TSTP Solution File: ARI611_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI611_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 17:02:16 EDT 2022
% Result : Theorem 0.06s 0.28s
% Output : Proof 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 84 ( 12 unt; 2 typ; 0 def)
% Number of atoms : 385 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 482 ( 196 ~; 95 |; 59 &)
% ( 130 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number arithmetic : 509 ( 172 atm; 0 fun; 250 num; 87 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 0 usr; 5 con; 0-0 aty)
% Number of variables : 87 ( 65 !; 13 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: $int > $o ).
tff(q_type,type,
q: $int > $o ).
tff(1,plain,
^ [X: $int] :
refl(
( ( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
<=> ( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
<=> ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $int] :
rewrite(
( ( ( ~ $lesseq(X,8)
& ~ $greatereq(X,18) )
<=> q(X) )
<=> ( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $greatereq(X,18) )
<=> q(X) )
<=> ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $int] :
rewrite(
( ( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) )
<=> ( ( ~ $lesseq(X,8)
& ~ $greatereq(X,18) )
<=> q(X) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) )
<=> ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $greatereq(X,18) )
<=> q(X) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) )
<=> ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ~ ( ( ! [X: $int] :
( ( $less(5,X)
& $less(X,15) )
<=> p(X) )
& ! [X: $int] :
( ( $less(8,X)
& $less(X,18) )
<=> q(X) ) )
=> ? [X: $int] :
( p(X)
& q(X) ) )
<=> ~ ( ~ ( ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) )
& ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) ) )
| ? [X: $int] :
( p(X)
& q(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ ( ( ! [X: $int] :
( ( $less(5,X)
& $less(X,15) )
<=> p(X) )
& ! [X: $int] :
( ( $less(8,X)
& $less(X,18) )
<=> q(X) ) )
=> ? [X: $int] :
( p(X)
& q(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interv_5_15_and_8_18_intersect) ).
tff(10,plain,
~ ( ~ ( ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) )
& ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) ) )
| ? [X: $int] :
( p(X)
& q(X) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) )
& ! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) ) ),
inference(or_elim,[status(thm)],[10]) ).
tff(12,plain,
! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $lesseq(18,X) )
<=> q(X) ),
inference(modus_ponens,[status(thm)],[12,7]) ).
tff(14,plain,
! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $greatereq(X,18) )
<=> q(X) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
! [X: $int] :
( ( ~ $lesseq(X,8)
& ~ $greatereq(X,18) )
<=> q(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) ),
inference(modus_ponens,[status(thm)],[15,4]) ).
tff(17,plain,
! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) ),
inference(modus_ponens,[status(thm)],[16,2]) ).
tff(18,plain,
( ( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| q(9) )
<=> ( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| q(9) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( $true
<=> q(9) )
<=> q(9) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ $false
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( $greatereq(9,18)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( $lesseq(9,8)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( $lesseq(9,8)
| $greatereq(9,18) )
<=> ( $false
| $false ) ),
inference(monotonicity,[status(thm)],[23,22]) ).
tff(25,plain,
( ( $lesseq(9,8)
| $greatereq(9,18) )
<=> $false ),
inference(transitivity,[status(thm)],[24,21]) ).
tff(26,plain,
( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> $true ),
inference(transitivity,[status(thm)],[26,20]) ).
tff(28,plain,
( ( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> q(9) )
<=> ( $true
<=> q(9) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> q(9) )
<=> q(9) ),
inference(transitivity,[status(thm)],[28,19]) ).
tff(30,plain,
( ( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| ( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> q(9) ) )
<=> ( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| q(9) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| ( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> q(9) ) )
<=> ( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| q(9) ) ),
inference(transitivity,[status(thm)],[30,18]) ).
tff(32,plain,
( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| ( ~ ( $lesseq(9,8)
| $greatereq(9,18) )
<=> q(9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X: $int] :
( ~ ( $lesseq(X,8)
| $greatereq(X,18) )
<=> q(X) )
| q(9) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
q(9),
inference(unit_resolution,[status(thm)],[33,17]) ).
tff(35,plain,
^ [X: $int] :
refl(
( ( ~ p(X)
| ~ q(X) )
<=> ( ~ p(X)
| ~ q(X) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $int] :
( ~ p(X)
| ~ q(X) )
<=> ! [X: $int] :
( ~ p(X)
| ~ q(X) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
^ [X: $int] :
trans(
monotonicity(
rewrite(
( ( p(X)
& q(X) )
<=> ~ ( ~ p(X)
| ~ q(X) ) )),
( ~ ( p(X)
& q(X) )
<=> ~ ~ ( ~ p(X)
| ~ q(X) ) )),
rewrite(
( ~ ~ ( ~ p(X)
| ~ q(X) )
<=> ( ~ p(X)
| ~ q(X) ) )),
( ~ ( p(X)
& q(X) )
<=> ( ~ p(X)
| ~ q(X) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $int] :
~ ( p(X)
& q(X) )
<=> ! [X: $int] :
( ~ p(X)
| ~ q(X) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ~ ? [X: $int] :
( p(X)
& q(X) )
<=> ~ ? [X: $int] :
( p(X)
& q(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(or_elim,[status(thm)],[10]) ).
tff(41,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(modus_ponens,[status(thm)],[41,39]) ).
tff(43,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(modus_ponens,[status(thm)],[44,39]) ).
tff(46,plain,
~ ? [X: $int] :
( p(X)
& q(X) ),
inference(modus_ponens,[status(thm)],[45,39]) ).
tff(47,plain,
^ [X: $int] :
refl(
$oeq(
~ ( p(X)
& q(X) ),
~ ( p(X)
& q(X) ))),
inference(bind,[status(th)],]) ).
tff(48,plain,
! [X: $int] :
~ ( p(X)
& q(X) ),
inference(nnf-neg,[status(sab)],[46,47]) ).
tff(49,plain,
! [X: $int] :
( ~ p(X)
| ~ q(X) ),
inference(modus_ponens,[status(thm)],[48,38]) ).
tff(50,plain,
! [X: $int] :
( ~ p(X)
| ~ q(X) ),
inference(modus_ponens,[status(thm)],[49,36]) ).
tff(51,plain,
( ( ~ ! [X: $int] :
( ~ p(X)
| ~ q(X) )
| ~ p(9)
| ~ q(9) )
<=> ( ~ ! [X: $int] :
( ~ p(X)
| ~ q(X) )
| ~ p(9)
| ~ q(9) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ~ ! [X: $int] :
( ~ p(X)
| ~ q(X) )
| ~ p(9)
| ~ q(9) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [X: $int] :
( ~ p(X)
| ~ q(X) )
| ~ p(9)
| ~ q(9) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ p(9),
inference(unit_resolution,[status(thm)],[53,50,34]) ).
tff(55,plain,
^ [X: $int] :
refl(
( ( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
<=> ( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
<=> ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [X: $int] :
rewrite(
( ( ( ~ $lesseq(X,5)
& ~ $greatereq(X,15) )
<=> p(X) )
<=> ( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $greatereq(X,15) )
<=> p(X) )
<=> ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
^ [X: $int] :
rewrite(
( ( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) )
<=> ( ( ~ $lesseq(X,5)
& ~ $greatereq(X,15) )
<=> p(X) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) )
<=> ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $greatereq(X,15) )
<=> p(X) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) )
<=> ! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) ),
inference(and_elim,[status(thm)],[11]) ).
tff(63,plain,
! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $lesseq(15,X) )
<=> p(X) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $greatereq(X,15) )
<=> p(X) ),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
! [X: $int] :
( ( ~ $lesseq(X,5)
& ~ $greatereq(X,15) )
<=> p(X) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
( ( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| p(9) )
<=> ( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| p(9) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( $true
<=> p(9) )
<=> p(9) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( $greatereq(9,15)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( $lesseq(9,5)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( $lesseq(9,5)
| $greatereq(9,15) )
<=> ( $false
| $false ) ),
inference(monotonicity,[status(thm)],[71,70]) ).
tff(73,plain,
( ( $lesseq(9,5)
| $greatereq(9,15) )
<=> $false ),
inference(transitivity,[status(thm)],[72,21]) ).
tff(74,plain,
( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> $true ),
inference(transitivity,[status(thm)],[74,20]) ).
tff(76,plain,
( ( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> p(9) )
<=> ( $true
<=> p(9) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> p(9) )
<=> p(9) ),
inference(transitivity,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| ( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> p(9) ) )
<=> ( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| p(9) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| ( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> p(9) ) )
<=> ( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| p(9) ) ),
inference(transitivity,[status(thm)],[78,68]) ).
tff(80,plain,
( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| ( ~ ( $lesseq(9,5)
| $greatereq(9,15) )
<=> p(9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X: $int] :
( ~ ( $lesseq(X,5)
| $greatereq(X,15) )
<=> p(X) )
| p(9) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,67,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ARI611_1 : TPTP v8.1.0. Released v5.1.0.
% 0.06/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.26 % Computer : n004.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue Aug 30 00:45:49 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.06/0.28 % SZS status Theorem
% 0.06/0.28 % SZS output start Proof
% See solution above
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