0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : satallax -s schedule_3_1 -E eprover -P picomus -M modes -p tstp -t %d %s 0.02/0.23 % Computer : n139.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sun Jul 15 13:33:55 CDT 2018 0.02/0.23 % CPUTime : 144.95/145.17 % SZS status Theorem 144.95/145.17 % Mode: mode328 144.95/145.17 % Inferences: 9280 144.95/145.17 % SZS output start Proof 144.95/145.17 thf(ty_subst, type, subst : $tType). 144.95/145.17 thf(ty_term, type, term : $tType). 144.95/145.17 thf(ty_hoasvar, type, hoasvar : (subst>term>subst>$o)). 144.95/145.17 thf(ty_push, type, push : (term>subst>subst)). 144.95/145.17 thf(ty_hoaslam, type, hoaslam : (subst>(subst>term>term)>term)). 144.95/145.17 thf(ty_hoasap, type, hoasap : (subst>term>subst>term>term)). 144.95/145.17 thf(ty_eigen__0, type, eigen__0 : term). 144.95/145.17 thf(ty_ap, type, ap : (term>term>term)). 144.95/145.17 thf(ty_id, type, id : subst). 144.95/145.17 thf(ty_one, type, one : term). 144.95/145.17 thf(ty_sub, type, sub : (term>subst>term)). 144.95/145.17 thf(ty_lam, type, lam : (term>term)). 144.95/145.17 thf(ty_sh, type, sh : subst). 144.95/145.17 thf(ty_var, type, var : (term>$o)). 144.95/145.17 thf(ty_comp, type, comp : (subst>subst>subst)). 144.95/145.17 thf(h0, assumption, (![X1:term>$o]:(![X2:term]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). 144.95/145.17 thf(eigendef_eigen__0, definition, (eigen__0 = (eps__0 @ (^[X1:term]:(~((~((![X2:subst>term>term]:(~((((sub @ X1) @ ((push @ one) @ sh)) = ((X2 @ sh) @ one)))))))))))), introduced(definition,[new_symbols(definition,[eigen__0]))). 144.95/145.17 thf(sP1,plain,(sP1 <=> ((![X1:term]:(~((var @ (lam @ X1))))) => ((![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((X1 @ X2) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))) => ((![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))) => ((![X1:term>$o]:((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => (![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => (X1 @ ((sub @ X2) @ X3)))))))) => ((![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))) => ((~(((~(((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:subst]:(((comp @ id) @ X1) = X1))))))) => (~((![X1:subst]:(((comp @ X1) @ id) = X1))))))) => ((~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:term]:(((sub @ X1) @ id) = X1))))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X3 = X4)))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((((hoaslam @ id) @ X1) = ((hoaslam @ id) @ X2)) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~((((hoaslam @ id) @ X1) = ((((hoasap @ id) @ X2) @ id) @ X3)))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((((hoasvar @ id) @ ((hoaslam @ id) @ X1)) @ id))))) => ((![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))) => ((![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:term]:((((hoasvar @ id) @ X2) @ id) => (((X1 @ id) @ X2) @ id))) => (![X2:term]:((var @ X2) => (((X1 @ id) @ X2) @ id))))))) => ((![X1:subst>term>subst>$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:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((((hoasap @ id) @ X2) @ id) @ X3)) @ id))))) => (![X2:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((ap @ X2) @ X3)) @ id))))))))) => (![X1:term]:(~((![X2:subst>term>term]:(~((((sub @ X1) @ ((push @ one) @ sh)) = ((X2 @ sh) @ one))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])]))). 144.95/145.17 thf(sP2,plain,(sP2 <=> ((![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))) => ((![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))) => ((![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))) => ((![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))) => ((![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))) => sP1))))))),introduced(definition,[new_symbols(definition,[sP2])]))). 144.95/145.17 thf(sP3,plain,(sP3 <=> ((![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))) => ((![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))) => ((![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))) => ((![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))) => sP1)))),introduced(definition,[new_symbols(definition,[sP3])]))). 144.95/145.17 thf(sP4,plain,(sP4 <=> ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => sP2))))))))))),introduced(definition,[new_symbols(definition,[sP4])]))). 144.95/145.17 thf(sP5,plain,(sP5 <=> ((![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))) => ((![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))) => sP1)),introduced(definition,[new_symbols(definition,[sP5])]))). 144.95/145.17 thf(sP6,plain,(sP6 <=> ((![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))) => sP1),introduced(definition,[new_symbols(definition,[sP6])]))). 144.95/145.17 thf(sP7,plain,(sP7 <=> ((![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))) => sP5),introduced(definition,[new_symbols(definition,[sP7])]))). 144.95/145.17 thf(sP8,plain,(sP8 <=> ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))) => sP3),introduced(definition,[new_symbols(definition,[sP8])]))). 144.95/145.17 thf(sP9,plain,(sP9 <=> ((![X1:term]:(((sub @ X1) @ id) = X1)) => sP4),introduced(definition,[new_symbols(definition,[sP9])]))). 144.95/145.17 thf(sP10,plain,(sP10 <=> (![X1:term]:(~((![X2:subst>term>term]:(~((((sub @ X1) @ ((push @ one) @ sh)) = ((X2 @ sh) @ one)))))))),introduced(definition,[new_symbols(definition,[sP10])]))). 144.95/145.17 thf(sP11,plain,(sP11 <=> ((![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))) => ((![X1:term>$o]:((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => (![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => (X1 @ ((sub @ X2) @ X3)))))))) => ((![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))) => ((~(((~(((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:subst]:(((comp @ id) @ X1) = X1))))))) => (~((![X1:subst]:(((comp @ X1) @ id) = X1))))))) => ((~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:term]:(((sub @ X1) @ id) = X1))))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X3 = X4)))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((((hoaslam @ id) @ X1) = ((hoaslam @ id) @ X2)) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~((((hoaslam @ id) @ X1) = ((((hoasap @ id) @ X2) @ id) @ X3)))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((((hoasvar @ id) @ ((hoaslam @ id) @ X1)) @ id))))) => ((![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))) => ((![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:term]:((((hoasvar @ id) @ X2) @ id) => (((X1 @ id) @ X2) @ id))) => (![X2:term]:((var @ X2) => (((X1 @ id) @ X2) @ id))))))) => ((![X1:subst>term>subst>$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:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((((hoasap @ id) @ X2) @ id) @ X3)) @ id))))) => (![X2:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((ap @ X2) @ X3)) @ id))))))))) => sP10))))))))))))),introduced(definition,[new_symbols(definition,[sP11])]))). 144.95/145.17 thf(sP12,plain,(sP12 <=> ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((((hoasvar @ id) @ ((hoaslam @ id) @ X1)) @ id))))) => ((![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))) => ((![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:term]:((((hoasvar @ id) @ X2) @ id) => (((X1 @ id) @ X2) @ id))) => (![X2:term]:((var @ X2) => (((X1 @ id) @ X2) @ id))))))) => ((![X1:subst>term>subst>$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:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((((hoasap @ id) @ X2) @ id) @ X3)) @ id))))) => (![X2:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((ap @ X2) @ X3)) @ id))))))))) => sP10)))),introduced(definition,[new_symbols(definition,[sP12])]))). 144.95/145.17 thf(sP13,plain,(sP13 <=> ((~(((~(((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:subst]:(((comp @ id) @ X1) = X1))))))) => (~((![X1:subst]:(((comp @ X1) @ id) = X1))))))) => ((~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:term]:(((sub @ X1) @ id) = X1))))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X3 = X4)))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((((hoaslam @ id) @ X1) = ((hoaslam @ id) @ X2)) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~((((hoaslam @ id) @ X1) = ((((hoasap @ id) @ X2) @ id) @ X3)))))))) => sP12)))))),introduced(definition,[new_symbols(definition,[sP13])]))). 144.95/145.17 thf(sP14,plain,(sP14 <=> (((push @ one) @ sh) = id),introduced(definition,[new_symbols(definition,[sP14])]))). 144.95/145.17 thf(sP15,plain,(sP15 <=> ((![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:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((((hoasap @ id) @ X2) @ id) @ X3)) @ id))))) => (![X2:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((ap @ X2) @ X3)) @ id))))))))) => sP10),introduced(definition,[new_symbols(definition,[sP15])]))). 144.95/145.17 thf(sP16,plain,(sP16 <=> (![X1:subst>term>term]:(~((((sub @ eigen__0) @ ((push @ one) @ sh)) = ((X1 @ sh) @ one))))),introduced(definition,[new_symbols(definition,[sP16])]))). 144.95/145.17 thf(sP17,plain,(sP17 <=> ((((sub @ eigen__0) @ id) = eigen__0) => ((((sub @ eigen__0) @ id) = eigen__0) => (eigen__0 = eigen__0))),introduced(definition,[new_symbols(definition,[sP17])]))). 144.95/145.17 thf(sP18,plain,(sP18 <=> (![X1:term]:((((sub @ eigen__0) @ id) = eigen__0) => ((((sub @ eigen__0) @ id) = X1) => (eigen__0 = X1)))),introduced(definition,[new_symbols(definition,[sP18])]))). 144.95/145.17 thf(sP19,plain,(sP19 <=> ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((((hoaslam @ id) @ X1) = ((hoaslam @ id) @ X2)) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~((((hoaslam @ id) @ X1) = ((((hoasap @ id) @ X2) @ id) @ X3)))))))) => sP12)),introduced(definition,[new_symbols(definition,[sP19])]))). 144.95/145.17 thf(sP20,plain,(sP20 <=> ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => sP2),introduced(definition,[new_symbols(definition,[sP20])]))). 144.95/145.17 thf(sP21,plain,(sP21 <=> (![X1:term]:(((sub @ X1) @ id) = X1)),introduced(definition,[new_symbols(definition,[sP21])]))). 144.95/145.17 thf(sP22,plain,(sP22 <=> ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X3 = X4)))))) => sP19),introduced(definition,[new_symbols(definition,[sP22])]))). 144.95/145.17 thf(sP23,plain,(sP23 <=> (((sub @ eigen__0) @ id) = eigen__0),introduced(definition,[new_symbols(definition,[sP23])]))). 144.95/145.17 thf(sP24,plain,(sP24 <=> ((~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~(sP21))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X1 = X2)))))) => sP22)),introduced(definition,[new_symbols(definition,[sP24])]))). 144.95/145.17 thf(sP25,plain,(sP25 <=> ((![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))) => ((![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:term]:((((hoasvar @ id) @ X2) @ id) => (((X1 @ id) @ X2) @ id))) => (![X2:term]:((var @ X2) => (((X1 @ id) @ X2) @ id))))))) => sP15)),introduced(definition,[new_symbols(definition,[sP25])]))). 144.95/145.17 thf(sP26,plain,(sP26 <=> ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => (sP14 => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => sP20))))),introduced(definition,[new_symbols(definition,[sP26])]))). 144.95/145.17 thf(sP27,plain,(sP27 <=> ((![X1:subst]:(((comp @ X1) @ id) = X1)) => (sP14 => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => sP20)))),introduced(definition,[new_symbols(definition,[sP27])]))). 144.95/145.17 thf(sP28,plain,(sP28 <=> ((![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))) => sP13),introduced(definition,[new_symbols(definition,[sP28])]))). 144.95/145.17 thf(sP29,plain,(sP29 <=> ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~((((hoaslam @ id) @ X1) = ((((hoasap @ id) @ X2) @ id) @ X3)))))))) => sP12),introduced(definition,[new_symbols(definition,[sP29])]))). 144.95/145.17 thf(sP30,plain,(sP30 <=> ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => sP26)),introduced(definition,[new_symbols(definition,[sP30])]))). 144.95/145.17 thf(sP31,plain,(sP31 <=> ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => sP30)),introduced(definition,[new_symbols(definition,[sP31])]))). 144.95/145.17 thf(sP32,plain,(sP32 <=> ((![X1:subst]:(((comp @ id) @ X1) = X1)) => sP30),introduced(definition,[new_symbols(definition,[sP32])]))). 144.95/145.17 thf(sP33,plain,(sP33 <=> ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X1 = X2)))))) => sP22),introduced(definition,[new_symbols(definition,[sP33])]))). 144.95/145.17 thf(sP34,plain,(sP34 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP34])]))). 144.95/145.17 thf(sP35,plain,(sP35 <=> (sP14 => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => sP20))),introduced(definition,[new_symbols(definition,[sP35])]))). 144.95/145.17 thf(sP36,plain,(sP36 <=> ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => sP9),introduced(definition,[new_symbols(definition,[sP36])]))). 144.95/145.17 thf(sP37,plain,(sP37 <=> ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => sP20)),introduced(definition,[new_symbols(definition,[sP37])]))). 144.95/145.17 thf(sP38,plain,(sP38 <=> ((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => sP36),introduced(definition,[new_symbols(definition,[sP38])]))). 144.95/145.17 thf(sP39,plain,(sP39 <=> ((![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((X1 @ X2) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))) => sP11),introduced(definition,[new_symbols(definition,[sP39])]))). 144.95/145.17 thf(sP40,plain,(sP40 <=> ((![X1:subst>term>subst>$o]:((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ X2) @ X3) @ ((comp @ X5) @ X4)) => (((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4)))))) => ((![X2:subst]:(![X3:term]:(![X4:subst]:(![X5:subst]:((((X1 @ ((comp @ X2) @ X5)) @ ((sub @ X3) @ X5)) @ X4) => (((X1 @ X2) @ X3) @ ((comp @ X5) @ X4))))))) => ((![X2:term]:((((hoasvar @ id) @ X2) @ id) => (((X1 @ id) @ X2) @ id))) => (![X2:term]:((var @ X2) => (((X1 @ id) @ X2) @ id))))))) => sP15),introduced(definition,[new_symbols(definition,[sP40])]))). 144.95/145.17 thf(sP41,plain,(sP41 <=> ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))) => sP8),introduced(definition,[new_symbols(definition,[sP41])]))). 144.95/145.17 thf(sP42,plain,(sP42 <=> ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => sP26),introduced(definition,[new_symbols(definition,[sP42])]))). 144.95/145.17 thf(sP43,plain,(sP43 <=> (![X1:term]:(![X2:term]:((X1 = eigen__0) => ((X1 = X2) => (eigen__0 = X2))))),introduced(definition,[new_symbols(definition,[sP43])]))). 144.95/145.17 thf(sP44,plain,(sP44 <=> ((![X1:term>$o]:((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => (![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => (X1 @ ((sub @ X2) @ X3)))))))) => sP28),introduced(definition,[new_symbols(definition,[sP44])]))). 144.95/145.17 thf(sP45,plain,(sP45 <=> (![X1:term]:(![X2:term]:(![X3:term]:((X2 = X1) => ((X2 = X3) => (X1 = X3)))))),introduced(definition,[new_symbols(definition,[sP45])]))). 144.95/145.17 thf(sP46,plain,(sP46 <=> ((var @ one) => sP20),introduced(definition,[new_symbols(definition,[sP46])]))). 144.95/145.17 thf(sP47,plain,(sP47 <=> (((sub @ eigen__0) @ ((push @ one) @ sh)) = ((sub @ eigen__0) @ id)),introduced(definition,[new_symbols(definition,[sP47])]))). 144.95/145.17 thf(sP48,plain,(sP48 <=> (sP23 => sP34),introduced(definition,[new_symbols(definition,[sP48])]))). 144.95/145.17 thf(def_axapp,definition,(axapp = (![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))))). 144.95/145.17 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))). 144.95/145.17 thf(def_axvarid,definition,(axvarid = sP21)). 144.95/145.17 thf(def_axabs,definition,(axabs = (![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))))). 144.95/145.17 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))). 144.95/145.17 thf(def_axidl,definition,(axidl = (![X1:subst]:(((comp @ id) @ X1) = X1)))). 144.95/145.17 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))). 144.95/145.17 thf(def_axassoc,definition,(axassoc = (![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))))). 144.95/145.17 thf(def_axmap,definition,(axmap = (![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))))). 144.95/145.17 thf(def_axidr,definition,(axidr = (![X1:subst]:(((comp @ X1) @ id) = X1)))). 144.95/145.17 thf(def_axvarshift,definition,(axvarshift = sP14)). 144.95/145.17 thf(def_axscons,definition,(axscons = (![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)))). 144.95/145.17 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))). 144.95/145.17 thf(def_ulamvarsh,definition,(ulamvarsh = (![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))))). 144.95/145.17 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))). 144.95/145.17 thf(def_apinj1,definition,(apinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))))). 144.95/145.17 thf(def_apinj2,definition,(apinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))))). 144.95/145.17 thf(def_laminj,definition,(laminj = (![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))))). 144.95/145.17 thf(def_shinj,definition,(shinj = (![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))))). 144.95/145.17 thf(def_lamnotap,definition,(lamnotap = (![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))))). 144.95/145.17 thf(def_apnotvar,definition,(apnotvar = (![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))))). 144.95/145.17 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))). 144.95/145.17 thf(def_induction,definition,(induction = (![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((X1 @ X2) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))))). 144.95/145.17 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))). 144.95/145.17 thf(def_induction2lem,definition,(induction2lem = (![X1:term>$o]:((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => (![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => (X1 @ ((sub @ X2) @ X3)))))))))). 144.95/145.17 thf(def_induction2,definition,(induction2 = (![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))))). 144.95/145.17 thf(def_substmonoid,definition,(substmonoid = (~(((~(((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:subst]:(((comp @ id) @ X1) = X1))))))) => (~((![X1:subst]:(((comp @ X1) @ id) = X1))))))))). 144.95/145.17 thf(def_termmset,definition,(termmset = (~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~(sP21))))))). 144.95/145.17 thf(def_hoasapinj1,definition,(hoasapinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X1 = X2)))))))). 144.95/145.17 thf(def_hoasapinj2,definition,(hoasapinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((((hoasap @ id) @ X1) @ id) @ X3) = ((((hoasap @ id) @ X2) @ id) @ X4)) => (X3 = X4)))))))). 144.95/145.17 thf(def_hoaslaminj,definition,(hoaslaminj = (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => ((((hoaslam @ id) @ X1) = ((hoaslam @ id) @ X2)) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))))). 144.95/145.17 thf(def_hoaslamnotap,definition,(hoaslamnotap = (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~((((hoaslam @ id) @ X1) = ((((hoasap @ id) @ X2) @ id) @ X3)))))))))). 144.95/145.17 thf(def_hoaslamnotvar,definition,(hoaslamnotvar = (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((((hoasvar @ id) @ ((hoaslam @ id) @ X1)) @ id))))))). 144.95/145.17 thf(def_hoasapnotvar,definition,(hoasapnotvar = (![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))))). 144.95/145.17 thf(def_hoasinduction_lem1,definition,(hoasinduction_lem1 = (![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:term]:((((hoasvar @ id) @ X2) @ id) => (((X1 @ id) @ X2) @ id))) => (![X2:term]:((var @ X2) => (((X1 @ id) @ X2) @ id))))))))). 144.95/145.17 thf(def_hoasinduction_lem2,definition,(hoasinduction_lem2 = (![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:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((((hoasap @ id) @ X2) @ id) @ X3)) @ id))))) => (![X2:term]:(![X3:term]:((((X1 @ id) @ X2) @ id) => ((((X1 @ id) @ X3) @ id) => (((X1 @ id) @ ((ap @ X2) @ X3)) @ id))))))))))). 144.95/145.17 thf(def_hoasinduction_lem3b,definition,(hoasinduction_lem3b = sP10)). 144.95/145.17 thf(def_hoasinduction_lem3b_gthm,definition,(hoasinduction_lem3b_gthm = (axapp => (axvarcons => (axvarid => (axabs => (axclos => (axidl => (axshiftcons => (axassoc => (axmap => (axidr => (axvarshift => (axscons => (ulamvar1 => (ulamvarsh => (ulamvarind => (apinj1 => (apinj2 => (laminj => (shinj => (lamnotap => (apnotvar => (lamnotvar => (induction => (pushprop => (induction2lem => (induction2 => (substmonoid => (termmset => (hoasapinj1 => (hoasapinj2 => (hoaslaminj => (hoaslamnotap => (hoaslamnotvar => (hoasapnotvar => (hoasinduction_lem1 => (hoasinduction_lem2 => hoasinduction_lem3b)))))))))))))))))))))))))))))))))))))). 144.95/145.17 thf(thm,conjecture,hoasinduction_lem3b_gthm). 144.95/145.17 thf(h1,negated_conjecture,(~(sP38)),inference(assume_negation,[status(cth)],[thm])). 144.95/145.17 thf(1,plain,(sP38 | ~(sP36)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(2,plain,(sP36 | ~(sP9)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(3,plain,(sP9 | sP21),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(4,plain,(sP9 | ~(sP4)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(5,plain,(sP4 | ~(sP31)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(6,plain,(sP31 | ~(sP32)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(7,plain,(sP32 | ~(sP30)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(8,plain,(sP30 | ~(sP42)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(9,plain,(sP42 | ~(sP26)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(10,plain,(sP26 | ~(sP27)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(11,plain,(sP27 | ~(sP35)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(12,plain,(sP35 | sP14),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(13,plain,(sP35 | ~(sP37)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(14,plain,(sP37 | ~(sP46)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(15,plain,(sP46 | ~(sP20)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(16,plain,(sP20 | ~(sP2)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(17,plain,(sP2 | ~(sP41)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(18,plain,(sP41 | ~(sP8)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(19,plain,(sP8 | ~(sP3)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(20,plain,(sP3 | ~(sP7)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(21,plain,(sP7 | ~(sP5)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(22,plain,(sP5 | ~(sP6)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(23,plain,(sP6 | ~(sP1)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(24,plain,(sP1 | ~(sP39)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(25,plain,(sP39 | ~(sP11)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(26,plain,(sP11 | ~(sP44)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(27,plain,(sP44 | ~(sP28)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(28,plain,(sP28 | ~(sP13)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(29,plain,(sP13 | ~(sP24)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(30,plain,(sP24 | ~(sP33)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(31,plain,(sP33 | ~(sP22)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(32,plain,(sP22 | ~(sP19)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(33,plain,(sP19 | ~(sP29)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(34,plain,(sP29 | ~(sP12)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(35,plain,(sP12 | ~(sP25)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(36,plain,(sP25 | ~(sP40)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(37,plain,(sP40 | ~(sP15)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(38,plain,(sP15 | ~(sP10)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(39,plain,(sP10 | sP16),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). 144.95/145.17 thf(40,plain,(~(sP21) | sP23),inference(all_rule,[status(thm)],[])). 144.95/145.17 thf(41,plain,sP45,inference(eq_trans3,[status(thm)],[])). 144.95/145.17 thf(42,plain,(~(sP45) | sP43),inference(all_rule,[status(thm)],[])). 144.95/145.17 thf(43,plain,(~(sP43) | sP18),inference(all_rule,[status(thm)],[])). 144.95/145.17 thf(44,plain,((~(sP48) | ~(sP23)) | sP34),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(45,plain,((~(sP17) | ~(sP23)) | sP48),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(46,plain,(~(sP18) | sP17),inference(all_rule,[status(thm)],[])). 144.95/145.17 thf(47,plain,(~(sP16) | ~(sP47)),inference(all_rule,[status(thm)],[])). 144.95/145.17 thf(48,plain,((sP47 | ~(sP34)) | ~(sP14)),inference(prop_rule,[status(thm)],[])). 144.95/145.17 thf(49,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[h1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48])). 144.95/145.17 thf(50,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[49,h0])). 144.95/145.17 thf(0,theorem,hoasinduction_lem3b_gthm,inference(contra,[status(thm),contra(discharge,[h1])],[49,h1])). 144.95/145.17 % SZS output end Proof 144.95/145.18 EOF