TSTP Solution File: ARI181_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI181_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 17:00:51 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 32 ( 15 unt; 1 typ; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 67 ~; 12 |; 0 &)
% ( 13 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number arithmetic : 262 ( 57 atm; 64 fun; 110 num; 31 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 28 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $int > $int ).
tff(1,plain,
( ~ $greatereq(f(f(f(6))),9)
<=> ~ $greatereq(f(f(f(6))),9) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ! [U: $int] : $greater(f(U),U)
=> $greatereq(f(f(f(6))),9) )
<=> ~ ( ~ ! [U: $int] : ~ $lesseq(f(U),U)
| $greatereq(f(f(f(6))),9) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ! [U: $int] : $greater(f(U),U)
=> $greatereq(f(f(f(6))),9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(4,plain,
~ ( ~ ! [U: $int] : ~ $lesseq(f(U),U)
| $greatereq(f(f(f(6))),9) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ $greatereq(f(f(f(6))),9),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ $greatereq(f(f(f(6))),9),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [U: $int] :
refl(
( ~ $greatereq($sum(U,$product(-1,f(U))),0)
<=> ~ $greatereq($sum(U,$product(-1,f(U))),0) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
<=> ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [U: $int] :
rewrite(
( ~ $lesseq($sum(f(U),$product(-1,U)),0)
<=> ~ $greatereq($sum(U,$product(-1,f(U))),0) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [U: $int] : ~ $lesseq($sum(f(U),$product(-1,U)),0)
<=> ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [U: $int] :
rewrite(
( ~ $lesseq(f(U),U)
<=> ~ $lesseq($sum(f(U),$product(-1,U)),0) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [U: $int] : ~ $lesseq(f(U),U)
<=> ! [U: $int] : ~ $lesseq($sum(f(U),$product(-1,U)),0) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [U: $int] : ~ $lesseq(f(U),U)
<=> ! [U: $int] : ~ $lesseq(f(U),U) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
! [U: $int] : ~ $lesseq(f(U),U),
inference(or_elim,[status(thm)],[4]) ).
tff(15,plain,
! [U: $int] : ~ $lesseq(f(U),U),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [U: $int] : ~ $lesseq($sum(f(U),$product(-1,U)),0),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0),
inference(modus_ponens,[status(thm)],[16,10]) ).
tff(18,plain,
! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0),
inference(modus_ponens,[status(thm)],[18,8]) ).
tff(20,plain,
( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $greatereq($sum(f(6),$product(-1,f(f(6)))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
~ $greatereq($sum(f(6),$product(-1,f(f(6)))),0),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $lesseq(f(6),6) )
<=> ( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $lesseq(f(6),6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ $greatereq($sum(6,$product(-1,f(6))),0)
<=> ~ $lesseq(f(6),6) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $greatereq($sum(6,$product(-1,f(6))),0) )
<=> ( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $lesseq(f(6),6) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $greatereq($sum(6,$product(-1,f(6))),0) )
<=> ( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $lesseq(f(6),6) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $greatereq($sum(6,$product(-1,f(6))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $lesseq(f(6),6) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ $lesseq(f(6),6),
inference(unit_resolution,[status(thm)],[27,19]) ).
tff(29,plain,
( ~ ! [U: $int] : ~ $greatereq($sum(U,$product(-1,f(U))),0)
| ~ $greatereq($sum(f(f(6)),$product(-1,f(f(f(6))))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
~ $greatereq($sum(f(f(6)),$product(-1,f(f(f(6))))),0),
inference(unit_resolution,[status(thm)],[29,19]) ).
tff(31,plain,
$false,
inference(theory_lemma,[status(thm)],[30,28,21,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI181_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 22:18:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------