0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.09/0.29 % Computer : n020.cluster.edu
0.09/0.29 % Model : x86_64 x86_64
0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.29 % Memory : 8042.1875MB
0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
0.09/0.29 % CPULimit : 960
0.09/0.29 % WCLimit : 120
0.09/0.29 % DateTime : Thu Jul 2 08:30:02 EDT 2020
0.09/0.29 % CPUTime :
38.59/38.78 % SZS status Theorem
38.59/38.78 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
38.59/38.78 % Inferences: 541
38.59/38.78 % SZS output start Proof
38.59/38.78 thf(def_axapp,definition,(axapp = (![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))))).
38.59/38.78 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))).
38.59/38.78 thf(def_axvarid,definition,(axvarid = (![X1:term]:(((sub @ X1) @ id) = X1)))).
38.59/38.78 thf(def_axabs,definition,(axabs = (![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))))).
38.59/38.78 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
38.59/38.78 thf(def_axidl,definition,(axidl = (![X1:subst]:(((comp @ id) @ X1) = X1)))).
38.59/38.78 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
38.59/38.78 thf(def_axassoc,definition,(axassoc = (![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))))).
38.59/38.78 thf(def_axmap,definition,(axmap = (![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))))).
38.59/38.78 thf(def_axidr,definition,(axidr = (![X1:subst]:(((comp @ X1) @ id) = X1)))).
38.59/38.78 thf(def_axvarshift,definition,(axvarshift = (((push @ one) @ sh) = id))).
38.59/38.78 thf(def_axscons,definition,(axscons = (![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)))).
38.59/38.78 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))).
38.59/38.78 thf(def_ulamvarsh,definition,(ulamvarsh = (![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))))).
38.59/38.78 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))).
38.59/38.78 thf(def_apinj1,definition,(apinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))))).
38.59/38.78 thf(def_apinj2,definition,(apinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))))).
38.59/38.78 thf(def_laminj,definition,(laminj = (![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))))).
38.59/38.78 thf(def_shinj,definition,(shinj = (![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))))).
38.59/38.78 thf(def_lamnotap,definition,(lamnotap = (![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))))).
38.59/38.78 thf(def_apnotvar,definition,(apnotvar = (![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))))).
38.59/38.78 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))).
38.59/38.78 thf(def_induction,definition,(induction = (![X1:term>$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))))))).
38.59/38.78 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))).
38.59/38.78 thf(def_induction2lem,definition,(induction2lem = (![X1:term>$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)))))))))).
38.59/38.78 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))))))).
38.59/38.78 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))))))))).
38.59/38.78 thf(def_termmset,definition,(termmset = (~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:term]:(((sub @ X1) @ id) = X1))))))))).
38.59/38.78 thf(def_hoasap,definition,(hoasap = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(ap @ ((sub @ X2) @ X3))))))).
38.59/38.78 thf(def_hoaslam,definition,(hoaslam = (^[X1:subst]:(^[X2:subst>term>term]:(lam @ ((X2 @ sh) @ one)))))).
38.59/38.78 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)))))))).
38.59/38.78 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)))))))).
38.59/38.78 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))))))))))).
38.59/38.78 thf(def_hoaslaminj_gthm,definition,(hoaslaminj_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)))))))))))))))))))))))))))))))).
38.59/38.78 thf(thm,conjecture,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![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)))) => ((![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)))))) => ((![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]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ X2) @ id)) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ 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)))))) => (((lam @ ((X1 @ sh) @ one)) = (lam @ ((X2 @ sh) @ one))) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4)))))))))))))))))))))))))))))))))))))))).
38.59/38.78 thf(h0,negated_conjecture,(~(((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![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)))) => ((![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))) => ((![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))) => ((![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))) => ((![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))) => ((![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))) => ((![X1:term]:(~((var @ (lam @ X1))))) => ((![X1:term>$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]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ X2) @ id)) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ 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)))))) => (((lam @ ((X1 @ sh) @ one)) = (lam @ ((X2 @ sh) @ one))) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
38.59/38.78 thf(ax1261, axiom, (p1|~(p3)), file('', ax1261)).
38.59/38.78 thf(ax1263, axiom, ~(p1), file('', ax1263)).
38.59/38.78 thf(ax1259, axiom, (p3|~(p5)), file('', ax1259)).
38.59/38.78 thf(ax1257, axiom, (p5|~(p7)), file('', ax1257)).
38.59/38.78 thf(ax1255, axiom, (p7|~(p9)), file('', ax1255)).
38.59/38.78 thf(ax1253, axiom, (p9|~(p11)), file('', ax1253)).
38.59/38.78 thf(ax1251, axiom, (p11|~(p13)), file('', ax1251)).
38.59/38.78 thf(ax1249, axiom, (p13|~(p15)), file('', ax1249)).
38.59/38.78 thf(ax1247, axiom, (p15|~(p17)), file('', ax1247)).
38.59/38.78 thf(ax1245, axiom, (p17|~(p19)), file('', ax1245)).
38.59/38.78 thf(ax1243, axiom, (p19|~(p21)), file('', ax1243)).
38.59/38.78 thf(ax1241, axiom, (p21|~(p23)), file('', ax1241)).
38.59/38.78 thf(ax1239, axiom, (p23|~(p25)), file('', ax1239)).
38.59/38.78 thf(ax1237, axiom, (p25|~(p27)), file('', ax1237)).
38.59/38.78 thf(ax1235, axiom, (p27|~(p29)), file('', ax1235)).
38.59/38.78 thf(ax1233, axiom, (p29|~(p31)), file('', ax1233)).
38.59/38.78 thf(ax1231, axiom, (p31|~(p33)), file('', ax1231)).
38.59/38.78 thf(ax1229, axiom, (p33|~(p35)), file('', ax1229)).
38.59/38.78 thf(ax1227, axiom, (p35|~(p37)), file('', ax1227)).
38.59/38.78 thf(ax1225, axiom, (p37|~(p39)), file('', ax1225)).
38.59/38.78 thf(ax1223, axiom, (p39|~(p41)), file('', ax1223)).
38.59/38.78 thf(ax1221, axiom, (p41|~(p43)), file('', ax1221)).
38.59/38.78 thf(ax1219, axiom, (p43|~(p45)), file('', ax1219)).
38.59/38.78 thf(ax1217, axiom, (p45|~(p47)), file('', ax1217)).
38.59/38.78 thf(ax1215, axiom, (p47|~(p49)), file('', ax1215)).
38.59/38.78 thf(ax1213, axiom, (p49|~(p51)), file('', ax1213)).
38.59/38.78 thf(ax1211, axiom, (p51|~(p53)), file('', ax1211)).
38.59/38.78 thf(pax36, axiom, (p36=>![X155:term, X156:term]:((flam @ X155)=(flam @ X156)=>(X155)=(X156))), file('', pax36)).
38.59/38.78 thf(ax1228, axiom, (p35|p36), file('', ax1228)).
38.59/38.78 thf(nax53, axiom, (p53<=(~((~((![X144:subst, X145:subst, X142:subst]:(fcomp @ (fcomp @ X144 @ X145) @ X142)=(fcomp @ X144 @ (fcomp @ X145 @ X142))=>~(![X144:subst]:(fcomp @ fid @ X144)=(X144))))=>~(![X144:subst]:(fcomp @ X144 @ fid)=(X144))))=>(~((![X146:term, X145:subst, X142:subst]:(fsub @ (fsub @ X146 @ X145) @ X142)=(fsub @ X146 @ (fcomp @ X145 @ X142))=>~(![X146:term]:(fsub @ X146 @ fid)=(X146))))=>(![X146:term, X147:term, X148:term, X143:term]:((fap @ (fsub @ X146 @ fid) @ X148)=(fap @ (fsub @ X147 @ fid) @ X143)=>(X146)=(X147))=>(![X146:term, X147:term, X148:term, X143:term]:((fap @ (fsub @ X146 @ fid) @ X148)=(fap @ (fsub @ X147 @ fid) @ X143)=>(X148)=(X143))=>![X149:subst > term > term]:(![X150:subst, X148:term, X151:subst]:(fsub @ (X149 @ X150 @ X148) @ X151)=(X149 @ (fcomp @ X150 @ X151) @ (fsub @ X148 @ X151))=>![X152:subst > term > term]:(![X153:subst, X154:term, X70:subst]:(fsub @ (X152 @ X153 @ X154) @ X70)=(X152 @ (fcomp @ X153 @ X70) @ (fsub @ X154 @ X70))=>((flam @ (X149 @ fsh @ fone))=(flam @ (X152 @ fsh @ fone))=>![X153:subst, X154:term]:(X149 @ X153 @ X154)=(X152 @ X153 @ X154))))))))), file('', nax53)).
38.59/38.78 thf(pax4, axiom, (p4=>![X165:term, X160:subst]:(fsub @ fone @ (fpush @ X165 @ X160))=(X165)), file('', pax4)).
38.59/38.78 thf(ax1260, axiom, (p3|p4), file('', ax1260)).
38.59/38.78 thf(pax14, axiom, (p14=>![X163:term, X160:subst]:(fcomp @ fsh @ (fpush @ X163 @ X160))=(X160)), file('', pax14)).
38.59/38.78 thf(ax1250, axiom, (p13|p14), file('', ax1250)).
38.59/38.78 thf(c_0_34, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1261])).
38.59/38.78 thf(c_0_35, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1263])).
38.59/38.78 thf(c_0_36, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1259])).
38.59/38.78 thf(c_0_37, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_34])).
38.59/38.78 thf(c_0_38, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_35])).
38.59/38.78 thf(c_0_39, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax1257])).
38.59/38.78 thf(c_0_40, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_36])).
38.59/38.78 thf(c_0_41, plain, ~p3, inference(sr,[status(thm)],[c_0_37, c_0_38])).
38.59/38.78 thf(c_0_42, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax1255])).
38.59/38.78 thf(c_0_43, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_39])).
38.59/38.78 thf(c_0_44, plain, ~p5, inference(sr,[status(thm)],[c_0_40, c_0_41])).
38.59/38.78 thf(c_0_45, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax1253])).
38.59/38.78 thf(c_0_46, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_42])).
38.59/38.78 thf(c_0_47, plain, ~p7, inference(sr,[status(thm)],[c_0_43, c_0_44])).
38.59/38.78 thf(c_0_48, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax1251])).
38.59/38.78 thf(c_0_49, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_45])).
38.59/38.78 thf(c_0_50, plain, ~p9, inference(sr,[status(thm)],[c_0_46, c_0_47])).
38.59/38.78 thf(c_0_51, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax1249])).
38.59/38.78 thf(c_0_52, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_48])).
38.59/38.78 thf(c_0_53, plain, ~p11, inference(sr,[status(thm)],[c_0_49, c_0_50])).
38.59/38.78 thf(c_0_54, plain, (p15|~p17), inference(fof_simplification,[status(thm)],[ax1247])).
38.59/38.78 thf(c_0_55, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_51])).
38.59/38.78 thf(c_0_56, plain, ~p13, inference(sr,[status(thm)],[c_0_52, c_0_53])).
38.59/38.78 thf(c_0_57, plain, (p17|~p19), inference(fof_simplification,[status(thm)],[ax1245])).
38.59/38.78 thf(c_0_58, plain, (p15|~p17), inference(split_conjunct,[status(thm)],[c_0_54])).
38.59/38.78 thf(c_0_59, plain, ~p15, inference(sr,[status(thm)],[c_0_55, c_0_56])).
38.59/38.78 thf(c_0_60, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax1243])).
38.59/38.78 thf(c_0_61, plain, (p17|~p19), inference(split_conjunct,[status(thm)],[c_0_57])).
38.59/38.78 thf(c_0_62, plain, ~p17, inference(sr,[status(thm)],[c_0_58, c_0_59])).
38.59/38.78 thf(c_0_63, plain, (p21|~p23), inference(fof_simplification,[status(thm)],[ax1241])).
38.59/38.78 thf(c_0_64, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_60])).
38.59/38.78 thf(c_0_65, plain, ~p19, inference(sr,[status(thm)],[c_0_61, c_0_62])).
38.59/38.78 thf(c_0_66, plain, (p23|~p25), inference(fof_simplification,[status(thm)],[ax1239])).
38.59/38.78 thf(c_0_67, plain, (p21|~p23), inference(split_conjunct,[status(thm)],[c_0_63])).
38.59/38.78 thf(c_0_68, plain, ~p21, inference(sr,[status(thm)],[c_0_64, c_0_65])).
38.59/38.78 thf(c_0_69, plain, (p25|~p27), inference(fof_simplification,[status(thm)],[ax1237])).
38.59/38.78 thf(c_0_70, plain, (p23|~p25), inference(split_conjunct,[status(thm)],[c_0_66])).
38.59/38.78 thf(c_0_71, plain, ~p23, inference(sr,[status(thm)],[c_0_67, c_0_68])).
38.59/38.78 thf(c_0_72, plain, (p27|~p29), inference(fof_simplification,[status(thm)],[ax1235])).
38.59/38.78 thf(c_0_73, plain, (p25|~p27), inference(split_conjunct,[status(thm)],[c_0_69])).
38.59/38.78 thf(c_0_74, plain, ~p25, inference(sr,[status(thm)],[c_0_70, c_0_71])).
38.59/38.78 thf(c_0_75, plain, (p29|~p31), inference(fof_simplification,[status(thm)],[ax1233])).
38.59/38.78 thf(c_0_76, plain, (p27|~p29), inference(split_conjunct,[status(thm)],[c_0_72])).
38.59/38.78 thf(c_0_77, plain, ~p27, inference(sr,[status(thm)],[c_0_73, c_0_74])).
38.59/38.78 thf(c_0_78, plain, (p31|~p33), inference(fof_simplification,[status(thm)],[ax1231])).
38.59/38.78 thf(c_0_79, plain, (p29|~p31), inference(split_conjunct,[status(thm)],[c_0_75])).
38.59/38.78 thf(c_0_80, plain, ~p29, inference(sr,[status(thm)],[c_0_76, c_0_77])).
38.59/38.78 thf(c_0_81, plain, (p33|~p35), inference(fof_simplification,[status(thm)],[ax1229])).
38.59/38.78 thf(c_0_82, plain, (p31|~p33), inference(split_conjunct,[status(thm)],[c_0_78])).
38.59/38.78 thf(c_0_83, plain, ~p31, inference(sr,[status(thm)],[c_0_79, c_0_80])).
38.59/38.78 thf(c_0_84, plain, (p35|~p37), inference(fof_simplification,[status(thm)],[ax1227])).
38.59/38.78 thf(c_0_85, plain, (p33|~p35), inference(split_conjunct,[status(thm)],[c_0_81])).
38.59/38.78 thf(c_0_86, plain, ~p33, inference(sr,[status(thm)],[c_0_82, c_0_83])).
38.59/38.78 thf(c_0_87, plain, (p37|~p39), inference(fof_simplification,[status(thm)],[ax1225])).
38.59/38.78 thf(c_0_88, plain, (p35|~p37), inference(split_conjunct,[status(thm)],[c_0_84])).
38.59/38.78 thf(c_0_89, plain, ~p35, inference(sr,[status(thm)],[c_0_85, c_0_86])).
38.59/38.78 thf(c_0_90, plain, (p39|~p41), inference(fof_simplification,[status(thm)],[ax1223])).
38.59/38.78 thf(c_0_91, plain, (p37|~p39), inference(split_conjunct,[status(thm)],[c_0_87])).
38.59/38.78 thf(c_0_92, plain, ~p37, inference(sr,[status(thm)],[c_0_88, c_0_89])).
38.59/38.78 thf(c_0_93, plain, (p41|~p43), inference(fof_simplification,[status(thm)],[ax1221])).
38.59/38.78 thf(c_0_94, plain, (p39|~p41), inference(split_conjunct,[status(thm)],[c_0_90])).
38.59/38.78 thf(c_0_95, plain, ~p39, inference(sr,[status(thm)],[c_0_91, c_0_92])).
38.59/38.78 thf(c_0_96, plain, (p43|~p45), inference(fof_simplification,[status(thm)],[ax1219])).
38.59/38.78 thf(c_0_97, plain, (p41|~p43), inference(split_conjunct,[status(thm)],[c_0_93])).
38.59/38.78 thf(c_0_98, plain, ~p41, inference(sr,[status(thm)],[c_0_94, c_0_95])).
38.59/38.78 thf(c_0_99, plain, (p45|~p47), inference(fof_simplification,[status(thm)],[ax1217])).
38.59/38.78 thf(c_0_100, plain, (p43|~p45), inference(split_conjunct,[status(thm)],[c_0_96])).
38.59/38.78 thf(c_0_101, plain, ~p43, inference(sr,[status(thm)],[c_0_97, c_0_98])).
38.59/38.78 thf(c_0_102, plain, (p47|~p49), inference(fof_simplification,[status(thm)],[ax1215])).
38.59/38.78 thf(c_0_103, plain, (p45|~p47), inference(split_conjunct,[status(thm)],[c_0_99])).
38.59/38.78 thf(c_0_104, plain, ~p45, inference(sr,[status(thm)],[c_0_100, c_0_101])).
38.59/38.78 thf(c_0_105, plain, (p49|~p51), inference(fof_simplification,[status(thm)],[ax1213])).
38.59/38.78 thf(c_0_106, plain, (p47|~p49), inference(split_conjunct,[status(thm)],[c_0_102])).
38.59/38.78 thf(c_0_107, plain, ~p47, inference(sr,[status(thm)],[c_0_103, c_0_104])).
38.59/38.78 thf(c_0_108, plain, (p51|~p53), inference(fof_simplification,[status(thm)],[ax1211])).
38.59/38.78 thf(c_0_109, plain, (p49|~p51), inference(split_conjunct,[status(thm)],[c_0_105])).
38.59/38.78 thf(c_0_110, plain, ~p49, inference(sr,[status(thm)],[c_0_106, c_0_107])).
38.59/38.78 thf(c_0_111, plain, ![X1887:term, X1888:term]:(~p36|((flam @ X1887)!=(flam @ X1888)|(X1887)=(X1888))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax36])])])).
38.59/38.78 thf(c_0_112, plain, (p35|p36), inference(split_conjunct,[status(thm)],[ax1228])).
38.59/38.78 thf(c_0_113, plain, ![X1844:subst, X1845:subst, X1846:subst, X1847:subst, X1848:subst, X1849:term, X1850:subst, X1851:subst, X1852:term, X1853:term, X1854:term, X1855:term, X1856:term, X1857:term, X1858:term, X1859:term, X1860:term, X1862:subst, X1863:term, X1864:subst, X1866:subst, X1867:term, X1868:subst]:(((((fcomp @ (fcomp @ X1844 @ X1845) @ X1846)=(fcomp @ X1844 @ (fcomp @ X1845 @ X1846))|p53)&((fcomp @ fid @ X1847)=(X1847)|p53))&((fcomp @ X1848 @ fid)=(X1848)|p53))&((((fsub @ (fsub @ X1849 @ X1850) @ X1851)=(fsub @ X1849 @ (fcomp @ X1850 @ X1851))|p53)&((fsub @ X1852 @ fid)=(X1852)|p53))&(((fap @ (fsub @ X1853 @ fid) @ X1855)!=(fap @ (fsub @ X1854 @ fid) @ X1856)|(X1853)=(X1854)|p53)&(((fap @ (fsub @ X1857 @ fid) @ X1859)!=(fap @ (fsub @ X1858 @ fid) @ X1860)|(X1859)=(X1860)|p53)&(((fsub @ (esk849_0 @ X1862 @ X1863) @ X1864)=(esk849_0 @ (fcomp @ X1862 @ X1864) @ (fsub @ X1863 @ X1864))|p53)&(((fsub @ (esk850_0 @ X1866 @ X1867) @ X1868)=(esk850_0 @ (fcomp @ X1866 @ X1868) @ (fsub @ X1867 @ X1868))|p53)&(((flam @ (esk849_0 @ fsh @ fone))=(flam @ (esk850_0 @ fsh @ fone))|p53)&((esk849_0 @ esk851_0 @ esk852_0)!=(esk850_0 @ esk851_0 @ esk852_0)|p53)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax53])])])])])])).
38.59/38.78 thf(c_0_114, plain, (p51|~p53), inference(split_conjunct,[status(thm)],[c_0_108])).
38.59/38.78 thf(c_0_115, plain, ~p51, inference(sr,[status(thm)],[c_0_109, c_0_110])).
38.59/38.78 thf(c_0_116, plain, ![X1943:term, X1944:subst]:(~p4|(fsub @ fone @ (fpush @ X1943 @ X1944))=(X1943)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
38.59/38.78 thf(c_0_117, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1260])).
38.59/38.78 thf(c_0_118, plain, ![X1:term, X2:term]:((X1)=(X2)|~p36|(flam @ X1)!=(flam @ X2)), inference(split_conjunct,[status(thm)],[c_0_111])).
38.59/38.78 thf(c_0_119, plain, p36, inference(sr,[status(thm)],[c_0_112, c_0_89])).
38.59/38.78 thf(c_0_120, plain, ((flam @ (esk849_0 @ fsh @ fone))=(flam @ (esk850_0 @ fsh @ fone))|p53), inference(split_conjunct,[status(thm)],[c_0_113])).
38.59/38.78 thf(c_0_121, plain, ~p53, inference(sr,[status(thm)],[c_0_114, c_0_115])).
38.59/38.78 thf(c_0_122, plain, ![X1:term, X4:subst, X6:subst]:((fsub @ (esk849_0 @ X4 @ X1) @ X6)=(esk849_0 @ (fcomp @ X4 @ X6) @ (fsub @ X1 @ X6))|p53), inference(split_conjunct,[status(thm)],[c_0_113])).
38.59/38.78 thf(c_0_123, plain, ![X4:subst, X1:term]:((fsub @ fone @ (fpush @ X1 @ X4))=(X1)|~p4), inference(split_conjunct,[status(thm)],[c_0_116])).
38.59/38.78 thf(c_0_124, plain, p4, inference(sr,[status(thm)],[c_0_117, c_0_41])).
38.59/38.78 thf(c_0_125, plain, ![X1925:term, X1926:subst]:(~p14|(fcomp @ fsh @ (fpush @ X1925 @ X1926))=(X1926)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax14])])])).
38.59/38.78 thf(c_0_126, plain, (p13|p14), inference(split_conjunct,[status(thm)],[ax1250])).
38.59/38.78 thf(c_0_127, plain, ![X1:term, X2:term]:((X1)=(X2)|(flam @ X1)!=(flam @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118, c_0_119])])).
38.59/38.78 thf(c_0_128, plain, (flam @ (esk849_0 @ fsh @ fone))=(flam @ (esk850_0 @ fsh @ fone)), inference(sr,[status(thm)],[c_0_120, c_0_121])).
38.59/38.78 thf(c_0_129, plain, ![X1:term, X4:subst, X6:subst]:((fsub @ (esk850_0 @ X4 @ X1) @ X6)=(esk850_0 @ (fcomp @ X4 @ X6) @ (fsub @ X1 @ X6))|p53), inference(split_conjunct,[status(thm)],[c_0_113])).
38.59/38.78 thf(c_0_130, plain, ![X1:term, X4:subst, X6:subst]:(esk849_0 @ (fcomp @ X4 @ X6) @ (fsub @ X1 @ X6))=(fsub @ (esk849_0 @ X4 @ X1) @ X6), inference(sr,[status(thm)],[c_0_122, c_0_121])).
38.59/38.78 thf(c_0_131, plain, ![X4:subst, X1:term]:(fsub @ fone @ (fpush @ X1 @ X4))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123, c_0_124])])).
38.59/38.78 thf(c_0_132, plain, ![X1:term, X4:subst]:((fcomp @ fsh @ (fpush @ X1 @ X4))=(X4)|~p14), inference(split_conjunct,[status(thm)],[c_0_125])).
38.59/38.78 thf(c_0_133, plain, p14, inference(sr,[status(thm)],[c_0_126, c_0_56])).
38.59/38.78 thf(c_0_134, plain, ![X1:term]:((X1)=(esk849_0 @ fsh @ fone)|(flam @ X1)!=(flam @ (esk850_0 @ fsh @ fone))), inference(spm,[status(thm)],[c_0_127, c_0_128])).
38.59/38.78 thf(c_0_135, plain, ![X1:term, X4:subst, X6:subst]:(esk850_0 @ (fcomp @ X4 @ X6) @ (fsub @ X1 @ X6))=(fsub @ (esk850_0 @ X4 @ X1) @ X6), inference(sr,[status(thm)],[c_0_129, c_0_121])).
38.59/38.78 thf(c_0_136, plain, ![X1:term, X4:subst, X6:subst]:(esk849_0 @ (fcomp @ X4 @ (fpush @ X1 @ X6)) @ X1)=(fsub @ (esk849_0 @ X4 @ fone) @ (fpush @ X1 @ X6)), inference(spm,[status(thm)],[c_0_130, c_0_131])).
38.59/38.78 thf(c_0_137, plain, ![X1:term, X4:subst]:(fcomp @ fsh @ (fpush @ X1 @ X4))=(X4), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132, c_0_133])])).
38.59/38.78 thf(c_0_138, plain, (esk849_0 @ fsh @ fone)=(esk850_0 @ fsh @ fone), inference(er,[status(thm)],[c_0_134])).
38.59/38.78 thf(c_0_139, plain, (p53|(esk849_0 @ esk851_0 @ esk852_0)!=(esk850_0 @ esk851_0 @ esk852_0)), inference(split_conjunct,[status(thm)],[c_0_113])).
38.59/38.78 thf(c_0_140, plain, ![X1:term, X4:subst, X6:subst]:(esk850_0 @ (fcomp @ X4 @ (fpush @ X1 @ X6)) @ X1)=(fsub @ (esk850_0 @ X4 @ fone) @ (fpush @ X1 @ X6)), inference(spm,[status(thm)],[c_0_135, c_0_131])).
38.59/38.78 thf(c_0_141, plain, ![X4:subst, X1:term]:(fsub @ (esk850_0 @ fsh @ fone) @ (fpush @ X1 @ X4))=(esk849_0 @ X4 @ X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_138])).
38.59/38.78 thf(c_0_142, plain, (esk849_0 @ esk851_0 @ esk852_0)!=(esk850_0 @ esk851_0 @ esk852_0), inference(sr,[status(thm)],[c_0_139, c_0_121])).
38.59/38.78 thf(c_0_143, plain, ![X4:subst, X1:term]:(esk849_0 @ X4 @ X1)=(esk850_0 @ X4 @ X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140, c_0_137]), c_0_141])).
38.59/38.78 thf(c_0_144, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142, c_0_143])]), ['proof']).
38.59/38.78 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
38.59/38.78 thf(0,theorem,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => ((![X1:term>$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)))))) => ((![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]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ X2) @ id)) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ 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)))))) => (((lam @ ((X1 @ sh) @ one)) = (lam @ ((X2 @ sh) @ one))) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
38.59/38.78 % SZS output end Proof
38.59/38.79 EOF