%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP189^1 : 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 : n005.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 01:45:23 PM UTC 2025
% Result : Theorem 21.99s 22.30s
% Output : Proof 21.99s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_late_freeRes,type,
late_freeRes: $tType ).
thf(ty_pi,type,
pi: $tType ).
thf(ty_name,type,
name: $tType ).
thf(ty_q,type,
q: pi ).
thf(ty_late_FreeR,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(ty_late_transitions,type,
late_transitions: pi > late_residual > $o ).
thf(ty_par,type,
par: pi > pi > pi ).
thf(ty_p2,type,
p2: pi ).
thf(ty_fresh_1641682979reeRes,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(ty_alpha,type,
alpha: late_freeRes ).
thf(ty_x,type,
x: name ).
thf(ty_res,type,
res: name > pi > pi ).
thf(ty_p,type,
p: pi ).
thf(sP1,plain,
( sP1
<=> ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ ( par @ p2 @ q ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: late_freeRes,X2: pi,X3: name] :
( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ X1 @ X2 ) )
=> ( ( fresh_1641682979reeRes @ X3 @ X1 )
=> ( late_transitions @ ( res @ X3 @ ( par @ p @ q ) ) @ ( late_FreeR @ X1 @ ( res @ X3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: name] :
( sP1
=> ( ( fresh_1641682979reeRes @ X1 @ alpha )
=> ( late_transitions @ ( res @ X1 @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ X1 @ ( par @ p2 @ q ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( fresh_1641682979reeRes @ x @ alpha )
=> ( late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( fresh_1641682979reeRes @ x @ alpha ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: pi,X2: late_freeRes,X3: pi,X4: name] :
( ( late_transitions @ X1 @ ( late_FreeR @ X2 @ X3 ) )
=> ( ( fresh_1641682979reeRes @ X4 @ X2 )
=> ( late_transitions @ ( res @ X4 @ X1 ) @ ( late_FreeR @ X2 @ ( res @ X4 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: pi,X2: name] :
( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ X1 ) )
=> ( ( fresh_1641682979reeRes @ X2 @ alpha )
=> ( late_transitions @ ( res @ X2 @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
sP6 ).
thf(h0,negated_conjecture,
~ sP6,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP4
| ~ sP7
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| ~ sP1
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_11_ResF,axiom,
sP8 ).
thf(fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
sP1 ).
thf(fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062,axiom,
sP7 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,fact_11_ResF,fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062]) ).
thf(0,theorem,
sP6,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP189^1 : TPTP v9.2.0. Released v7.5.0.
% 0.04/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 17:51:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 21.99/22.30 % SZS status Theorem
% 21.99/22.30 % Mode: cade22sinegrackle2xfaf3
% 21.99/22.30 % Steps: 1469
% 21.99/22.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------