%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP091^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %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 : Thu Oct 9 01:46:56 PM UTC 2025
% Result : Theorem 25.77s 26.40s
% Output : Proof 25.77s
% 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_set_Secrecy_KS,type,
set_Secrecy_KS: $tType ).
thf(ty_secrecy_Expression,type,
secrecy_Expression: $tType ).
thf(ty_secrecy_Secrets,type,
secrecy_Secrets: $tType ).
thf(ty_q,type,
q: secrecy_specID ).
thf(ty_secret,type,
secret: secrecy_Secrets ).
thf(ty_secrecy_sE,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(ty_member_Secrecy_KS,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(ty_secrecy_sKS,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(ty_knowle945212990e_know,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(ty_ine,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(ty_localSecrets,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(ty_m,type,
m: secrecy_KS ).
thf(sP1,plain,
( sP1
<=> ( ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) )
= ( ~ ( ine @ q @ ( secrecy_sE @ secret ) )
=> ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( knowle945212990e_know @ q @ m ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( m
= ( secrecy_sKS @ secret ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: secrecy_Secrets] :
( ( knowle945212990e_know @ q @ ( secrecy_sKS @ X1 ) )
= ( ~ ( ine @ q @ ( secrecy_sE @ X1 ) )
=> ( member_Secrecy_KS @ ( secrecy_sKS @ X1 ) @ ( localSecrets @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: secrecy_specID,X2: secrecy_Secrets] :
( ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X2 ) )
= ( ~ ( ine @ X1 @ ( secrecy_sE @ X2 ) )
=> ( member_Secrecy_KS @ ( secrecy_sKS @ X2 ) @ ( localSecrets @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( secrecy_sKS @ secret )
= m ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( q = q ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: secrecy_KS,X2: secrecy_KS] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: secrecy_KS] :
( ( m = X1 )
=> ( X1 = m ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ine @ q @ ( secrecy_sE @ secret ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj_0,conjecture,
~ sP10 ).
thf(h0,negated_conjecture,
sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP12
| sP2
| ~ sP7
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( sP13
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP1
| sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
sP7,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| ~ sP3
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP11
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
sP8,
inference(eq_sym,[status(thm)],[]) ).
thf(fact_0_not__knowQm,axiom,
~ sP2 ).
thf(fact_1_a2,axiom,
sP3 ).
thf(fact_8_know_Osimps_I2_J,axiom,
sP5 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,fact_0_not__knowQm,fact_1_a2,fact_8_know_Osimps_I2_J,h0]) ).
thf(0,theorem,
~ sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.41 % Problem : ITP091^1 : TPTP v9.2.0. Released v7.5.0.
% 0.10/0.41 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.16/0.62 % Computer : n015.cluster.edu
% 0.16/0.62 % Model : x86_64 x86_64
% 0.16/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.62 % Memory : 8042.1875MB
% 0.16/0.62 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.62 % CPULimit : 300
% 0.16/0.62 % WCLimit : 300
% 0.16/0.62 % DateTime : Wed Oct 8 18:37:39 EDT 2025
% 0.16/0.63 % CPUTime :
% 25.77/26.40 % SZS status Theorem
% 25.77/26.40 % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 25.77/26.40 % Inferences: 454
% 25.77/26.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------