TSTP Solution File: SWV011-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV011-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 : Thu Sep 29 15:09:37 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of formulae : 24 ( 6 unt; 7 typ; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 68 ( 40 ~; 22 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_holds_type,type,
b_holds: $i > $o ).
tff(key_type,type,
key: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(a_holds_type,type,
a_holds: $i > $o ).
tff(b_type,type,
b: $i ).
tff(generate_key_type,type,
generate_key: $i > $i ).
tff(an_a_nonce_type,type,
an_a_nonce: $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
<=> ( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
<=> ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
<=> ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(5,plain,
! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( a_holds(key(generate_key(an_a_nonce),b))
<=> a_holds(key(generate_key(an_a_nonce),b)) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
a_holds(key(generate_key(an_a_nonce),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_13) ).
tff(10,plain,
a_holds(key(generate_key(an_a_nonce),b)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( b_holds(key(generate_key(an_a_nonce),a))
<=> b_holds(key(generate_key(an_a_nonce),a)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
b_holds(key(generate_key(an_a_nonce),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_11) ).
tff(13,plain,
b_holds(key(generate_key(an_a_nonce),a)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) )
<=> ( ~ ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [A: $i] :
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,13,10,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV011-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 01:19:03 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.
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------