%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV011+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:31:20 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 111 ( 62 ~; 24 |; 14 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 11 !; 7 ?; 21 :)
% 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,
^ [U: $i] :
refl(( ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) )
<=> ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) )
<=> ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( a_holds(key(U,b))
& b_holds(key(U,a)) )
<=> ~ ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) )),
( ~ ( a_holds(key(U,b))
& b_holds(key(U,a)) )
<=> ~ ~ ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) )),
rewrite(( ~ ~ ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) )
<=> ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) )),
( ~ ( a_holds(key(U,b))
& b_holds(key(U,a)) )
<=> ( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [U: $i] :
~ ( a_holds(key(U,b))
& b_holds(key(U,a)) )
<=> ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) )
<=> ~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(7,plain,
~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) ),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) ),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
~ ? [U: $i] :
( a_holds(key(U,b))
& b_holds(key(U,a)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
^ [U: $i] :
refl($oeq(~ ( a_holds(key(U,b))
& b_holds(key(U,a)) ),
~ ( a_holds(key(U,b))
& b_holds(key(U,a)) ))),
inference(bind,[status(th)],[]) ).
tff(12,plain,
! [U: $i] :
~ ( a_holds(key(U,b))
& b_holds(key(U,a)) ),
inference(nnf-neg,[status(sab)],[10,11]) ).
tff(13,plain,
! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ),
inference(modus_ponens,[status(thm)],[12,4]) ).
tff(14,plain,
! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) ),
inference(modus_ponens,[status(thm)],[13,2]) ).
tff(15,plain,
( a_holds(key(generate_key(an_a_nonce),b))
<=> a_holds(key(generate_key(an_a_nonce),b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
a_holds(key(generate_key(an_a_nonce),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(17,plain,
a_holds(key(generate_key(an_a_nonce),b)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( b_holds(key(generate_key(an_a_nonce),a))
<=> b_holds(key(generate_key(an_a_nonce),a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
b_holds(key(generate_key(an_a_nonce),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(20,plain,
b_holds(key(generate_key(an_a_nonce),a)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) )
<=> ( ~ ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,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(23,plain,
( ~ ! [U: $i] :
( ~ a_holds(key(U,b))
| ~ b_holds(key(U,a)) )
| ~ a_holds(key(generate_key(an_a_nonce),b))
| ~ b_holds(key(generate_key(an_a_nonce),a)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV011+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:21:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------