%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP184^1 : 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 : n012.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 01:45:22 PM UTC 2025
% Result : Theorem 20.25s 20.53s
% Output : Proof 20.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_pi,type,
pi: $tType ).
thf(ty_late_transitions,type,
late_transitions: pi > late_residual > $o ).
thf(ty_late_BoundR,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(ty_q,type,
q: pi ).
thf(ty_p,type,
p: pi ).
thf(ty_par,type,
par: pi > pi > pi ).
thf(ty_x,type,
x: name ).
thf(ty_strong2129052853vative,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(ty_q2,type,
q2: pi ).
thf(ty_r,type,
r: pi ).
thf(ty_rel,type,
rel: set_Pr1834926343_pi_pi ).
thf(ty_a,type,
a: late_subject ).
thf(sP1,plain,
( sP1
<=> ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) )
=> ~ ( strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: pi] :
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X1 ) )
=> ~ ( strong2129052853vative @ X1 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj_0,conjecture,
~ sP2 ).
thf(h0,negated_conjecture,
sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP1
| ~ sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062,axiom,
sP3 ).
thf(fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062,axiom,
sP4 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062,fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062]) ).
thf(0,theorem,
~ sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ITP184^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 8 18:36:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 20.25/20.53 % SZS status Theorem
% 20.25/20.53 % Mode: cade22sinegrackle2xfaf3
% 20.25/20.53 % Steps: 543
% 20.25/20.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------