TSTP Solution File: ARI594_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI594_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 17:02:12 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 53 ( 16 unt; 1 typ; 0 def)
% Number of atoms : 219 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 293 ( 145 ~; 90 |; 20 &)
% ( 34 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number arithmetic : 371 ( 104 atm; 33 fun; 178 num; 56 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 0 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 38 !; 13 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: $int > $o ).
tff(1,plain,
^ [X: $int] :
refl(
( ~ p($product(3,X))
<=> ~ p($product(3,X)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $int] : ~ p($product(3,X))
<=> ! [X: $int] : ~ p($product(3,X)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ~ ? [X: $int] : p($product(3,X))
<=> ~ ? [X: $int] : p($product(3,X)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ! [Z: $int] :
( ( $lesseq(5,Z)
& $lesseq(Z,7) )
=> p(Z) )
=> ? [X: $int] : p($product(3,X)) )
<=> ~ ( ~ ! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) )
| ? [X: $int] : p($product(3,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ( ! [Z: $int] :
( ( $lesseq(5,Z)
& $lesseq(Z,7) )
=> p(Z) )
=> ? [X: $int] : p($product(3,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists_X_in_5_to_7_div_3) ).
tff(6,plain,
~ ( ~ ! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) )
| ? [X: $int] : p($product(3,X)) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
~ ? [X: $int] : p($product(3,X)),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
~ ? [X: $int] : p($product(3,X)),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
~ ? [X: $int] : p($product(3,X)),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
~ ? [X: $int] : p($product(3,X)),
inference(modus_ponens,[status(thm)],[9,3]) ).
tff(11,plain,
~ ? [X: $int] : p($product(3,X)),
inference(modus_ponens,[status(thm)],[10,3]) ).
tff(12,plain,
~ ? [X: $int] : p($product(3,X)),
inference(modus_ponens,[status(thm)],[11,3]) ).
tff(13,plain,
~ ? [X: $int] : p($product(3,X)),
inference(modus_ponens,[status(thm)],[12,3]) ).
tff(14,plain,
^ [X: $int] : refl($oeq(~ p($product(3,X)),~ p($product(3,X)))),
inference(bind,[status(th)],]) ).
tff(15,plain,
! [X: $int] : ~ p($product(3,X)),
inference(nnf-neg,[status(sab)],[13,14]) ).
tff(16,plain,
! [X: $int] : ~ p($product(3,X)),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) )
<=> ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ p($product(3,2))
<=> ~ p(6) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p($product(3,2)) )
<=> ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p($product(3,2)) )
<=> ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p($product(3,2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ p(6),
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
^ [Z: $int] :
refl(
( ( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
<=> ( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
<=> ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [Z: $int] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( $greatereq(Z,5)
& $lesseq(Z,7) )
<=> ~ ( ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
( ~ ( $greatereq(Z,5)
& $lesseq(Z,7) )
<=> ~ ~ ( ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
rewrite(
( ~ ~ ( ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
<=> ( ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
( ~ ( $greatereq(Z,5)
& $lesseq(Z,7) )
<=> ( ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
( ( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) )
<=> ( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
rewrite(
( ( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
<=> ( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
( ( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) )
<=> ( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [Z: $int] :
( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) )
<=> ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [Z: $int] :
rewrite(
( ( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) )
<=> ( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) )
<=> ! [Z: $int] :
( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) )
<=> ! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) ),
inference(or_elim,[status(thm)],[6]) ).
tff(32,plain,
! [Z: $int] :
( p(Z)
| ~ ( $lesseq(5,Z)
& $lesseq(Z,7) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Z: $int] :
( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
! [Z: $int] :
( p(Z)
| ~ ( $greatereq(Z,5)
& $lesseq(Z,7) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
( ( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6) )
<=> ( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( p(6)
| $false
| $false )
<=> p(6) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( $lesseq(6,7)
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ $lesseq(6,7)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ~ $lesseq(6,7)
<=> $false ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( $greatereq(6,5)
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ $greatereq(6,5)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ~ $greatereq(6,5)
<=> $false ),
inference(transitivity,[status(thm)],[44,39]) ).
tff(46,plain,
( ( p(6)
| ~ $greatereq(6,5)
| ~ $lesseq(6,7) )
<=> ( p(6)
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[45,42]) ).
tff(47,plain,
( ( p(6)
| ~ $greatereq(6,5)
| ~ $lesseq(6,7) )
<=> p(6) ),
inference(transitivity,[status(thm)],[46,38]) ).
tff(48,plain,
( ( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6)
| ~ $greatereq(6,5)
| ~ $lesseq(6,7) )
<=> ( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6)
| ~ $greatereq(6,5)
| ~ $lesseq(6,7) )
<=> ( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6) ) ),
inference(transitivity,[status(thm)],[48,37]) ).
tff(50,plain,
( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6)
| ~ $greatereq(6,5)
| ~ $lesseq(6,7) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [Z: $int] :
( p(Z)
| ~ $greatereq(Z,5)
| ~ $lesseq(Z,7) )
| p(6) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,36,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI594_1 : TPTP v8.1.0. Released v5.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 00:39:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------