0.07/0.12	% Problem  : SLH0057^1 : TPTP v8.2.0. Released v8.2.0.
0.07/0.13	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.13/0.34	% Computer : n020.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 03:20:01 EDT 2023
0.13/0.34	% CPUTime  : 
0.20/0.56	% SZS status Theorem
0.20/0.56	% Mode: cade22sinegrackle2x6978
0.20/0.56	% Steps: 2264
0.20/0.56	% SZS output start Proof
0.20/0.56	thf(ty_real, type, real : $tType).
0.20/0.56	thf(ty_set_or1222579329274155063t_real, type, set_or1222579329274155063t_real : (real>real>set_real)).
0.20/0.56	thf(ty_zero_zero_real, type, zero_zero_real : real).
0.20/0.56	thf(ty_topolo5044208981011980120l_real, type, topolo5044208981011980120l_real : (set_real>(real>real)>$o)).
0.20/0.56	thf(ty_f, type, f : (real>real)).
0.20/0.56	thf(ty_hensto5963834015518849588l_real, type, hensto5963834015518849588l_real : ((real>real)>set_real>$o)).
0.20/0.56	thf(ty_a, type, a : real).
0.20/0.56	thf(sP1,plain,sP1 <=> (![X1:real]:(![X2:real>real]:(((topolo5044208981011980120l_real @ ((set_or1222579329274155063t_real @ zero_zero_real) @ X1)) @ X2) => ((hensto5963834015518849588l_real @ X2) @ ((set_or1222579329274155063t_real @ zero_zero_real) @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])).
0.20/0.56	thf(sP2,plain,sP2 <=> (![X1:real>real]:(((topolo5044208981011980120l_real @ ((set_or1222579329274155063t_real @ zero_zero_real) @ a)) @ X1) => ((hensto5963834015518849588l_real @ X1) @ ((set_or1222579329274155063t_real @ zero_zero_real) @ a)))),introduced(definition,[new_symbols(definition,[sP2])])).
0.20/0.56	thf(sP3,plain,sP3 <=> ((hensto5963834015518849588l_real @ f) @ ((set_or1222579329274155063t_real @ zero_zero_real) @ a)),introduced(definition,[new_symbols(definition,[sP3])])).
0.20/0.56	thf(sP4,plain,sP4 <=> (((topolo5044208981011980120l_real @ ((set_or1222579329274155063t_real @ zero_zero_real) @ a)) @ f) => sP3),introduced(definition,[new_symbols(definition,[sP4])])).
0.20/0.56	thf(sP5,plain,sP5 <=> (![X1:real]:(![X2:real]:(![X3:real>real]:(((topolo5044208981011980120l_real @ ((set_or1222579329274155063t_real @ X1) @ X2)) @ X3) => ((hensto5963834015518849588l_real @ X3) @ ((set_or1222579329274155063t_real @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP5])])).
0.20/0.56	thf(sP6,plain,sP6 <=> ((topolo5044208981011980120l_real @ ((set_or1222579329274155063t_real @ zero_zero_real) @ a)) @ f),introduced(definition,[new_symbols(definition,[sP6])])).
0.20/0.56	thf(conj_0,conjecture,sP3).
0.20/0.56	thf(h0,negated_conjecture,(~(sP3)),inference(assume_negation,[status(cth)],[conj_0])).
0.20/0.56	thf(1,plain,((~(sP4) | ~(sP6)) | sP3),inference(prop_rule,[status(thm)],[])).
0.20/0.56	thf(2,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])).
0.20/0.56	thf(3,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])).
0.20/0.56	thf(4,plain,(~(sP5) | sP1),inference(all_rule,[status(thm)],[])).
0.20/0.56	thf(fact_29_integrable__continuous__real,axiom,sP5).
0.20/0.56	thf(fact_4_cont__0a,axiom,sP6).
0.20/0.56	thf(5,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,h0,fact_29_integrable__continuous__real,fact_4_cont__0a])).
0.20/0.56	thf(0,theorem,sP3,inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])).
0.20/0.56	% SZS output end Proof
0.20/0.56	EOF