TSTP Solution File: ARI189_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI189_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 17:00:53 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 21 ( 8 unt; 1 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 39 ( 18 ~; 10 |; 0 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 91 ( 0 atm; 26 fun; 44 num; 21 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 20 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: $int > $o ).
tff(1,plain,
^ [U: $int] :
refl(
( p($product(2,U))
<=> p($product(2,U)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [U: $int] : p($product(2,U))
<=> ! [U: $int] : p($product(2,U)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [U: $int] : p($product(2,U))
<=> ! [U: $int] : p($product(2,U)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ! [U: $int] : p($product(2,U))
=> p(10) )
<=> ~ ( p(10)
| ~ ! [U: $int] : p($product(2,U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ( ! [U: $int] : p($product(2,U))
=> p(10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(6,plain,
~ ( p(10)
| ~ ! [U: $int] : p($product(2,U)) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [U: $int] : p($product(2,U)),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
! [U: $int] : p($product(2,U)),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [U: $int] : p($product(2,U)),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [U: $int] : p($product(2,U)),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ p(10)
<=> ~ p(10) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
~ p(10),
inference(or_elim,[status(thm)],[6]) ).
tff(13,plain,
~ p(10),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [U: $int] : p($product(2,U))
| p(10) )
<=> ( ~ ! [U: $int] : p($product(2,U))
| p(10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( p($product(2,5))
<=> p(10) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ~ ! [U: $int] : p($product(2,U))
| p($product(2,5)) )
<=> ( ~ ! [U: $int] : p($product(2,U))
| p(10) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [U: $int] : p($product(2,U))
| p($product(2,5)) )
<=> ( ~ ! [U: $int] : p($product(2,U))
| p(10) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [U: $int] : p($product(2,U))
| p($product(2,5)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [U: $int] : p($product(2,U))
| p(10) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ARI189_1 : TPTP v8.1.0. Released v5.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 22:32:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------