%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP090^1 : 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 : n026.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 01:45:01 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_specID,type,
secrecy_specID: $tType ).
thf(ty_secrecy_Keys,type,
secrecy_Keys: $tType ).
thf(ty_member_Secrecy_KS,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(ty_q,type,
q: secrecy_specID ).
thf(ty_ine,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(ty_secrecy_kKS,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(ty_knowle945212990e_know,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(ty_secrecy_kE,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(ty_key,type,
key: secrecy_Keys ).
thf(ty_localSecrets,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(sP1,plain,
( sP1
<=> ( m
= ( secrecy_kKS @ key ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( secrecy_kKS @ key )
= m ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ine @ q @ ( secrecy_kE @ key ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: secrecy_specID,X2: secrecy_Keys] :
( ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X2 ) )
= ( ~ ( ine @ X1 @ ( secrecy_kE @ X2 ) )
=> ( member_Secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( localSecrets @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( knowle945212990e_know @ q @ m ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: secrecy_Keys] :
( ( knowle945212990e_know @ q @ ( secrecy_kKS @ X1 ) )
= ( ~ ( ine @ q @ ( secrecy_kE @ X1 ) )
=> ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
~ sP5 ).
thf(h0,negated_conjecture,
sP5,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP3
| sP9
| ~ sP2
| sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
~ sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| sP3
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP7
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP1
| sP2 ),
inference(symeq,[status(thm)],[]) ).
thf(fact_8_know_Osimps_I1_J,axiom,
sP7 ).
thf(fact_1_a1,axiom,
sP1 ).
thf(fact_0_not__knowQm,axiom,
~ sP9 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,h0,fact_8_know_Osimps_I1_J,fact_1_a1,fact_0_not__knowQm]) ).
thf(0,theorem,
~ sP5,
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP090^1 : TPTP v9.2.0. Released v7.5.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.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 : Wed Oct 8 18:39:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % Mode: cade22sinegrackle2x6978
% 0.20/0.49 % Steps: 1303
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------