0.04/0.12	% Problem  : SLH0171^1 : TPTP v8.2.0. Released v8.2.0.
0.04/0.13	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.13/0.34	% Computer : n001.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 : 30
0.13/0.34	% WCLimit  : 30
0.13/0.34	% DateTime : Mon Jul  3 04:13:59 EDT 2023
0.13/0.34	% CPUTime  : 
0.43/1.00	% SZS status Theorem
0.43/1.00	% Mode: cade22sinegrackle2x6978
0.43/1.00	% Steps: 15853
0.43/1.00	% SZS output start Proof
0.43/1.00	thf(ty_real, type, real : $tType).
0.43/1.00	thf(ty_probab4737552673497767871pace_a, type, probab4737552673497767871pace_a : $tType).
0.43/1.00	thf(ty_a, type, a : $tType).
0.43/1.00	thf(ty_s, type, s : probab4737552673497767871pace_a).
0.43/1.00	thf(ty_times_times_real, type, times_times_real : (real>real>real)).
0.43/1.00	thf(ty_c, type, c : real).
0.43/1.00	thf(ty_zero_zero_real, type, zero_zero_real : real).
0.43/1.00	thf(ty_f, type, f : (a>real)).
0.43/1.00	thf(ty_probab7312716125271441302able_a, type, probab7312716125271441302able_a : (probab4737552673497767871pace_a>(a>real)>$o)).
0.43/1.00	thf(sP1,plain,sP1 <=> (![X1:real]:(![X2:a>real]:(((probab7312716125271441302able_a @ s) @ (^[X3:a]:((times_times_real @ X1) @ (X2 @ X3)))) = ((~((X1 = zero_zero_real))) => ((probab7312716125271441302able_a @ s) @ X2))))),introduced(definition,[new_symbols(definition,[sP1])])).
0.43/1.00	thf(sP2,plain,sP2 <=> (((probab7312716125271441302able_a @ s) @ (^[X1:a]:((times_times_real @ c) @ (f @ X1)))) = ((~((c = zero_zero_real))) => ((probab7312716125271441302able_a @ s) @ f))),introduced(definition,[new_symbols(definition,[sP2])])).
0.43/1.00	thf(sP3,plain,sP3 <=> (![X1:a>real]:(((probab7312716125271441302able_a @ s) @ (^[X2:a]:((times_times_real @ c) @ (X1 @ X2)))) = ((~((c = zero_zero_real))) => ((probab7312716125271441302able_a @ s) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
0.43/1.00	thf(sP4,plain,sP4 <=> ((probab7312716125271441302able_a @ s) @ (^[X1:a]:((times_times_real @ c) @ (f @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
0.43/1.00	thf(sP5,plain,sP5 <=> ((~((c = zero_zero_real))) => ((probab7312716125271441302able_a @ s) @ f)),introduced(definition,[new_symbols(definition,[sP5])])).
0.43/1.00	thf(sP6,plain,sP6 <=> (![X1:probab4737552673497767871pace_a]:(![X2:real]:(![X3:a>real]:(((probab7312716125271441302able_a @ X1) @ (^[X4:a]:((times_times_real @ X2) @ (X3 @ X4)))) = ((~((X2 = zero_zero_real))) => ((probab7312716125271441302able_a @ X1) @ X3)))))),introduced(definition,[new_symbols(definition,[sP6])])).
0.43/1.00	thf(sP7,plain,sP7 <=> ((probab7312716125271441302able_a @ s) @ f),introduced(definition,[new_symbols(definition,[sP7])])).
0.43/1.00	thf(conj_0,conjecture,sP4).
0.43/1.00	thf(h0,negated_conjecture,(~(sP4)),inference(assume_negation,[status(cth)],[conj_0])).
0.43/1.00	thf(1,plain,(sP5 | ~(sP7)),inference(prop_rule,[status(thm)],[])).
0.43/1.00	thf(2,plain,((~(sP2) | sP4) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
0.43/1.00	thf(3,plain,(~(sP3) | sP2),inference(all_rule,[status(thm)],[])).
0.43/1.00	thf(4,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])).
0.43/1.00	thf(5,plain,(~(sP6) | sP1),inference(all_rule,[status(thm)],[])).
0.43/1.00	thf(fact_2_qbs__integrable__mult__iff,axiom,sP6).
0.43/1.00	thf(fact_0_assms,axiom,sP7).
0.43/1.00	thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,fact_2_qbs__integrable__mult__iff,fact_0_assms])).
0.43/1.00	thf(0,theorem,sP4,inference(contra,[status(thm),contra(discharge,[h0])],[6,h0])).
0.43/1.00	% SZS output end Proof
0.43/1.00	EOF