0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.12/0.33	% Computer   : n003.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 11:53:47 EDT 2019
0.12/0.33	% CPUTime    : 
140.86/130.46	% SZS status Theorem
140.86/130.46	% Mode: mode406:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
140.86/130.46	% Inferences: 4888
140.86/130.46	% SZS output start Proof
140.86/130.46	thf(ty_subst, type, subst : $tType).
140.86/130.46	thf(ty_term, type, term : $tType).
140.86/130.46	thf(ty_push, type, push : (term>subst>subst)).
140.86/130.46	thf(ty_hoaslam, type, hoaslam : (subst>(subst>term>term)>term)).
140.86/130.46	thf(ty_eigen__1, type, eigen__1 : term).
140.86/130.46	thf(ty_eigen__0, type, eigen__0 : (subst>term>subst>$o)).
140.86/130.46	thf(ty_id, type, id : subst).
140.86/130.46	thf(ty_one, type, one : term).
140.86/130.46	thf(ty_sub, type, sub : (term>subst>term)).
140.86/130.46	thf(ty_lam, type, lam : (term>term)).
140.86/130.46	thf(ty_sh, type, sh : subst).
140.86/130.46	thf(ty_comp, type, comp : (subst>subst>subst)).
140.86/130.46	thf(sP1,plain,sP1 <=> (![X1:term]:((((eigen__0 @ id) @ X1) @ id) => (((eigen__0 @ id) @ ((sub @ eigen__1) @ ((push @ X1) @ id))) @ id))),introduced(definition,[new_symbols(definition,[sP1])])).
140.86/130.46	thf(sP2,plain,sP2 <=> (((sub @ eigen__1) @ id) = eigen__1),introduced(definition,[new_symbols(definition,[sP2])])).
140.86/130.46	thf(sP3,plain,sP3 <=> (((push @ one) @ sh) = id),introduced(definition,[new_symbols(definition,[sP3])])).
140.86/130.46	thf(sP4,plain,sP4 <=> (eigen__1 = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])).
140.86/130.46	thf(sP5,plain,sP5 <=> (![X1:subst]:(![X2:subst]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP5])])).
140.86/130.46	thf(sP6,plain,sP6 <=> (id = id),introduced(definition,[new_symbols(definition,[sP6])])).
140.86/130.46	thf(sP7,plain,sP7 <=> (((sub @ eigen__1) @ ((push @ one) @ sh)) = eigen__1),introduced(definition,[new_symbols(definition,[sP7])])).
140.86/130.46	thf(sP8,plain,sP8 <=> (![X1:subst>term>subst>$o]:((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ ((sub @ X2) @ ((push @ one) @ sh)))) @ id))))),introduced(definition,[new_symbols(definition,[sP8])])).
140.86/130.46	thf(sP9,plain,sP9 <=> (((eigen__0 @ id) @ (lam @ ((sub @ eigen__1) @ ((push @ one) @ sh)))) @ id),introduced(definition,[new_symbols(definition,[sP9])])).
140.86/130.46	thf(sP10,plain,sP10 <=> (id = ((push @ one) @ sh)),introduced(definition,[new_symbols(definition,[sP10])])).
140.86/130.46	thf(sP11,plain,sP11 <=> (![X1:subst]:((((push @ one) @ sh) = X1) => (X1 = ((push @ one) @ sh)))),introduced(definition,[new_symbols(definition,[sP11])])).
140.86/130.46	thf(sP12,plain,sP12 <=> (sP1 => sP9),introduced(definition,[new_symbols(definition,[sP12])])).
140.86/130.46	thf(sP13,plain,sP13 <=> (![X1:term]:((![X2:term]:((((eigen__0 @ id) @ X2) @ id) => (((eigen__0 @ id) @ ((sub @ X1) @ ((push @ X2) @ id))) @ id))) => (((eigen__0 @ id) @ (lam @ ((sub @ X1) @ ((push @ one) @ sh)))) @ id))),introduced(definition,[new_symbols(definition,[sP13])])).
140.86/130.46	thf(sP14,plain,sP14 <=> (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => ((![X2:term]:((((eigen__0 @ id) @ X2) @ id) => (((eigen__0 @ id) @ ((X1 @ id) @ X2)) @ id))) => (((eigen__0 @ id) @ ((hoaslam @ id) @ X1)) @ id)))),introduced(definition,[new_symbols(definition,[sP14])])).
140.86/130.46	thf(sP15,plain,sP15 <=> (sP14 => sP13),introduced(definition,[new_symbols(definition,[sP15])])).
140.86/130.46	thf(sP16,plain,sP16 <=> (((eigen__0 @ id) @ (lam @ eigen__1)) @ id),introduced(definition,[new_symbols(definition,[sP16])])).
140.86/130.46	thf(sP17,plain,sP17 <=> (![X1:term]:(((sub @ X1) @ id) = X1)),introduced(definition,[new_symbols(definition,[sP17])])).
140.86/130.46	thf(sP18,plain,sP18 <=> (sP3 => sP10),introduced(definition,[new_symbols(definition,[sP18])])).
140.86/130.46	thf(sP19,plain,sP19 <=> ((lam @ ((sub @ eigen__1) @ ((push @ one) @ sh))) = (lam @ eigen__1)),introduced(definition,[new_symbols(definition,[sP19])])).
140.86/130.46	thf(sP20,plain,sP20 <=> (((sub @ eigen__1) @ id) = ((sub @ eigen__1) @ ((push @ one) @ sh))),introduced(definition,[new_symbols(definition,[sP20])])).
140.86/130.46	thf(def_axvarid,definition,(axvarid = sP17)).
140.86/130.46	thf(def_axvarshift,definition,(axvarshift = sP3)).
140.86/130.46	thf(def_hoasinduction_lem3aa,definition,(hoasinduction_lem3aa = sP8)).
140.86/130.46	thf(def_hoasinduction_lem3,definition,(hoasinduction_lem3 = (![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id))))))))).
140.86/130.46	thf(def_hoasinduction_lem3_lthm,definition,(hoasinduction_lem3_lthm = (axvarid => (axvarshift => (hoasinduction_lem3aa => hoasinduction_lem3))))).
140.86/130.46	thf(thm,conjecture,(sP17 => (sP3 => (sP8 => (![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id))))))))))).
140.86/130.46	thf(h0,negated_conjecture,(~((sP17 => (sP3 => (sP8 => (![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id)))))))))))),inference(assume_negation,[status(cth)],[thm])).
140.86/130.46	thf(h1,assumption,sP17,introduced(assumption,[])).
140.86/130.46	thf(h2,assumption,(~((sP3 => (sP8 => (![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id))))))))))),introduced(assumption,[])).
140.86/130.46	thf(h3,assumption,sP3,introduced(assumption,[])).
140.86/130.46	thf(h4,assumption,(~((sP8 => (![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id)))))))))),introduced(assumption,[])).
140.86/130.46	thf(h5,assumption,sP8,introduced(assumption,[])).
140.86/130.46	thf(h6,assumption,(~((![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id))))))))),introduced(assumption,[])).
140.86/130.46	thf(h7,assumption,(~(((![X1:subst]:(![X2:term]:(![X3:subst]:(![X4:subst]:((((eigen__0 @ X1) @ X2) @ ((comp @ X4) @ X3)) => (((eigen__0 @ ((comp @ X1) @ X4)) @ ((sub @ X2) @ X4)) @ X3)))))) => ((![X1:subst]:(![X2:term]:(![X3:subst]:(![X4:subst]:((((eigen__0 @ ((comp @ X1) @ X4)) @ ((sub @ X2) @ X4)) @ X3) => (((eigen__0 @ X1) @ X2) @ ((comp @ X4) @ X3))))))) => (sP14 => (![X1:term]:((![X2:term]:((((eigen__0 @ id) @ X2) @ id) => (((eigen__0 @ id) @ ((sub @ X1) @ ((push @ X2) @ id))) @ id))) => (((eigen__0 @ id) @ (lam @ X1)) @ id)))))))),introduced(assumption,[])).
140.86/130.46	thf(h8,assumption,(![X1:subst]:(![X2:term]:(![X3:subst]:(![X4:subst]:((((eigen__0 @ X1) @ X2) @ ((comp @ X4) @ X3)) => (((eigen__0 @ ((comp @ X1) @ X4)) @ ((sub @ X2) @ X4)) @ X3)))))),introduced(assumption,[])).
140.86/130.46	thf(h9,assumption,(~(((![X1:subst]:(![X2:term]:(![X3:subst]:(![X4:subst]:((((eigen__0 @ ((comp @ X1) @ X4)) @ ((sub @ X2) @ X4)) @ X3) => (((eigen__0 @ X1) @ X2) @ ((comp @ X4) @ X3))))))) => (sP14 => (![X1:term]:((![X2:term]:((((eigen__0 @ id) @ X2) @ id) => (((eigen__0 @ id) @ ((sub @ X1) @ ((push @ X2) @ id))) @ id))) => (((eigen__0 @ id) @ (lam @ X1)) @ id))))))),introduced(assumption,[])).
140.86/130.46	thf(h10,assumption,(![X1:subst]:(![X2:term]:(![X3:subst]:(![X4:subst]:((((eigen__0 @ ((comp @ X1) @ X4)) @ ((sub @ X2) @ X4)) @ X3) => (((eigen__0 @ X1) @ X2) @ ((comp @ X4) @ X3))))))),introduced(assumption,[])).
140.86/130.46	thf(h11,assumption,(~((sP14 => (![X1:term]:((![X2:term]:((((eigen__0 @ id) @ X2) @ id) => (((eigen__0 @ id) @ ((sub @ X1) @ ((push @ X2) @ id))) @ id))) => (((eigen__0 @ id) @ (lam @ X1)) @ id)))))),introduced(assumption,[])).
140.86/130.46	thf(h12,assumption,sP14,introduced(assumption,[])).
140.86/130.46	thf(h13,assumption,(~((![X1:term]:((![X2:term]:((((eigen__0 @ id) @ X2) @ id) => (((eigen__0 @ id) @ ((sub @ X1) @ ((push @ X2) @ id))) @ id))) => (((eigen__0 @ id) @ (lam @ X1)) @ id))))),introduced(assumption,[])).
140.86/130.46	thf(h14,assumption,(~((sP1 => sP16))),introduced(assumption,[])).
140.86/130.46	thf(h15,assumption,sP1,introduced(assumption,[])).
140.86/130.46	thf(h16,assumption,(~(sP16)),introduced(assumption,[])).
140.86/130.46	thf(1,plain,((sP20 | ~(sP4)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(2,plain,(((~(sP2) | sP7) | ~(sP20)) | ~(sP4)),inference(confrontation_rule,[status(thm)],[])).
140.86/130.46	thf(3,plain,sP4,inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(4,plain,(sP19 | ~(sP7)),inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(5,plain,((((~(sP9) | sP16) | ~(sP6)) | ~(sP19)) | ~(sP6)),inference(mating_rule,[status(thm)],[])).
140.86/130.46	thf(6,plain,((~(sP12) | ~(sP1)) | sP9),inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(7,plain,sP6,inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(8,plain,(~(sP13) | sP12),inference(all_rule,[status(thm)],[])).
140.86/130.46	thf(9,plain,((~(sP15) | ~(sP14)) | sP13),inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(10,plain,(~(sP8) | sP15),inference(all_rule,[status(thm)],[])).
140.86/130.46	thf(11,plain,(~(sP17) | sP2),inference(all_rule,[status(thm)],[])).
140.86/130.46	thf(12,plain,((~(sP18) | ~(sP3)) | sP10),inference(prop_rule,[status(thm)],[])).
140.86/130.46	thf(13,plain,(~(sP11) | sP18),inference(all_rule,[status(thm)],[])).
140.86/130.46	thf(14,plain,(~(sP5) | sP11),inference(all_rule,[status(thm)],[])).
140.86/130.46	thf(15,plain,sP5,inference(@eq_sym,[status(thm)],[])).
140.86/130.46	thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1,h3,h5,h12,h15,h16])).
140.86/130.46	thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,16,h15,h16])).
140.86/130.46	thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h13,17,h14])).
140.86/130.46	thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,18,h12,h13])).
140.86/130.46	thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,19,h10,h11])).
140.86/130.46	thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9])).
140.86/130.46	thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,21,h7])).
140.86/130.46	thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,22,h5,h6])).
140.86/130.46	thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,23,h3,h4])).
140.86/130.46	thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,24,h1,h2])).
140.86/130.46	thf(0,theorem,(sP17 => (sP3 => (sP8 => (![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((X2 @ id) @ X3)) @ id))) => (((X1 @ id) @ ((hoaslam @ id) @ X2)) @ id)))) => (![X2:term]:((![X3:term]:((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((sub @ X2) @ ((push @ X3) @ id))) @ id))) => (((X1 @ id) @ (lam @ X2)) @ id)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[25,h0])).
140.86/130.46	% SZS output end Proof
140.98/130.46	EOF