%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP187^1 : 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 : n027.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 20.25s 20.76s
% Output : Proof 20.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_pi,type,
pi: $tType ).
thf(ty_late_FreeR,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(ty_product_Pair_pi_pi,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(ty_late_transitions,type,
late_transitions: pi > late_residual > $o ).
thf(ty_late_TauR,type,
late_TauR: late_freeRes ).
thf(ty_subs,type,
subs: pi > name > name > pi ).
thf(ty_p2,type,
p2: pi ).
thf(ty_p,type,
p: pi ).
thf(ty_res,type,
res: name > pi > pi ).
thf(ty_par,type,
par: pi > pi > pi ).
thf(ty_x,type,
x: name ).
thf(ty_q,type,
q: pi ).
thf(ty_member558706512_pi_pi,type,
member558706512_pi_pi: product_prod_pi_pi > 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_y,type,
y: name ).
thf(sP1,plain,
( sP1
<=> ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: pi] :
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X1 ) )
=> ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X1 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj_0,conjecture,
~ sP4 ).
thf(h0,negated_conjecture,
sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP3
| ~ sP1
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062,axiom,
sP1 ).
thf(fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
sP2 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062,fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062]) ).
thf(0,theorem,
~ sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP187^1 : TPTP v9.2.0. Released v7.5.0.
% 0.12/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36 % Computer : n027.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 8 18:07:53 EDT 2025
% 0.13/0.36 % CPUTime :
% 20.25/20.76 % SZS status Theorem
% 20.25/20.76 % Mode: cade22sinegrackle2xfaf3
% 20.25/20.76 % Steps: 1594
% 20.25/20.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------