TSTP Solution File: ARI593_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI593_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 14 unt; 1 typ; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 80 ( 49 ~; 10 |; 10 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number arithmetic : 122 ( 0 atm; 33 fun; 62 num; 27 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 0 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 12 !; 13 ?; 27 :)
% 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,
( ~ ( ( p(5)
& p(6)
& p(7) )
=> ? [X: $int] : p($product(3,X)) )
<=> ~ ( ~ ( p(5)
& p(6)
& p(7) )
| ? [X: $int] : p($product(3,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ( ( p(5)
& p(6)
& p(7) )
=> ? [X: $int] : p($product(3,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_X_in_5_6_7_div_3) ).
tff(6,plain,
~ ( ~ ( p(5)
& p(6)
& p(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,
( p(6)
<=> p(6) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( p(5)
& p(6)
& p(7) ),
inference(or_elim,[status(thm)],[6]) ).
tff(19,plain,
p(6),
inference(and_elim,[status(thm)],[18]) ).
tff(20,plain,
p(6),
inference(modus_ponens,[status(thm)],[19,17]) ).
tff(21,plain,
( ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) )
<=> ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ p($product(3,2))
<=> ~ p(6) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p($product(3,2)) )
<=> ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p($product(3,2)) )
<=> ( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p($product(3,2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X: $int] : ~ p($product(3,X))
| ~ p(6) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,20,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI593_1 : TPTP v8.1.0. Released v5.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.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 00:37:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------