%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP086^1 : 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 01:45:00 PM UTC 2025
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_secrecy_specID,type,
secrecy_specID: $tType ).
thf(ty_secrecy_chanID,type,
secrecy_chanID: $tType ).
thf(ty_ins,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(ty_correctCompositionIn,type,
correctCompositionIn: secrecy_specID > $o ).
thf(ty_loc,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(ty_exprChannel,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(ty_m,type,
m: secrecy_Expression ).
thf(ty_pq,type,
pq: secrecy_specID ).
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_ch,type,
ch: secrecy_chanID ).
thf(ty_p,type,
p: secrecy_specID ).
thf(ty_q,type,
q: secrecy_specID ).
thf(ty_member1967978193chanID,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(sP1,plain,
( sP1
<=> ( exprChannel @ ch @ m ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( member1967978193chanID @ ch @ ( loc @ pq ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_chanID] :
( ( ( subcomponents @ pq )
= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ pq )
=> ( ~ ( member1967978193chanID @ X3 @ ( loc @ pq ) )
=> ( ( member1967978193chanID @ X3 @ ( ins @ X1 ) )
=> ( member1967978193chanID @ X3 @ ( ins @ pq ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( member1967978193chanID @ ch @ ( ins @ pq ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( member1967978193chanID @ ch @ ( ins @ pq ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( member1967978193chanID @ ch @ ( ins @ p ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID,X4: secrecy_chanID] :
( ( ( subcomponents @ X1 )
= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ X1 )
=> ( ~ ( member1967978193chanID @ X4 @ ( loc @ X1 ) )
=> ( ( member1967978193chanID @ X4 @ ( ins @ X2 ) )
=> ( member1967978193chanID @ X4 @ ( ins @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ( ( correctCompositionIn @ pq )
=> ( ~ sP2
=> sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( correctCompositionIn @ pq )
=> ( ~ sP2
=> sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: secrecy_specID,X2: secrecy_chanID] :
( ( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ pq )
=> ( ~ ( member1967978193chanID @ X2 @ ( loc @ pq ) )
=> ( ( member1967978193chanID @ X2 @ ( ins @ p ) )
=> ( member1967978193chanID @ X2 @ ( ins @ pq ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: secrecy_chanID] :
( sP5
=> ( ( correctCompositionIn @ pq )
=> ( ~ ( member1967978193chanID @ X1 @ ( loc @ pq ) )
=> ( ( member1967978193chanID @ X1 @ ( ins @ p ) )
=> ( member1967978193chanID @ X1 @ ( ins @ pq ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( member1967978193chanID @ ch @ ( ins @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( correctCompositionIn @ pq ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP2
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: secrecy_chanID] :
( ( member1967978193chanID @ X1 @ ( ins @ pq ) )
=> ~ ( exprChannel @ X1 @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(conj_0,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP9
| ~ sP5
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| ~ sP13
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP15
| sP2
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP10
| ~ sP14
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| ~ sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_6_correctCompositionIn__L1,axiom,
sP8 ).
thf(fact_4_assms_I1_J,axiom,
sP5 ).
thf(fact_3_assms_I5_J,axiom,
sP16 ).
thf(fact_2_assms_I3_J,axiom,
sP13 ).
thf(fact_1_assms_I4_J,axiom,
sP1 ).
thf(fact_0_assms_I2_J,axiom,
sP14 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,h0,fact_6_correctCompositionIn__L1,fact_4_assms_I1_J,fact_3_assms_I5_J,fact_2_assms_I3_J,fact_1_assms_I4_J,fact_0_assms_I2_J]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP086^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 18:22:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % Mode: cade22sinegrackle2x6978
% 0.21/0.45 % Steps: 180
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------