0.09/0.10	% Problem  : SLH0263^1 : TPTP v8.2.0. Released v8.2.0.
0.09/0.10	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.10/0.30	% Computer : n028.cluster.edu
0.10/0.30	% Model    : x86_64 x86_64
0.10/0.30	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	% Memory   : 8042.1875MB
0.10/0.30	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.30	% CPULimit : 30
0.10/0.30	% WCLimit  : 30
0.10/0.30	% DateTime : Mon Jul  3 04:17:43 EDT 2023
0.10/0.30	% CPUTime  : 
25.44/25.49	% SZS status Theorem
25.44/25.49	% Mode: cade22sinegrackle2xfaf3
25.44/25.49	% Steps: 81274
25.44/25.49	% SZS output start Proof
25.44/25.49	thf(ty_a, type, a : $tType).
25.44/25.49	thf(ty_nat, type, nat : $tType).
25.44/25.49	thf(ty_set_a, type, set_a : $tType).
25.44/25.49	thf(ty_real, type, real : $tType).
25.44/25.49	thf(ty_member_a, type, member_a : (a>set_a>$o)).
25.44/25.49	thf(ty_i, type, i : real).
25.44/25.49	thf(ty_eigen__0, type, eigen__0 : a).
25.44/25.49	thf(ty_c, type, c : real).
25.44/25.49	thf(ty_zero_zero_real, type, zero_zero_real : real).
25.44/25.49	thf(ty_zero_zero_nat, type, zero_zero_nat : nat).
25.44/25.49	thf(ty_top_top_set_a, type, top_top_set_a : set_a).
25.44/25.49	thf(ty_risk_F170160801229183585ccount, type, risk_F170160801229183585ccount : (risk_Free_account>nat>real)).
25.44/25.49	thf(ty_ord_less_nat, type, ord_less_nat : (nat>nat>$o)).
25.44/25.49	thf(ty_rho, type, rho : (nat>real)).
25.44/25.49	thf(ty_risk_F1914734008469130493eserve, type, risk_F1914734008469130493eserve : (risk_Free_account>real)).
25.44/25.49	thf(ty_groups2740460157737275248a_real, type, groups2740460157737275248a_real : ((a>real)>set_a>real)).
25.44/25.49	thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)).
25.44/25.49	thf(ty_risk_F1245088672346398815dger_a, type, risk_F1245088672346398815dger_a : ((nat>real)>real>(a>risk_Free_account)>a>risk_Free_account)).
25.44/25.49	thf(ty_l, type, l : (a>risk_Free_account)).
25.44/25.49	thf(ty_times_times_real, type, times_times_real : (real>real>real)).
25.44/25.49	thf(ty_one_one_real, type, one_one_real : real).
25.44/25.49	thf(sP1,plain,sP1 <=> (((times_times_real @ c) @ ((plus_plus_real @ one_one_real) @ i)) = ((times_times_real @ ((plus_plus_real @ one_one_real) @ i)) @ c)),introduced(definition,[new_symbols(definition,[sP1])])).
25.44/25.49	thf(sP2,plain,sP2 <=> (((groups2740460157737275248a_real @ (^[X1:a]:(risk_F1914734008469130493eserve @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X1)))) @ top_top_set_a) = ((times_times_real @ ((plus_plus_real @ one_one_real) @ i)) @ c)),introduced(definition,[new_symbols(definition,[sP2])])).
25.44/25.49	thf(sP3,plain,sP3 <=> (sP2 => (~((![X1:nat]:(((ord_less_nat @ zero_zero_nat) @ X1) => (((groups2740460157737275248a_real @ (^[X2:a]:((risk_F170160801229183585ccount @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X2)) @ X1))) @ top_top_set_a) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP3])])).
25.44/25.49	thf(sP4,plain,sP4 <=> (times_times_real = (^[X1:real]:(^[X2:real]:((times_times_real @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
25.44/25.49	thf(sP5,plain,sP5 <=> ((times_times_real @ c) = (^[X1:real]:((times_times_real @ X1) @ c))),introduced(definition,[new_symbols(definition,[sP5])])).
25.44/25.49	thf(sP6,plain,sP6 <=> (![X1:nat]:(((ord_less_nat @ zero_zero_nat) @ X1) => (((groups2740460157737275248a_real @ (^[X2:a]:((risk_F170160801229183585ccount @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X2)) @ X1))) @ top_top_set_a) = zero_zero_real))),introduced(definition,[new_symbols(definition,[sP6])])).
25.44/25.49	thf(sP7,plain,sP7 <=> $false,introduced(definition,[new_symbols(definition,[sP7])])).
25.44/25.49	thf(sP8,plain,sP8 <=> (![X1:real]:(((times_times_real @ c) @ X1) = ((times_times_real @ X1) @ c))),introduced(definition,[new_symbols(definition,[sP8])])).
25.44/25.49	thf(sP9,plain,sP9 <=> (((groups2740460157737275248a_real @ (^[X1:a]:(risk_F1914734008469130493eserve @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X1)))) @ top_top_set_a) = ((times_times_real @ c) @ ((plus_plus_real @ one_one_real) @ i))),introduced(definition,[new_symbols(definition,[sP9])])).
25.44/25.49	thf(sP10,plain,sP10 <=> (![X1:real]:((times_times_real @ X1) = (^[X2:real]:((times_times_real @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])).
25.44/25.49	thf(conj_0,conjecture,(~(sP3))).
25.44/25.49	thf(h0,negated_conjecture,sP3,inference(assume_negation,[status(cth)],[conj_0])).
25.44/25.49	thf(h1,assumption,((member_a @ eigen__0) @ top_top_set_a),introduced(assumption,[])).
25.44/25.49	thf(1,plain,(~(sP8) | sP1),inference(all_rule,[status(thm)],[])).
25.44/25.49	thf(2,plain,(((~(sP9) | sP2) | sP7) | ~(sP1)),inference(confrontation_rule,[status(thm)],[])).
25.44/25.49	thf(3,plain,(~(sP5) | sP8),inference(prop_rule,[status(thm)],[])).
25.44/25.49	thf(4,plain,~(sP7),inference(prop_rule,[status(thm)],[])).
25.44/25.49	thf(5,plain,(~(sP10) | sP5),inference(all_rule,[status(thm)],[])).
25.44/25.49	thf(6,plain,((~(sP3) | ~(sP2)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
25.44/25.49	thf(7,plain,(~(sP4) | sP10),inference(prop_rule,[status(thm)],[])).
25.44/25.49	thf(fact_308_mult_Ocommute,axiom,sP4).
25.44/25.49	thf(fact_3__092_060open_062_I_092_060Sum_062a_092_060in_062UNIV_O_Acash__reserve_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_Aa_J_J_A_061_Ac_A_K_A_I1_A_L_Ai_J_092_060close_062,axiom,sP9).
25.44/25.49	thf(fact_2__092_060open_062_092_060forall_062n_0620_O_A_I_092_060Sum_062a_092_060in_062UNIV_O_A_092_060pi_062_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_Aa_J_An_J_A_061_A0_092_060close_062,axiom,sP6).
25.44/25.49	thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,h0,fact_308_mult_Ocommute,fact_3__092_060open_062_I_092_060Sum_062a_092_060in_062UNIV_O_Acash__reserve_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_Aa_J_J_A_061_Ac_A_K_A_I1_A_L_Ai_J_092_060close_062,fact_2__092_060open_062_092_060forall_062n_0620_O_A_I_092_060Sum_062a_092_060in_062UNIV_O_A_092_060pi_062_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_Aa_J_An_J_A_061_A0_092_060close_062])).
25.44/25.49	thf(fact_932_UNIV__witness,axiom,(~((![X1:a]:(~(((member_a @ X1) @ top_top_set_a))))))).
25.44/25.49	thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_932_UNIV__witness,8,h1])).
25.44/25.49	thf(0,theorem,(~(sP3)),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])).
25.44/25.49	% SZS output end Proof
25.44/25.49	EOF