%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP041^1 : 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 : n029.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 01:44:52 PM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_produc190496183real_c,type,
produc190496183real_c: $tType ).
thf(ty_finite1398487019real_c,type,
finite1398487019real_c: $tType ).
thf(ty_denota231621370t_unit,type,
denota231621370t_unit: $tType ).
thf(ty_oDE_a_c,type,
oDE_a_c: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_set_Sum_sum_c_c,type,
set_Sum_sum_c_c: $tType ).
thf(ty_denota161327353_a_b_c,type,
denota161327353_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c ).
thf(ty_s,type,
s: real ).
thf(ty_denota1997846518gree_c,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(ty_denota1293057250_a_b_c,type,
denota1293057250_a_b_c: denota231621370t_unit > oDE_a_c > set_Sum_sum_c_c ).
thf(ty_aa,type,
aa: finite1398487019real_c ).
thf(ty_ba,type,
ba: finite1398487019real_c ).
thf(ty_sol,type,
sol: real > finite1398487019real_c ).
thf(ty_ode,type,
ode: oDE_a_c ).
thf(ty_uminus1381786404um_c_c,type,
uminus1381786404um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(ty_j,type,
j: denota231621370t_unit ).
thf(ty_produc394644079real_c,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(ty_denota1896987029_a_b_c,type,
denota1896987029_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > produc190496183real_c ).
thf(sP1,plain,
( sP1
<=> ( denota1997846518gree_c @ ( denota161327353_a_b_c @ j @ ode @ ( produc394644079real_c @ aa @ ba ) @ ( sol @ s ) ) @ ( denota1896987029_a_b_c @ j @ ode @ ( sol @ s ) ) @ ( denota1293057250_a_b_c @ j @ ode ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
denota1997846518gree_c @ ( denota161327353_a_b_c @ j @ ode @ ( produc394644079real_c @ aa @ ba ) @ ( sol @ s ) ) @ ( produc394644079real_c @ aa @ ba ) @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ j @ ode ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h1,h2,h0])],[h2,h0]) ).
thf(fact_1__092_060open_062Vagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Iaa_M_Aba_J_A_I_N_AsemBV_AJ_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Imk__xode_AJ_AODE_A_Isol_As_J_J_A_IsemBV_AJ_AODE_J_092_060close_062,axiom,
~ ( ( denota1997846518gree_c @ ( denota161327353_a_b_c @ j @ ode @ ( produc394644079real_c @ aa @ ba ) @ ( sol @ s ) ) @ ( produc394644079real_c @ aa @ ba ) @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ j @ ode ) ) )
=> ~ sP1 ) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_1__092_060open_062Vagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Iaa_M_Aba_J_A_I_N_AsemBV_AJ_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Imk__xode_AJ_AODE_A_Isol_As_J_J_A_IsemBV_AJ_AODE_J_092_060close_062,1,h1,h2]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP041^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 18:12:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: cade22sinegrackle2x6978
% 0.20/0.42 % Steps: 0
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------