0.03/0.12	% Problem  : SLH0564^1 : TPTP v8.2.0. Released v8.2.0.
0.03/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.12/0.33	% Computer : n029.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 30
0.12/0.33	% WCLimit  : 30
0.12/0.33	% DateTime : Mon Jul  3 05:34:12 EDT 2023
0.12/0.34	% CPUTime  : 
24.89/24.90	% SZS status Theorem
24.89/24.90	% Mode: cade22sinegrackle2xfaf3
24.89/24.90	% Steps: 98178
24.89/24.90	% SZS output start Proof
24.89/24.90	thf(ty_real, type, real : $tType).
24.89/24.90	thf(ty_set_a, type, set_a : $tType).
24.89/24.90	thf(ty_a, type, a : $tType).
24.89/24.90	thf(ty_groups2740460157737275248a_real, type, groups2740460157737275248a_real : ((a>real)>set_a>real)).
24.89/24.90	thf(ty_f, type, f : (a>real)).
24.89/24.90	thf(ty_member_a, type, member_a : (a>set_a>$o)).
24.89/24.90	thf(ty_i, type, i : set_a).
24.89/24.90	thf(ty_insert_a, type, insert_a : (a>set_a>set_a)).
24.89/24.90	thf(ty_times_times_real, type, times_times_real : (real>real>real)).
24.89/24.90	thf(ty_j, type, j : a).
24.89/24.90	thf(ty_minus_minus_set_a, type, minus_minus_set_a : (set_a>set_a>set_a)).
24.89/24.90	thf(ty_finite_finite_a, type, finite_finite_a : (set_a>$o)).
24.89/24.90	thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)).
24.89/24.90	thf(ty_bot_bot_set_a, type, bot_bot_set_a : set_a).
24.89/24.90	thf(sP1,plain,sP1 <=> (finite_finite_a @ i),introduced(definition,[new_symbols(definition,[sP1])])).
24.89/24.90	thf(sP2,plain,sP2 <=> (![X1:set_a]:(![X2:a]:(![X3:a>real]:((finite_finite_a @ X1) => (((member_a @ X2) @ X1) => (((groups2740460157737275248a_real @ X3) @ X1) = ((plus_plus_real @ (X3 @ X2)) @ ((groups2740460157737275248a_real @ X3) @ ((minus_minus_set_a @ X1) @ ((insert_a @ X2) @ bot_bot_set_a)))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
24.89/24.90	thf(sP3,plain,sP3 <=> (((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ i) = ((plus_plus_real @ ((times_times_real @ (f @ j)) @ (f @ j))) @ ((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ ((minus_minus_set_a @ i) @ ((insert_a @ j) @ bot_bot_set_a))))),introduced(definition,[new_symbols(definition,[sP3])])).
24.89/24.90	thf(sP4,plain,sP4 <=> (![X1:a>real]:(sP1 => (((member_a @ j) @ i) => (((groups2740460157737275248a_real @ X1) @ i) = ((plus_plus_real @ (X1 @ j)) @ ((groups2740460157737275248a_real @ X1) @ ((minus_minus_set_a @ i) @ ((insert_a @ j) @ bot_bot_set_a)))))))),introduced(definition,[new_symbols(definition,[sP4])])).
24.89/24.90	thf(sP5,plain,sP5 <=> (sP1 => (((member_a @ j) @ i) => sP3)),introduced(definition,[new_symbols(definition,[sP5])])).
24.89/24.90	thf(sP6,plain,sP6 <=> (![X1:a]:(![X2:a>real]:(sP1 => (((member_a @ X1) @ i) => (((groups2740460157737275248a_real @ X2) @ i) = ((plus_plus_real @ (X2 @ X1)) @ ((groups2740460157737275248a_real @ X2) @ ((minus_minus_set_a @ i) @ ((insert_a @ X1) @ bot_bot_set_a))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
24.89/24.90	thf(sP7,plain,sP7 <=> (((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ i) = ((plus_plus_real @ ((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ ((insert_a @ j) @ bot_bot_set_a))) @ ((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ ((minus_minus_set_a @ i) @ ((insert_a @ j) @ bot_bot_set_a))))),introduced(definition,[new_symbols(definition,[sP7])])).
24.89/24.90	thf(sP8,plain,sP8 <=> ((member_a @ j) @ i),introduced(definition,[new_symbols(definition,[sP8])])).
24.89/24.90	thf(sP9,plain,sP9 <=> (sP8 => sP3),introduced(definition,[new_symbols(definition,[sP9])])).
24.89/24.90	thf(sP10,plain,sP10 <=> (((plus_plus_real @ ((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ ((insert_a @ j) @ bot_bot_set_a))) @ ((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ ((minus_minus_set_a @ i) @ ((insert_a @ j) @ bot_bot_set_a)))) = ((plus_plus_real @ ((times_times_real @ (f @ j)) @ (f @ j))) @ ((groups2740460157737275248a_real @ (^[X1:a]:((times_times_real @ (f @ X1)) @ (f @ X1)))) @ ((minus_minus_set_a @ i) @ ((insert_a @ j) @ bot_bot_set_a))))),introduced(definition,[new_symbols(definition,[sP10])])).
24.89/24.90	thf(conj_0,conjecture,sP10).
24.89/24.90	thf(h0,negated_conjecture,(~(sP10)),inference(assume_negation,[status(cth)],[conj_0])).
24.89/24.90	thf(1,plain,((~(sP9) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])).
24.89/24.90	thf(2,plain,((~(sP5) | ~(sP1)) | sP9),inference(prop_rule,[status(thm)],[])).
24.89/24.90	thf(3,plain,(~(sP4) | sP5),inference(all_rule,[status(thm)],[])).
24.89/24.90	thf(4,plain,(((~(sP7) | sP10) | ~(sP7)) | ~(sP3)),inference(confrontation_rule,[status(thm)],[])).
24.89/24.90	thf(5,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])).
24.89/24.90	thf(6,plain,(~(sP2) | sP6),inference(all_rule,[status(thm)],[])).
24.89/24.90	thf(fact_187_sum_Oremove,axiom,sP2).
24.89/24.90	thf(fact_2_calculation,axiom,sP7).
24.89/24.90	thf(fact_1_assms_I1_J,axiom,sP1).
24.89/24.90	thf(fact_0_assms_I3_J,axiom,sP8).
24.89/24.90	thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,fact_187_sum_Oremove,fact_2_calculation,fact_1_assms_I1_J,fact_0_assms_I3_J])).
24.89/24.90	thf(0,theorem,sP10,inference(contra,[status(thm),contra(discharge,[h0])],[7,h0])).
24.89/24.90	% SZS output end Proof
24.89/24.90	EOF