%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP087^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 Oct 9 01:45:00 PM UTC 2025
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_secrecy_KS,type,
secrecy_KS: $tType ).
thf(ty_secrecy_specID,type,
secrecy_specID: $tType ).
thf(ty_secrecy_Expression,type,
secrecy_Expression: $tType ).
thf(ty_secrecy_Keys,type,
secrecy_Keys: $tType ).
thf(ty_pq,type,
pq: secrecy_specID ).
thf(ty_ine,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(ty_m,type,
m: secrecy_KS ).
thf(ty_specKeysSecrets,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(ty_correctCompositionKS,type,
correctCompositionKS: secrecy_specID > $o ).
thf(ty_p,type,
p: secrecy_specID ).
thf(ty_key,type,
key: secrecy_Keys ).
thf(ty_bot_bo1785112429specID,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(ty_insert1671894227specID,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(ty_subcomponents,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(ty_q,type,
q: secrecy_specID ).
thf(ty_member_Secrecy_KS,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(ty_secrecy_kE,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(sP1,plain,
( sP1
<=> ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( correctCompositionKS @ pq )
=> ( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) )
=> ( ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) )
=> sP1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: secrecy_KS] :
( ( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ pq )
=> ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ pq ) )
=> ( ~ ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ p ) )
=> ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ q ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( correctCompositionKS @ pq ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID,X4: secrecy_KS] :
( ( ( subcomponents @ X1 )
= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ X1 )
=> ( ( member_Secrecy_KS @ X4 @ ( specKeysSecrets @ X1 ) )
=> ( ~ ( member_Secrecy_KS @ X4 @ ( specKeysSecrets @ X2 ) )
=> ( member_Secrecy_KS @ X4 @ ( specKeysSecrets @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_KS] :
( ( ( subcomponents @ pq )
= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) )
=> ( sP6
=> ( ( member_Secrecy_KS @ X3 @ ( specKeysSecrets @ pq ) )
=> ( ~ ( member_Secrecy_KS @ X3 @ ( specKeysSecrets @ X1 ) )
=> ( member_Secrecy_KS @ X3 @ ( specKeysSecrets @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: secrecy_specID,X2: secrecy_KS] :
( ( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) ) )
=> ( sP6
=> ( ( member_Secrecy_KS @ X2 @ ( specKeysSecrets @ pq ) )
=> ( ~ ( member_Secrecy_KS @ X2 @ ( specKeysSecrets @ p ) )
=> ( member_Secrecy_KS @ X2 @ ( specKeysSecrets @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP11
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj_0,conjecture,
~ sP12 ).
thf(h0,negated_conjecture,
sP12,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
ine @ p @ ( secrecy_kE @ key ),
introduced(assumption,[]) ).
thf(h2,assumption,
ine @ q @ ( secrecy_kE @ key ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP12
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP5
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| ~ sP6
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP13
| ~ sP11
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_7_correctCompositionKS__PQ,axiom,
sP7 ).
thf(fact_3_subPQ,axiom,
sP11 ).
thf(fact_2_notKSP,axiom,
~ sP5 ).
thf(fact_1_notKSQ,axiom,
~ sP1 ).
thf(fact_0_cCompKS,axiom,
sP6 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,h0,fact_7_correctCompositionKS__PQ,fact_3_subPQ,fact_2_notKSP,fact_1_notKSQ,fact_0_cCompKS]) ).
thf(10,plain,
( ~ sP9
| ~ sP12
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP3
| sP5
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP2
| ~ sP6
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP13
| ~ sP11
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h0])],[10,11,12,13,14,15,16,17,h0,fact_7_correctCompositionKS__PQ,fact_3_subPQ,fact_2_notKSP,fact_1_notKSQ,fact_0_cCompKS]) ).
thf(fact_140_a11ext,axiom,
( ~ ( ine @ p @ ( secrecy_kE @ key ) )
=> ( ine @ q @ ( secrecy_kE @ key ) ) ) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_140_a11ext,9,18,h1,h2]) ).
thf(0,theorem,
~ sP12,
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP087^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 18:19:53 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % Mode: cade22sinegrackle2x6978
% 0.20/0.49 % Steps: 1227
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------