0.04/0.12	% Problem    : SLH0482^1 : TPTP v8.2.0. Released v8.2.0.
0.12/0.13	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.12/0.35	Computer   : n016.cluster.edu
0.12/0.35	Model      : x86_64 x86_64
0.12/0.35	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.35	RAMPerCPU  : 8042.1875MB
0.12/0.35	OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.35	% CPULimit   : 30
0.12/0.35	% DateTime   : Mon Jul  3 05:23:49 EDT 2023
0.12/0.35	% CPUTime    : 
19.88/20.07	% SZS status Theorem
19.88/20.07	% Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
19.88/20.07	% Inferences: 913
19.88/20.07	% SZS output start Proof
19.88/20.07	thf(ty_a, type, a : $tType).
19.88/20.07	thf(ty_risk_Free_account, type, risk_Free_account : $tType).
19.88/20.07	thf(ty_nat, type, nat : $tType).
19.88/20.07	thf(ty_real, type, real : $tType).
19.88/20.07	thf(ty_set_a, type, set_a : $tType).
19.88/20.07	thf(ty_zero_zero_real, type, zero_zero_real : real).
19.88/20.07	thf(ty_member_a, type, member_a : (a>set_a>$o)).
19.88/20.07	thf(ty_times_times_real, type, times_times_real : (real>real>real)).
19.88/20.07	thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)).
19.88/20.07	thf(ty_risk_F1245088672346398815dger_a, type, risk_F1245088672346398815dger_a : ((nat>real)>real>(a>risk_Free_account)>a>risk_Free_account)).
19.88/20.07	thf(ty_eigen__0, type, eigen__0 : a).
19.88/20.07	thf(ty_groups2740460157737275248a_real, type, groups2740460157737275248a_real : ((a>real)>set_a>real)).
19.88/20.07	thf(ty_i, type, i : real).
19.88/20.07	thf(ty_top_top_set_a, type, top_top_set_a : set_a).
19.88/20.07	thf(ty_zero_zero_nat, type, zero_zero_nat : nat).
19.88/20.07	thf(ty_ord_less_nat, type, ord_less_nat : (nat>nat>$o)).
19.88/20.07	thf(ty_l, type, l : (a>risk_Free_account)).
19.88/20.07	thf(ty_rho, type, rho : (nat>real)).
19.88/20.07	thf(ty_c, type, c : real).
19.88/20.07	thf(ty_risk_F1914734008469130493eserve, type, risk_F1914734008469130493eserve : (risk_Free_account>real)).
19.88/20.07	thf(ty_risk_Free_balanced_a, type, risk_Free_balanced_a : ((a>risk_Free_account)>real>$o)).
19.88/20.07	thf(ty_one_one_real, type, one_one_real : real).
19.88/20.07	thf(ty_risk_F170160801229183585ccount, type, risk_F170160801229183585ccount : (risk_Free_account>nat>real)).
19.88/20.07	thf(sP1,plain,sP1 <=> (![X1:nat]:(((ord_less_nat @ zero_zero_nat) @ X1) => (((groups2740460157737275248a_real @ (^[X2:a]:((risk_F170160801229183585ccount @ (l @ X2)) @ X1))) @ top_top_set_a) = zero_zero_real))),introduced(definition,[new_symbols(definition,[sP1])])).
19.88/20.07	thf(sP2,plain,sP2 <=> (((risk_Free_balanced_a @ (((risk_F1245088672346398815dger_a @ rho) @ i) @ l)) @ ((times_times_real @ ((plus_plus_real @ one_one_real) @ i)) @ c)) = (~(((((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)) => (~((![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,[sP2])])).
19.88/20.07	thf(sP3,plain,sP3 <=> ((c = ((groups2740460157737275248a_real @ (^[X1:a]:(risk_F1914734008469130493eserve @ (l @ X1)))) @ top_top_set_a)) => (((groups2740460157737275248a_real @ (^[X1:a]:(risk_F1914734008469130493eserve @ (l @ X1)))) @ top_top_set_a) = c)),introduced(definition,[new_symbols(definition,[sP3])])).
19.88/20.07	thf(sP4,plain,sP4 <=> (![X1:real]:(![X2:real]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
19.88/20.07	thf(sP5,plain,sP5 <=> (![X1:a>risk_Free_account]:((risk_Free_balanced_a @ X1) = (^[X2:real]:(~(((((groups2740460157737275248a_real @ (^[X3:a]:(risk_F1914734008469130493eserve @ (X1 @ X3)))) @ top_top_set_a) = X2) => (~((![X3:nat]:(((ord_less_nat @ zero_zero_nat) @ X3) => (((groups2740460157737275248a_real @ (^[X4:a]:((risk_F170160801229183585ccount @ (X1 @ X4)) @ X3))) @ top_top_set_a) = zero_zero_real))))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
19.88/20.07	thf(sP6,plain,sP6 <=> (risk_Free_balanced_a = (^[X1:a>risk_Free_account]:(^[X2:real]:(~(((((groups2740460157737275248a_real @ (^[X3:a]:(risk_F1914734008469130493eserve @ (X1 @ X3)))) @ top_top_set_a) = X2) => (~((![X3:nat]:(((ord_less_nat @ zero_zero_nat) @ X3) => (((groups2740460157737275248a_real @ (^[X4:a]:((risk_F170160801229183585ccount @ (X1 @ X4)) @ X3))) @ top_top_set_a) = zero_zero_real))))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
19.88/20.07	thf(sP7,plain,sP7 <=> (![X1:real]:(((risk_Free_balanced_a @ (((risk_F1245088672346398815dger_a @ rho) @ i) @ l)) @ X1) = (~(((((groups2740460157737275248a_real @ (^[X2:a]:(risk_F1914734008469130493eserve @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X2)))) @ top_top_set_a) = X1) => (~((![X2:nat]:(((ord_less_nat @ zero_zero_nat) @ X2) => (((groups2740460157737275248a_real @ (^[X3:a]:((risk_F170160801229183585ccount @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X3)) @ X2))) @ top_top_set_a) = zero_zero_real)))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
19.88/20.07	thf(sP8,plain,sP8 <=> ((((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)) => (~((![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,[sP8])])).
19.88/20.07	thf(sP9,plain,sP9 <=> ((risk_Free_balanced_a @ (((risk_F1245088672346398815dger_a @ rho) @ i) @ l)) = (^[X1:real]:(~(((((groups2740460157737275248a_real @ (^[X2:a]:(risk_F1914734008469130493eserve @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X2)))) @ top_top_set_a) = X1) => (~((![X2:nat]:(((ord_less_nat @ zero_zero_nat) @ X2) => (((groups2740460157737275248a_real @ (^[X3:a]:((risk_F170160801229183585ccount @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X3)) @ X2))) @ top_top_set_a) = zero_zero_real)))))))))),introduced(definition,[new_symbols(definition,[sP9])])).
19.88/20.07	thf(sP10,plain,sP10 <=> (((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,[sP10])])).
19.88/20.07	thf(sP11,plain,sP11 <=> (((groups2740460157737275248a_real @ (^[X1:a]:(risk_F1914734008469130493eserve @ (l @ X1)))) @ top_top_set_a) = c),introduced(definition,[new_symbols(definition,[sP11])])).
19.88/20.07	thf(sP12,plain,sP12 <=> ((risk_Free_balanced_a @ (((risk_F1245088672346398815dger_a @ rho) @ i) @ l)) @ ((times_times_real @ ((plus_plus_real @ one_one_real) @ i)) @ c)),introduced(definition,[new_symbols(definition,[sP12])])).
19.88/20.07	thf(sP13,plain,sP13 <=> (![X1:set_a]:((((groups2740460157737275248a_real @ (^[X2:a]:(risk_F1914734008469130493eserve @ ((((risk_F1245088672346398815dger_a @ rho) @ i) @ l) @ X2)))) @ X1) = ((times_times_real @ ((plus_plus_real @ one_one_real) @ i)) @ c)) => ((![X2:nat]:(((ord_less_nat @ zero_zero_nat) @ X2) => (((groups2740460157737275248a_real @ (^[X3:a]:((risk_F170160801229183585ccount @ (l @ X3)) @ X2))) @ X1) = zero_zero_real))) => (c = ((groups2740460157737275248a_real @ (^[X2:a]:(risk_F1914734008469130493eserve @ (l @ X2)))) @ X1))))),introduced(definition,[new_symbols(definition,[sP13])])).
19.88/20.07	thf(sP14,plain,sP14 <=> (c = ((groups2740460157737275248a_real @ (^[X1:a]:(risk_F1914734008469130493eserve @ (l @ X1)))) @ top_top_set_a)),introduced(definition,[new_symbols(definition,[sP14])])).
19.88/20.07	thf(sP15,plain,sP15 <=> (![X1:real]:((c = X1) => (X1 = c))),introduced(definition,[new_symbols(definition,[sP15])])).
19.88/20.07	thf(sP16,plain,sP16 <=> (sP1 => sP14),introduced(definition,[new_symbols(definition,[sP16])])).
19.88/20.07	thf(sP17,plain,sP17 <=> (sP10 => sP16),introduced(definition,[new_symbols(definition,[sP17])])).
19.88/20.07	thf(conj_0,conjecture,sP11).
19.88/20.07	thf(h0,negated_conjecture,(~(sP11)),inference(assume_negation,[status(cth)],[conj_0])).
19.88/20.07	thf(h1,assumption,((member_a @ eigen__0) @ top_top_set_a),introduced(assumption,[])).
19.88/20.07	thf(1,plain,(sP8 | sP10),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(2,plain,((~(sP2) | ~(sP12)) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(3,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])).
19.88/20.07	thf(4,plain,(~(sP9) | sP7),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(5,plain,(~(sP5) | sP9),inference(all_rule,[status(thm)],[])).
19.88/20.07	thf(6,plain,((~(sP3) | ~(sP14)) | sP11),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(7,plain,(~(sP15) | sP3),inference(all_rule,[status(thm)],[])).
19.88/20.07	thf(8,plain,(~(sP4) | sP15),inference(all_rule,[status(thm)],[])).
19.88/20.07	thf(9,plain,sP4,inference(@eq_sym,[status(thm)],[])).
19.88/20.07	thf(10,plain,(~(sP6) | sP5),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(11,plain,((~(sP17) | ~(sP10)) | sP16),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(12,plain,((~(sP16) | ~(sP1)) | sP14),inference(prop_rule,[status(thm)],[])).
19.88/20.07	thf(13,plain,(~(sP13) | sP17),inference(all_rule,[status(thm)],[])).
19.88/20.07	thf(fact_11_local_Obalanced__alt__def,axiom,sP6).
19.88/20.07	thf(fact_2__092_060open_062balanced_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_J_A_I_I1_A_L_Ai_J_A_K_Ac_J_092_060close_062,axiom,sP12).
19.88/20.07	thf(fact_1_calculation,axiom,sP1).
19.88/20.07	thf(fact_0__092_060open_062_092_060And_062S_O_A_092_060lbrakk_062_I_092_060Sum_062a_092_060in_062S_O_Acash__reserve_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_Aa_J_J_A_061_A_I1_A_L_Ai_J_A_K_Ac_059_A_092_060forall_062n_0620_O_A_I_092_060Sum_062a_092_060in_062S_O_A_092_060pi_062_A_I_092_060L_062_Aa_J_An_J_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Ac_A_061_A_I_092_060Sum_062a_092_060in_062S_O_Acash__reserve_A_I_092_060L_062_Aa_J_J_092_060close_062,axiom,sP13).
19.88/20.07	thf(14,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h0,fact_11_local_Obalanced__alt__def,fact_2__092_060open_062balanced_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_J_A_I_I1_A_L_Ai_J_A_K_Ac_J_092_060close_062,fact_1_calculation,fact_0__092_060open_062_092_060And_062S_O_A_092_060lbrakk_062_I_092_060Sum_062a_092_060in_062S_O_Acash__reserve_A_Iupdate__ledger_A_092_060rho_062_Ai_A_092_060L_062_Aa_J_J_A_061_A_I1_A_L_Ai_J_A_K_Ac_059_A_092_060forall_062n_0620_O_A_I_092_060Sum_062a_092_060in_062S_O_A_092_060pi_062_A_I_092_060L_062_Aa_J_An_J_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Ac_A_061_A_I_092_060Sum_062a_092_060in_062S_O_Acash__reserve_A_I_092_060L_062_Aa_J_J_092_060close_062])).
19.88/20.07	thf(fact_285_UNIV__witness,axiom,(~((![X1:a]:(~(((member_a @ X1) @ top_top_set_a))))))).
19.88/20.07	thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_285_UNIV__witness,14,h1])).
19.88/20.07	thf(0,theorem,sP11,inference(contra,[status(thm),contra(discharge,[h0])],[15,h0])).
19.88/20.07	% SZS output end Proof
19.88/20.08	EOF