0.12/0.12	% Problem    : SLH0354^1 : TPTP v8.2.0. Released v8.2.0.
0.12/0.12	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.13/0.33	Computer   : n019.cluster.edu
0.13/0.33	Model      : x86_64 x86_64
0.13/0.33	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	RAMPerCPU  : 8042.1875MB
0.13/0.33	OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 30
0.13/0.34	% DateTime   : Mon Jul  3 04:23:50 EDT 2023
0.19/0.34	% CPUTime    : 
6.24/6.45	% SZS status Theorem
6.24/6.45	% Mode: mode9a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
6.24/6.45	% Inferences: 71
6.24/6.45	% SZS output start Proof
6.24/6.45	thf(ty_risk_Free_account, type, risk_Free_account : $tType).
6.24/6.45	thf(ty_set_nat, type, set_nat : $tType).
6.24/6.45	thf(ty_nat, type, nat : $tType).
6.24/6.45	thf(ty_real, type, real : $tType).
6.24/6.45	thf(ty_zero_zero_real, type, zero_zero_real : real).
6.24/6.45	thf(ty_collect_nat, type, collect_nat : ((nat>$o)>set_nat)).
6.24/6.45	thf(ty_suc, type, suc : (nat>nat)).
6.24/6.45	thf(ty_groups6591440286371151544t_real, type, groups6591440286371151544t_real : ((nat>real)>set_nat>real)).
6.24/6.45	thf(ty_ka, type, ka : nat).
6.24/6.45	thf(ty_ord_less_eq_nat, type, ord_less_eq_nat : (nat>nat>$o)).
6.24/6.45	thf(ty_alpha, type, alpha : risk_Free_account).
6.24/6.45	thf(ty_risk_F170160801229183585ccount, type, risk_F170160801229183585ccount : (risk_Free_account>nat>real)).
6.24/6.45	thf(sP1,plain,sP1 <=> ((risk_F170160801229183585ccount @ alpha) = (risk_F170160801229183585ccount @ alpha)),introduced(definition,[new_symbols(definition,[sP1])])).
6.24/6.45	thf(sP2,plain,sP2 <=> ((^[X1:nat]:(~((((ord_less_eq_nat @ X1) @ (suc @ ka)) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))) = (^[X1:nat]:(~((((ord_less_eq_nat @ X1) @ ka) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP2])])).
6.24/6.45	thf(sP3,plain,sP3 <=> (((groups6591440286371151544t_real @ (risk_F170160801229183585ccount @ alpha)) @ (collect_nat @ (^[X1:nat]:(~((((ord_less_eq_nat @ X1) @ (suc @ ka)) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))) = ((groups6591440286371151544t_real @ (risk_F170160801229183585ccount @ alpha)) @ (collect_nat @ (^[X1:nat]:(~((((ord_less_eq_nat @ X1) @ ka) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))))),introduced(definition,[new_symbols(definition,[sP3])])).
6.24/6.45	thf(sP4,plain,sP4 <=> (![X1:nat]:((~((((ord_less_eq_nat @ X1) @ (suc @ ka)) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))) = (~((((ord_less_eq_nat @ X1) @ ka) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))),introduced(definition,[new_symbols(definition,[sP4])])).
6.24/6.45	thf(sP5,plain,sP5 <=> ((collect_nat @ (^[X1:nat]:(~((((ord_less_eq_nat @ X1) @ (suc @ ka)) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real)))))) = (collect_nat @ (^[X1:nat]:(~((((ord_less_eq_nat @ X1) @ ka) => (((risk_F170160801229183585ccount @ alpha) @ X1) = zero_zero_real))))))),introduced(definition,[new_symbols(definition,[sP5])])).
6.24/6.45	thf(conj_0,conjecture,sP3).
6.24/6.45	thf(h0,negated_conjecture,(~(sP3)),inference(assume_negation,[status(cth)],[conj_0])).
6.24/6.45	thf(1,plain,sP1,inference(prop_rule,[status(thm)],[])).
6.24/6.45	thf(2,plain,(sP2 | ~(sP4)),inference(prop_rule,[status(thm)],[])).
6.24/6.45	thf(3,plain,(sP5 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
6.24/6.45	thf(4,plain,((sP3 | ~(sP1)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
6.24/6.45	thf(fact_0__092_060open_062_092_060And_062i_O_A_Ii_A_092_060le_062_ASuc_Ak_A_092_060and_062_A_092_060pi_062_A_092_060alpha_062_Ai_A_092_060noteq_062_A0_J_A_061_A_Ii_A_092_060le_062_Ak_A_092_060and_062_A_092_060pi_062_A_092_060alpha_062_Ai_A_092_060noteq_062_A0_J_092_060close_062,axiom,sP4).
6.24/6.45	thf(5,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,h0,fact_0__092_060open_062_092_060And_062i_O_A_Ii_A_092_060le_062_ASuc_Ak_A_092_060and_062_A_092_060pi_062_A_092_060alpha_062_Ai_A_092_060noteq_062_A0_J_A_061_A_Ii_A_092_060le_062_Ak_A_092_060and_062_A_092_060pi_062_A_092_060alpha_062_Ai_A_092_060noteq_062_A0_J_092_060close_062])).
6.24/6.45	thf(0,theorem,sP3,inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])).
6.24/6.45	% SZS output end Proof
6.24/6.45	EOF