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.32 Usage: tptp [options] [-file:]file
% 0.09/0.32 -h, -? prints this message.
% 0.09/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.32 -m, -model generate model.
% 0.09/0.32 -p, -proof generate proof.
% 0.09/0.32 -c, -core generate unsat core of named formulas.
% 0.09/0.32 -st, -statistics display statistics.
% 0.09/0.32 -t:timeout set timeout (in second).
% 0.09/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.32 -<param>:<value> configuration parameter and value.
% 0.09/0.32 -o:<output-file> file to place output in.
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------