TSTP Solution File: ALG264^3 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG264^3 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:57:50 EDT 2022
% Result : Theorem 187.70s 187.12s
% Output : Proof 187.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG264^3 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n022.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 : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 00:40:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 187.70/187.12 % SZS status Theorem
% 187.70/187.12 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 187.70/187.12 % Inferences: 19436
% 187.70/187.12 % SZS output start Proof
% 187.70/187.12 thf(def_axapp,definition,(axapp = (![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))))).
% 187.70/187.12 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))).
% 187.70/187.12 thf(def_axvarid,definition,(axvarid = (![X1:term]:(((sub @ X1) @ id) = X1)))).
% 187.70/187.12 thf(def_axabs,definition,(axabs = (![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))))).
% 187.70/187.12 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
% 187.70/187.12 thf(def_axidl,definition,(axidl = (![X1:subst]:(((comp @ id) @ X1) = X1)))).
% 187.70/187.12 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
% 187.70/187.12 thf(def_axassoc,definition,(axassoc = (![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))))).
% 187.70/187.12 thf(def_axmap,definition,(axmap = (![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))))).
% 187.70/187.12 thf(def_axidr,definition,(axidr = (![X1:subst]:(((comp @ X1) @ id) = X1)))).
% 187.70/187.12 thf(def_axvarshift,definition,(axvarshift = (((push @ one) @ sh) = id))).
% 187.70/187.12 thf(def_axscons,definition,(axscons = (![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)))).
% 187.70/187.12 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))).
% 187.70/187.12 thf(def_ulamvarsh,definition,(ulamvarsh = (![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))))).
% 187.70/187.12 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))).
% 187.70/187.12 thf(def_apinj1,definition,(apinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))))).
% 187.70/187.12 thf(def_apinj2,definition,(apinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))))).
% 187.70/187.12 thf(def_laminj,definition,(laminj = (![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))))).
% 187.70/187.12 thf(def_shinj,definition,(shinj = (![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))))).
% 187.70/187.12 thf(def_lamnotap,definition,(lamnotap = (![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))))).
% 187.70/187.12 thf(def_apnotvar,definition,(apnotvar = (![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))))).
% 187.70/187.12 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))).
% 187.70/187.12 thf(def_induction,definition,(induction = (![X1:term>$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))))))).
% 187.70/187.12 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))).
% 187.70/187.12 thf(def_induction2lem,definition,(induction2lem = (![X1:term>$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)))))))))).
% 187.70/187.12 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))))))).
% 187.70/187.12 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))))))))).
% 187.70/187.12 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))))))))).
% 187.70/187.12 thf(def_hoasap,definition,(hoasap = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(ap @ ((sub @ X2) @ X3))))))).
% 187.70/187.12 thf(def_hoaslam,definition,(hoaslam = (^[X1:subst]:(^[X2:subst>term>term]:(lam @ ((X2 @ sh) @ one)))))).
% 187.70/187.12 thf(def_hoasvar,definition,(hoasvar = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(var @ ((sub @ X2) @ X3))))))).
% 187.70/187.12 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)))))))).
% 187.70/187.12 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)))))))).
% 187.70/187.12 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))))))))))).
% 187.70/187.12 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)))))))))).
% 187.70/187.12 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))))))).
% 187.70/187.12 thf(def_hoasapnotvar,definition,(hoasapnotvar = (![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))))).
% 187.70/187.12 thf(def_hoasinduction_p_and_p_prime,definition,(hoasinduction_p_and_p_prime = (^[X1:subst>term>subst>$o]:(^[X2:term>$o]:(![X3:term]:((X2 @ X3) = (((X1 @ id) @ X3) @ id))))))).
% 187.70/187.12 thf(def_hoasinduction_lem2v2,definition,(hoasinduction_lem2v2 = (![X1:subst>term>subst>$o]:(![X2:term>$o]:((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ X3) @ X4) @ ((comp @ X6) @ X5)) => (((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5)))))) => ((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5) => (((X1 @ X3) @ X4) @ ((comp @ X6) @ X5))))))) => ((![X3:term]:(![X4:term]:((((X1 @ id) @ X3) @ id) => ((((X1 @ id) @ X4) @ id) => (((X1 @ id) @ ((((hoasap @ id) @ X3) @ id) @ X4)) @ id))))) => (((hoasinduction_p_and_p_prime @ X1) @ X2) => (![X3:term]:(![X4:term]:((X2 @ X3) => ((X2 @ X4) => (X2 @ ((ap @ X3) @ X4)))))))))))))).
% 187.70/187.12 thf(def_hoasinduction_lem2v2_gthm,definition,(hoasinduction_lem2v2_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_lem2v2)))))))))))))))))))))))))))))))))))).
% 187.70/187.12 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))))))))) => ((![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]:(~(((lam @ ((X1 @ sh) @ one)) = ((ap @ ((sub @ 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)))))) => (~((var @ ((sub @ (lam @ ((X1 @ sh) @ one))) @ id)))))) => ((![X1:term]:(![X2:term]:(~((var @ ((sub @ ((ap @ ((sub @ X1) @ id)) @ X2)) @ id)))))) => (![X1:subst>term>subst>$o]:(![X2:term>$o]:((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ X3) @ X4) @ ((comp @ X6) @ X5)) => (((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5)))))) => ((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5) => (((X1 @ X3) @ X4) @ ((comp @ X6) @ X5))))))) => ((![X3:term]:(![X4:term]:((((X1 @ id) @ X3) @ id) => ((((X1 @ id) @ X4) @ id) => (((X1 @ id) @ ((ap @ ((sub @ X3) @ id)) @ X4)) @ id))))) => ((![X3:term]:((X2 @ X3) = (((X1 @ id) @ X3) @ id))) => (![X3:term]:(![X4:term]:((X2 @ X3) => ((X2 @ X4) => (X2 @ ((ap @ X3) @ X4))))))))))))))))))))))))))))))))))))))))))))))).
% 187.70/187.12 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>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))) => ((~(((~(((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:subst]:(((comp @ id) @ X1) = X1))))))) => (~((![X1:subst]:(((comp @ X1) @ id) = X1))))))) => ((~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => (~((![X1:term]:(((sub @ X1) @ id) = X1))))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ X2) @ id)) @ X4)) => (X1 = X2)))))) => ((![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ ((sub @ X1) @ id)) @ X3) = ((ap @ ((sub @ X2) @ id)) @ X4)) => (X3 = X4)))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:subst>term>term]:((![X3:subst]:(![X4:term]:(![X5:subst]:(((sub @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ ((comp @ X3) @ X5)) @ ((sub @ X4) @ X5)))))) => (((lam @ ((X1 @ sh) @ one)) = (lam @ ((X2 @ sh) @ one))) => (![X3:subst]:(![X4:term]:(((X1 @ X3) @ X4) = ((X2 @ X3) @ X4))))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (![X2:term]:(![X3:term]:(~(((lam @ ((X1 @ sh) @ one)) = ((ap @ ((sub @ X2) @ id)) @ X3)))))))) => ((![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((var @ ((sub @ (lam @ ((X1 @ sh) @ one))) @ id)))))) => ((![X1:term]:(![X2:term]:(~((var @ ((sub @ ((ap @ ((sub @ X1) @ id)) @ X2)) @ id)))))) => (![X1:subst>term>subst>$o]:(![X2:term>$o]:((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ X3) @ X4) @ ((comp @ X6) @ X5)) => (((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5)))))) => ((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5) => (((X1 @ X3) @ X4) @ ((comp @ X6) @ X5))))))) => ((![X3:term]:(![X4:term]:((((X1 @ id) @ X3) @ id) => ((((X1 @ id) @ X4) @ id) => (((X1 @ id) @ ((ap @ ((sub @ X3) @ id)) @ X4)) @ id))))) => ((![X3:term]:((X2 @ X3) = (((X1 @ id) @ X3) @ id))) => (![X3:term]:(![X4:term]:((X2 @ X3) => ((X2 @ X4) => (X2 @ ((ap @ X3) @ X4)))))))))))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 187.70/187.12 thf(ax2682, axiom, (p1|~(p3)), file('<stdin>', ax2682)).
% 187.70/187.12 thf(ax2684, axiom, ~(p1), file('<stdin>', ax2684)).
% 187.70/187.12 thf(ax2680, axiom, (p3|~(p5)), file('<stdin>', ax2680)).
% 187.70/187.12 thf(ax2678, axiom, (p5|~(p7)), file('<stdin>', ax2678)).
% 187.70/187.12 thf(ax2676, axiom, (p7|~(p9)), file('<stdin>', ax2676)).
% 187.70/187.12 thf(ax2674, axiom, (p9|~(p11)), file('<stdin>', ax2674)).
% 187.70/187.12 thf(ax2672, axiom, (p11|~(p13)), file('<stdin>', ax2672)).
% 187.70/187.12 thf(ax2670, axiom, (p13|~(p15)), file('<stdin>', ax2670)).
% 187.70/187.12 thf(ax2668, axiom, (p15|~(p17)), file('<stdin>', ax2668)).
% 187.70/187.12 thf(ax2666, axiom, (p17|~(p19)), file('<stdin>', ax2666)).
% 187.70/187.12 thf(ax2664, axiom, (p19|~(p21)), file('<stdin>', ax2664)).
% 187.70/187.12 thf(ax2662, axiom, (p21|~(p23)), file('<stdin>', ax2662)).
% 187.70/187.12 thf(ax2660, axiom, (p23|~(p25)), file('<stdin>', ax2660)).
% 187.70/187.12 thf(ax2658, axiom, (p25|~(p27)), file('<stdin>', ax2658)).
% 187.70/187.12 thf(ax2656, axiom, (p27|~(p29)), file('<stdin>', ax2656)).
% 187.70/187.12 thf(ax2654, axiom, (p29|~(p31)), file('<stdin>', ax2654)).
% 187.70/187.12 thf(ax2652, axiom, (p31|~(p33)), file('<stdin>', ax2652)).
% 187.70/187.12 thf(ax2650, axiom, (p33|~(p35)), file('<stdin>', ax2650)).
% 187.70/187.12 thf(ax2648, axiom, (p35|~(p37)), file('<stdin>', ax2648)).
% 187.70/187.12 thf(ax2646, axiom, (p37|~(p39)), file('<stdin>', ax2646)).
% 187.70/187.12 thf(ax2644, axiom, (p39|~(p41)), file('<stdin>', ax2644)).
% 187.70/187.12 thf(ax2642, axiom, (p41|~(p43)), file('<stdin>', ax2642)).
% 187.70/187.12 thf(ax2640, axiom, (p43|~(p45)), file('<stdin>', ax2640)).
% 187.70/187.12 thf(ax2638, axiom, (p45|~(p47)), file('<stdin>', ax2638)).
% 187.70/187.12 thf(ax2636, axiom, (p47|~(p49)), file('<stdin>', ax2636)).
% 187.70/187.12 thf(ax2634, axiom, (p49|~(p51)), file('<stdin>', ax2634)).
% 187.70/187.12 thf(ax2584, axiom, (~(p104)|p103), file('<stdin>', ax2584)).
% 187.70/187.12 thf(ax2578, axiom, (~(p104)|p110), file('<stdin>', ax2578)).
% 187.70/187.12 thf(ax2572, axiom, (~(p104)|p116), file('<stdin>', ax2572)).
% 187.70/187.12 thf(ax2632, axiom, (p51|~(p53)), file('<stdin>', ax2632)).
% 187.70/187.12 thf(pax6, axiom, (p6=>![X404:term]:(fsub @ X404 @ fid)=(X404)), file('<stdin>', pax6)).
% 187.70/187.12 thf(ax2679, axiom, (p5|p6), file('<stdin>', ax2679)).
% 187.70/187.12 thf(ax2340, axiom, (~(p103)|p278), file('<stdin>', ax2340)).
% 187.70/187.12 thf(ax2585, axiom, p104, file('<stdin>', ax2585)).
% 187.70/187.12 thf(ax2430, axiom, (~(p110)|p220), file('<stdin>', ax2430)).
% 187.70/187.12 thf(ax2550, axiom, (~(p116)|p136), file('<stdin>', ax2550)).
% 187.70/187.12 thf(ax2554, axiom, (~(p110)|p132), file('<stdin>', ax2554)).
% 187.70/187.12 thf(ax2630, axiom, (p53|~(p55)), file('<stdin>', ax2630)).
% 187.70/187.12 thf(pax522, axiom, (p522=>![X367:term]:(f__0 @ fid @ f__2 @ fid=>(f__0 @ fid @ X367 @ fid=>f__0 @ fid @ (fap @ (fsub @ f__2 @ fid) @ X367) @ fid))), file('<stdin>', pax522)).
% 187.70/187.12 thf(ax2339, axiom, (~(p278)|p129|p277), file('<stdin>', ax2339)).
% 187.70/187.12 thf(ax2429, axiom, (~(p220)|p121|p219), file('<stdin>', ax2429)).
% 187.70/187.12 thf(ax2549, axiom, (~(p136)|p81|p135), file('<stdin>', ax2549)).
% 187.70/187.12 thf(ax2553, axiom, (~(p132)|p81|p131), file('<stdin>', ax2553)).
% 187.70/187.12 thf(ax2628, axiom, (p55|~(p57)), file('<stdin>', ax2628)).
% 187.70/187.12 thf(nax275, axiom, (p275<=(f__0 @ fid @ f__2 @ fid=>(f__0 @ fid @ f__3 @ fid=>f__1 @ (fap @ f__2 @ f__3)))), file('<stdin>', nax275)).
% 187.70/187.12 thf(nax217, axiom, (p217<=(f__0 @ fid @ f__3 @ fid=>f__0 @ fid @ (fap @ f__2 @ f__3) @ fid)), file('<stdin>', nax217)).
% 187.70/187.12 thf(nax133, axiom, (p133<=(f__1 @ f__2=>(f__1 @ f__3=>f__0 @ fid @ (fap @ f__2 @ f__3) @ fid))), file('<stdin>', nax133)).
% 187.70/187.12 thf(ax1985, axiom, (~(p76)|p522), file('<stdin>', ax1985)).
% 187.70/187.12 thf(ax2547, axiom, (~(p134)|~(p112)|~(p133)), file('<stdin>', ax2547)).
% 187.70/187.12 thf(ax2427, axiom, (~(p218)|~(p106)|~(p217)), file('<stdin>', ax2427)).
% 187.70/187.12 thf(ax2551, axiom, (~(p130)|~(p106)|~(p129)), file('<stdin>', ax2551)).
% 187.70/187.12 thf(ax2337, axiom, (~(p276)|~(p99)|~(p275)), file('<stdin>', ax2337)).
% 187.70/187.12 thf(ax2604, axiom, (p80|~(p81)), file('<stdin>', ax2604)).
% 187.70/187.12 thf(ax2605, axiom, (p79|~(p80)), file('<stdin>', ax2605)).
% 187.70/187.12 thf(ax2606, axiom, (p77|~(p79)), file('<stdin>', ax2606)).
% 187.70/187.12 thf(ax2614, axiom, (p70|~(p71)), file('<stdin>', ax2614)).
% 187.70/187.12 thf(ax2338, axiom, (~(p277)|p276), file('<stdin>', ax2338)).
% 187.70/187.12 thf(ax2428, axiom, (~(p219)|p218), file('<stdin>', ax2428)).
% 187.70/187.12 thf(ax2548, axiom, (~(p135)|p134), file('<stdin>', ax2548)).
% 187.70/187.12 thf(ax2431, axiom, (p133|~(p121)), file('<stdin>', ax2431)).
% 187.70/187.12 thf(ax2552, axiom, (~(p131)|p130), file('<stdin>', ax2552)).
% 187.70/187.12 thf(ax2567, axiom, (~(p78)|p112), file('<stdin>', ax2567)).
% 187.70/187.12 thf(ax2573, axiom, (~(p78)|p106), file('<stdin>', ax2573)).
% 187.70/187.12 thf(ax2579, axiom, (~(p78)|p99), file('<stdin>', ax2579)).
% 187.70/187.12 thf(ax2608, axiom, (p75|~(p77)), file('<stdin>', ax2608)).
% 187.70/187.12 thf(ax2610, axiom, (p73|~(p75)), file('<stdin>', ax2610)).
% 187.70/187.12 thf(ax2612, axiom, (p71|~(p73)), file('<stdin>', ax2612)).
% 187.70/187.12 thf(ax2615, axiom, (p69|~(p70)), file('<stdin>', ax2615)).
% 187.70/187.12 thf(ax2616, axiom, (p67|~(p69)), file('<stdin>', ax2616)).
% 187.70/187.12 thf(ax2618, axiom, (p65|~(p67)), file('<stdin>', ax2618)).
% 187.70/187.12 thf(ax2620, axiom, (p63|~(p65)), file('<stdin>', ax2620)).
% 187.70/187.12 thf(ax2622, axiom, (p61|~(p63)), file('<stdin>', ax2622)).
% 187.70/187.12 thf(ax2624, axiom, (p59|~(p61)), file('<stdin>', ax2624)).
% 187.70/187.12 thf(ax2626, axiom, (p57|~(p59)), file('<stdin>', ax2626)).
% 187.70/187.12 thf(ax2607, axiom, (p77|p78), file('<stdin>', ax2607)).
% 187.70/187.12 thf(ax2609, axiom, (p75|p76), file('<stdin>', ax2609)).
% 187.70/187.12 thf(c_0_76, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax2682])).
% 187.70/187.12 thf(c_0_77, plain, ~p1, inference(fof_simplification,[status(thm)],[ax2684])).
% 187.70/187.12 thf(c_0_78, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax2680])).
% 187.70/187.12 thf(c_0_79, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_76])).
% 187.70/187.12 thf(c_0_80, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_77])).
% 187.70/187.12 thf(c_0_81, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax2678])).
% 187.70/187.12 thf(c_0_82, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_78])).
% 187.70/187.12 thf(c_0_83, plain, ~p3, inference(sr,[status(thm)],[c_0_79, c_0_80])).
% 187.70/187.12 thf(c_0_84, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax2676])).
% 187.70/187.12 thf(c_0_85, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_81])).
% 187.70/187.12 thf(c_0_86, plain, ~p5, inference(sr,[status(thm)],[c_0_82, c_0_83])).
% 187.70/187.12 thf(c_0_87, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax2674])).
% 187.70/187.12 thf(c_0_88, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_84])).
% 187.70/187.12 thf(c_0_89, plain, ~p7, inference(sr,[status(thm)],[c_0_85, c_0_86])).
% 187.70/187.12 thf(c_0_90, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax2672])).
% 187.70/187.12 thf(c_0_91, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_87])).
% 187.70/187.12 thf(c_0_92, plain, ~p9, inference(sr,[status(thm)],[c_0_88, c_0_89])).
% 187.70/187.12 thf(c_0_93, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax2670])).
% 187.70/187.12 thf(c_0_94, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_90])).
% 187.70/187.12 thf(c_0_95, plain, ~p11, inference(sr,[status(thm)],[c_0_91, c_0_92])).
% 187.70/187.12 thf(c_0_96, plain, (p15|~p17), inference(fof_simplification,[status(thm)],[ax2668])).
% 187.70/187.12 thf(c_0_97, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_93])).
% 187.70/187.12 thf(c_0_98, plain, ~p13, inference(sr,[status(thm)],[c_0_94, c_0_95])).
% 187.70/187.12 thf(c_0_99, plain, (p17|~p19), inference(fof_simplification,[status(thm)],[ax2666])).
% 187.70/187.12 thf(c_0_100, plain, (p15|~p17), inference(split_conjunct,[status(thm)],[c_0_96])).
% 187.70/187.12 thf(c_0_101, plain, ~p15, inference(sr,[status(thm)],[c_0_97, c_0_98])).
% 187.70/187.12 thf(c_0_102, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax2664])).
% 187.70/187.12 thf(c_0_103, plain, (p17|~p19), inference(split_conjunct,[status(thm)],[c_0_99])).
% 187.70/187.12 thf(c_0_104, plain, ~p17, inference(sr,[status(thm)],[c_0_100, c_0_101])).
% 187.70/187.12 thf(c_0_105, plain, (p21|~p23), inference(fof_simplification,[status(thm)],[ax2662])).
% 187.70/187.12 thf(c_0_106, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_102])).
% 187.70/187.12 thf(c_0_107, plain, ~p19, inference(sr,[status(thm)],[c_0_103, c_0_104])).
% 187.70/187.12 thf(c_0_108, plain, (p23|~p25), inference(fof_simplification,[status(thm)],[ax2660])).
% 187.70/187.12 thf(c_0_109, plain, (p21|~p23), inference(split_conjunct,[status(thm)],[c_0_105])).
% 187.70/187.12 thf(c_0_110, plain, ~p21, inference(sr,[status(thm)],[c_0_106, c_0_107])).
% 187.70/187.12 thf(c_0_111, plain, (p25|~p27), inference(fof_simplification,[status(thm)],[ax2658])).
% 187.70/187.12 thf(c_0_112, plain, (p23|~p25), inference(split_conjunct,[status(thm)],[c_0_108])).
% 187.70/187.12 thf(c_0_113, plain, ~p23, inference(sr,[status(thm)],[c_0_109, c_0_110])).
% 187.70/187.12 thf(c_0_114, plain, (p27|~p29), inference(fof_simplification,[status(thm)],[ax2656])).
% 187.70/187.12 thf(c_0_115, plain, (p25|~p27), inference(split_conjunct,[status(thm)],[c_0_111])).
% 187.70/187.12 thf(c_0_116, plain, ~p25, inference(sr,[status(thm)],[c_0_112, c_0_113])).
% 187.70/187.12 thf(c_0_117, plain, (p29|~p31), inference(fof_simplification,[status(thm)],[ax2654])).
% 187.70/187.12 thf(c_0_118, plain, (p27|~p29), inference(split_conjunct,[status(thm)],[c_0_114])).
% 187.70/187.12 thf(c_0_119, plain, ~p27, inference(sr,[status(thm)],[c_0_115, c_0_116])).
% 187.70/187.12 thf(c_0_120, plain, (p31|~p33), inference(fof_simplification,[status(thm)],[ax2652])).
% 187.70/187.12 thf(c_0_121, plain, (p29|~p31), inference(split_conjunct,[status(thm)],[c_0_117])).
% 187.70/187.12 thf(c_0_122, plain, ~p29, inference(sr,[status(thm)],[c_0_118, c_0_119])).
% 187.70/187.12 thf(c_0_123, plain, (p33|~p35), inference(fof_simplification,[status(thm)],[ax2650])).
% 187.70/187.12 thf(c_0_124, plain, (p31|~p33), inference(split_conjunct,[status(thm)],[c_0_120])).
% 187.70/187.12 thf(c_0_125, plain, ~p31, inference(sr,[status(thm)],[c_0_121, c_0_122])).
% 187.70/187.12 thf(c_0_126, plain, (p35|~p37), inference(fof_simplification,[status(thm)],[ax2648])).
% 187.70/187.12 thf(c_0_127, plain, (p33|~p35), inference(split_conjunct,[status(thm)],[c_0_123])).
% 187.70/187.12 thf(c_0_128, plain, ~p33, inference(sr,[status(thm)],[c_0_124, c_0_125])).
% 187.70/187.12 thf(c_0_129, plain, (p37|~p39), inference(fof_simplification,[status(thm)],[ax2646])).
% 187.70/187.12 thf(c_0_130, plain, (p35|~p37), inference(split_conjunct,[status(thm)],[c_0_126])).
% 187.70/187.12 thf(c_0_131, plain, ~p35, inference(sr,[status(thm)],[c_0_127, c_0_128])).
% 187.70/187.12 thf(c_0_132, plain, (p39|~p41), inference(fof_simplification,[status(thm)],[ax2644])).
% 187.70/187.12 thf(c_0_133, plain, (p37|~p39), inference(split_conjunct,[status(thm)],[c_0_129])).
% 187.70/187.12 thf(c_0_134, plain, ~p37, inference(sr,[status(thm)],[c_0_130, c_0_131])).
% 187.70/187.12 thf(c_0_135, plain, (p41|~p43), inference(fof_simplification,[status(thm)],[ax2642])).
% 187.70/187.12 thf(c_0_136, plain, (p39|~p41), inference(split_conjunct,[status(thm)],[c_0_132])).
% 187.70/187.12 thf(c_0_137, plain, ~p39, inference(sr,[status(thm)],[c_0_133, c_0_134])).
% 187.70/187.12 thf(c_0_138, plain, (p43|~p45), inference(fof_simplification,[status(thm)],[ax2640])).
% 187.70/187.12 thf(c_0_139, plain, (p41|~p43), inference(split_conjunct,[status(thm)],[c_0_135])).
% 187.70/187.12 thf(c_0_140, plain, ~p41, inference(sr,[status(thm)],[c_0_136, c_0_137])).
% 187.70/187.12 thf(c_0_141, plain, (p45|~p47), inference(fof_simplification,[status(thm)],[ax2638])).
% 187.70/187.12 thf(c_0_142, plain, (p43|~p45), inference(split_conjunct,[status(thm)],[c_0_138])).
% 187.70/187.12 thf(c_0_143, plain, ~p43, inference(sr,[status(thm)],[c_0_139, c_0_140])).
% 187.70/187.12 thf(c_0_144, plain, (p47|~p49), inference(fof_simplification,[status(thm)],[ax2636])).
% 187.70/187.12 thf(c_0_145, plain, (p45|~p47), inference(split_conjunct,[status(thm)],[c_0_141])).
% 187.70/187.12 thf(c_0_146, plain, ~p45, inference(sr,[status(thm)],[c_0_142, c_0_143])).
% 187.70/187.12 thf(c_0_147, plain, (p49|~p51), inference(fof_simplification,[status(thm)],[ax2634])).
% 187.70/187.12 thf(c_0_148, plain, (p47|~p49), inference(split_conjunct,[status(thm)],[c_0_144])).
% 187.70/187.12 thf(c_0_149, plain, ~p47, inference(sr,[status(thm)],[c_0_145, c_0_146])).
% 187.70/187.12 thf(c_0_150, plain, (~p104|p103), inference(fof_simplification,[status(thm)],[ax2584])).
% 187.70/187.12 thf(c_0_151, plain, (~p104|p110), inference(fof_simplification,[status(thm)],[ax2578])).
% 187.70/187.12 thf(c_0_152, plain, (~p104|p116), inference(fof_simplification,[status(thm)],[ax2572])).
% 187.70/187.12 thf(c_0_153, plain, (p51|~p53), inference(fof_simplification,[status(thm)],[ax2632])).
% 187.70/187.12 thf(c_0_154, plain, (p49|~p51), inference(split_conjunct,[status(thm)],[c_0_147])).
% 187.70/187.12 thf(c_0_155, plain, ~p49, inference(sr,[status(thm)],[c_0_148, c_0_149])).
% 187.70/187.12 thf(c_0_156, plain, ![X2224:term]:(~p6|(fsub @ X2224 @ fid)=(X2224)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])])).
% 187.70/187.12 thf(c_0_157, plain, (p5|p6), inference(split_conjunct,[status(thm)],[ax2679])).
% 187.70/187.12 thf(c_0_158, plain, (~p103|p278), inference(fof_simplification,[status(thm)],[ax2340])).
% 187.70/187.12 thf(c_0_159, plain, (p103|~p104), inference(split_conjunct,[status(thm)],[c_0_150])).
% 187.70/187.12 thf(c_0_160, plain, p104, inference(split_conjunct,[status(thm)],[ax2585])).
% 187.70/187.12 thf(c_0_161, plain, (~p110|p220), inference(fof_simplification,[status(thm)],[ax2430])).
% 187.70/187.12 thf(c_0_162, plain, (p110|~p104), inference(split_conjunct,[status(thm)],[c_0_151])).
% 187.70/187.12 thf(c_0_163, plain, (~p116|p136), inference(fof_simplification,[status(thm)],[ax2550])).
% 187.70/187.12 thf(c_0_164, plain, (p116|~p104), inference(split_conjunct,[status(thm)],[c_0_152])).
% 187.70/187.12 thf(c_0_165, plain, (~p110|p132), inference(fof_simplification,[status(thm)],[ax2554])).
% 187.70/187.12 thf(c_0_166, plain, (p53|~p55), inference(fof_simplification,[status(thm)],[ax2630])).
% 187.70/187.12 thf(c_0_167, plain, (p51|~p53), inference(split_conjunct,[status(thm)],[c_0_153])).
% 187.70/187.12 thf(c_0_168, plain, ~p51, inference(sr,[status(thm)],[c_0_154, c_0_155])).
% 187.70/187.12 thf(c_0_169, plain, ![X2024:term]:(~p522|(~f__0 @ fid @ f__2 @ fid|(~f__0 @ fid @ X2024 @ fid|f__0 @ fid @ (fap @ (fsub @ f__2 @ fid) @ X2024) @ fid))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax522])])])).
% 187.70/187.12 thf(c_0_170, plain, ![X1:term]:((fsub @ X1 @ fid)=(X1)|~p6), inference(split_conjunct,[status(thm)],[c_0_156])).
% 187.70/187.12 thf(c_0_171, plain, p6, inference(sr,[status(thm)],[c_0_157, c_0_86])).
% 187.70/187.12 thf(c_0_172, plain, (~p278|p129|p277), inference(fof_simplification,[status(thm)],[ax2339])).
% 187.70/187.12 thf(c_0_173, plain, (p278|~p103), inference(split_conjunct,[status(thm)],[c_0_158])).
% 187.70/187.12 thf(c_0_174, plain, p103, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159, c_0_160])])).
% 187.70/187.12 thf(c_0_175, plain, (~p220|p121|p219), inference(fof_simplification,[status(thm)],[ax2429])).
% 187.70/187.12 thf(c_0_176, plain, (p220|~p110), inference(split_conjunct,[status(thm)],[c_0_161])).
% 187.70/187.12 thf(c_0_177, plain, p110, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162, c_0_160])])).
% 187.70/187.12 thf(c_0_178, plain, (~p136|p81|p135), inference(fof_simplification,[status(thm)],[ax2549])).
% 187.70/187.12 thf(c_0_179, plain, (p136|~p116), inference(split_conjunct,[status(thm)],[c_0_163])).
% 187.70/187.12 thf(c_0_180, plain, p116, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164, c_0_160])])).
% 187.70/187.12 thf(c_0_181, plain, (~p132|p81|p131), inference(fof_simplification,[status(thm)],[ax2553])).
% 187.70/187.12 thf(c_0_182, plain, (p132|~p110), inference(split_conjunct,[status(thm)],[c_0_165])).
% 187.70/187.12 thf(c_0_183, plain, (p55|~p57), inference(fof_simplification,[status(thm)],[ax2628])).
% 187.70/187.12 thf(c_0_184, plain, (p53|~p55), inference(split_conjunct,[status(thm)],[c_0_166])).
% 187.70/187.12 thf(c_0_185, plain, ~p53, inference(sr,[status(thm)],[c_0_167, c_0_168])).
% 187.70/187.12 thf(c_0_186, plain, ![X1:term]:(f__0 @ fid @ (fap @ (fsub @ f__2 @ fid) @ X1) @ fid|~p522|~f__0 @ fid @ f__2 @ fid|~f__0 @ fid @ X1 @ fid), inference(split_conjunct,[status(thm)],[c_0_169])).
% 187.70/187.12 thf(c_0_187, plain, ![X1:term]:(fsub @ X1 @ fid)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170, c_0_171])])).
% 187.70/187.12 thf(c_0_188, plain, ((f__0 @ fid @ f__2 @ fid|p275)&((f__0 @ fid @ f__3 @ fid|p275)&(~f__1 @ (fap @ f__2 @ f__3)|p275))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax275])])])).
% 187.70/187.12 thf(c_0_189, plain, ((f__0 @ fid @ f__3 @ fid|p217)&(~f__0 @ fid @ (fap @ f__2 @ f__3) @ fid|p217)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax217])])])).
% 187.70/187.12 thf(c_0_190, plain, ((f__1 @ f__2|p133)&((f__1 @ f__3|p133)&(~f__0 @ fid @ (fap @ f__2 @ f__3) @ fid|p133))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax133])])])).
% 187.70/187.12 thf(c_0_191, plain, (p129|p277|~p278), inference(split_conjunct,[status(thm)],[c_0_172])).
% 187.70/187.12 thf(c_0_192, plain, p278, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173, c_0_174])])).
% 187.70/187.12 thf(c_0_193, plain, (p121|p219|~p220), inference(split_conjunct,[status(thm)],[c_0_175])).
% 187.70/187.12 thf(c_0_194, plain, p220, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_176, c_0_177])])).
% 187.70/187.12 thf(c_0_195, plain, (p81|p135|~p136), inference(split_conjunct,[status(thm)],[c_0_178])).
% 187.70/187.12 thf(c_0_196, plain, p136, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179, c_0_180])])).
% 187.70/187.12 thf(c_0_197, plain, (p81|p131|~p132), inference(split_conjunct,[status(thm)],[c_0_181])).
% 187.70/187.12 thf(c_0_198, plain, p132, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182, c_0_177])])).
% 187.70/187.12 thf(c_0_199, plain, (~p76|p522), inference(fof_simplification,[status(thm)],[ax1985])).
% 187.70/187.12 thf(c_0_200, plain, (~p134|~p112|~p133), inference(fof_simplification,[status(thm)],[ax2547])).
% 187.70/187.12 thf(c_0_201, plain, (~p218|~p106|~p217), inference(fof_simplification,[status(thm)],[ax2427])).
% 187.70/187.12 thf(c_0_202, plain, (~p130|~p106|~p129), inference(fof_simplification,[status(thm)],[ax2551])).
% 187.70/187.12 thf(c_0_203, plain, (~p276|~p99|~p275), inference(fof_simplification,[status(thm)],[ax2337])).
% 187.70/187.12 thf(c_0_204, plain, (p80|~p81), inference(fof_simplification,[status(thm)],[ax2604])).
% 187.70/187.12 thf(c_0_205, plain, (p79|~p80), inference(fof_simplification,[status(thm)],[ax2605])).
% 187.70/187.12 thf(c_0_206, plain, (p77|~p79), inference(fof_simplification,[status(thm)],[ax2606])).
% 187.70/187.12 thf(c_0_207, plain, (p70|~p71), inference(fof_simplification,[status(thm)],[ax2614])).
% 187.70/187.12 thf(c_0_208, plain, (~p277|p276), inference(fof_simplification,[status(thm)],[ax2338])).
% 187.70/187.12 thf(c_0_209, plain, (~p219|p218), inference(fof_simplification,[status(thm)],[ax2428])).
% 187.70/187.12 thf(c_0_210, plain, (~p135|p134), inference(fof_simplification,[status(thm)],[ax2548])).
% 187.70/187.12 thf(c_0_211, plain, (p133|~p121), inference(fof_simplification,[status(thm)],[ax2431])).
% 187.70/187.12 thf(c_0_212, plain, (~p131|p130), inference(fof_simplification,[status(thm)],[ax2552])).
% 187.70/187.12 thf(c_0_213, plain, (~p78|p112), inference(fof_simplification,[status(thm)],[ax2567])).
% 187.70/187.12 thf(c_0_214, plain, (~p78|p106), inference(fof_simplification,[status(thm)],[ax2573])).
% 187.70/187.12 thf(c_0_215, plain, (~p78|p99), inference(fof_simplification,[status(thm)],[ax2579])).
% 187.70/187.12 thf(c_0_216, plain, (p75|~p77), inference(fof_simplification,[status(thm)],[ax2608])).
% 187.70/187.12 thf(c_0_217, plain, (p73|~p75), inference(fof_simplification,[status(thm)],[ax2610])).
% 187.70/187.12 thf(c_0_218, plain, (p71|~p73), inference(fof_simplification,[status(thm)],[ax2612])).
% 187.70/187.12 thf(c_0_219, plain, (p69|~p70), inference(fof_simplification,[status(thm)],[ax2615])).
% 187.70/187.12 thf(c_0_220, plain, (p67|~p69), inference(fof_simplification,[status(thm)],[ax2616])).
% 187.70/187.12 thf(c_0_221, plain, (p65|~p67), inference(fof_simplification,[status(thm)],[ax2618])).
% 187.70/187.12 thf(c_0_222, plain, (p63|~p65), inference(fof_simplification,[status(thm)],[ax2620])).
% 187.70/187.12 thf(c_0_223, plain, (p61|~p63), inference(fof_simplification,[status(thm)],[ax2622])).
% 187.70/187.12 thf(c_0_224, plain, (p59|~p61), inference(fof_simplification,[status(thm)],[ax2624])).
% 187.70/187.12 thf(c_0_225, plain, (p57|~p59), inference(fof_simplification,[status(thm)],[ax2626])).
% 187.70/187.12 thf(c_0_226, plain, (p55|~p57), inference(split_conjunct,[status(thm)],[c_0_183])).
% 187.70/187.12 thf(c_0_227, plain, ~p55, inference(sr,[status(thm)],[c_0_184, c_0_185])).
% 187.70/187.12 thf(c_0_228, plain, ![X1:term]:(f__0 @ fid @ (fap @ f__2 @ X1) @ fid|~f__0 @ fid @ f__2 @ fid|~f__0 @ fid @ X1 @ fid|~p522), inference(rw,[status(thm)],[c_0_186, c_0_187])).
% 187.70/187.12 thf(c_0_229, plain, (f__0 @ fid @ f__2 @ fid|p275), inference(split_conjunct,[status(thm)],[c_0_188])).
% 187.70/187.12 thf(c_0_230, plain, (f__0 @ fid @ f__3 @ fid|p217), inference(split_conjunct,[status(thm)],[c_0_189])).
% 187.70/187.12 thf(c_0_231, plain, (p133|~f__0 @ fid @ (fap @ f__2 @ f__3) @ fid), inference(split_conjunct,[status(thm)],[c_0_190])).
% 187.70/187.12 thf(c_0_232, plain, (p277|p129), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_191, c_0_192])])).
% 187.70/187.12 thf(c_0_233, plain, (p219|p121), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_193, c_0_194])])).
% 187.70/187.12 thf(c_0_234, plain, (p135|p81), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195, c_0_196])])).
% 187.70/187.12 thf(c_0_235, plain, (p131|p81), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197, c_0_198])])).
% 187.70/187.12 thf(c_0_236, plain, (p77|p78), inference(split_conjunct,[status(thm)],[ax2607])).
% 187.70/187.12 thf(c_0_237, plain, (p75|p76), inference(split_conjunct,[status(thm)],[ax2609])).
% 187.70/187.12 thf(c_0_238, plain, (p522|~p76), inference(split_conjunct,[status(thm)],[c_0_199])).
% 187.70/187.12 thf(c_0_239, plain, (~p134|~p112|~p133), inference(split_conjunct,[status(thm)],[c_0_200])).
% 187.70/187.12 thf(c_0_240, plain, (~p218|~p106|~p217), inference(split_conjunct,[status(thm)],[c_0_201])).
% 187.70/187.12 thf(c_0_241, plain, (~p130|~p106|~p129), inference(split_conjunct,[status(thm)],[c_0_202])).
% 187.70/187.12 thf(c_0_242, plain, (~p276|~p99|~p275), inference(split_conjunct,[status(thm)],[c_0_203])).
% 187.70/187.12 thf(c_0_243, plain, (p80|~p81), inference(split_conjunct,[status(thm)],[c_0_204])).
% 187.70/187.12 thf(c_0_244, plain, (p79|~p80), inference(split_conjunct,[status(thm)],[c_0_205])).
% 187.70/187.12 thf(c_0_245, plain, (p77|~p79), inference(split_conjunct,[status(thm)],[c_0_206])).
% 187.70/187.12 thf(c_0_246, plain, (p70|~p71), inference(split_conjunct,[status(thm)],[c_0_207])).
% 187.70/187.12 thf(c_0_247, plain, (p276|~p277), inference(split_conjunct,[status(thm)],[c_0_208])).
% 187.70/187.12 thf(c_0_248, plain, (p218|~p219), inference(split_conjunct,[status(thm)],[c_0_209])).
% 187.70/187.13 thf(c_0_249, plain, (p134|~p135), inference(split_conjunct,[status(thm)],[c_0_210])).
% 187.70/187.13 thf(c_0_250, plain, (p133|~p121), inference(split_conjunct,[status(thm)],[c_0_211])).
% 187.70/187.13 thf(c_0_251, plain, (p130|~p131), inference(split_conjunct,[status(thm)],[c_0_212])).
% 187.70/187.13 thf(c_0_252, plain, (p112|~p78), inference(split_conjunct,[status(thm)],[c_0_213])).
% 187.70/187.13 thf(c_0_253, plain, (p106|~p78), inference(split_conjunct,[status(thm)],[c_0_214])).
% 187.70/187.13 thf(c_0_254, plain, (p99|~p78), inference(split_conjunct,[status(thm)],[c_0_215])).
% 187.70/187.13 thf(c_0_255, plain, (p75|~p77), inference(split_conjunct,[status(thm)],[c_0_216])).
% 187.70/187.13 thf(c_0_256, plain, (p73|~p75), inference(split_conjunct,[status(thm)],[c_0_217])).
% 187.70/187.13 thf(c_0_257, plain, (p71|~p73), inference(split_conjunct,[status(thm)],[c_0_218])).
% 187.70/187.13 thf(c_0_258, plain, (p69|~p70), inference(split_conjunct,[status(thm)],[c_0_219])).
% 187.70/187.13 thf(c_0_259, plain, (p67|~p69), inference(split_conjunct,[status(thm)],[c_0_220])).
% 187.70/187.13 thf(c_0_260, plain, (p65|~p67), inference(split_conjunct,[status(thm)],[c_0_221])).
% 187.70/187.13 thf(c_0_261, plain, (p63|~p65), inference(split_conjunct,[status(thm)],[c_0_222])).
% 187.70/187.13 thf(c_0_262, plain, (p61|~p63), inference(split_conjunct,[status(thm)],[c_0_223])).
% 187.70/187.13 thf(c_0_263, plain, (p59|~p61), inference(split_conjunct,[status(thm)],[c_0_224])).
% 187.70/187.13 thf(c_0_264, plain, (p57|~p59), inference(split_conjunct,[status(thm)],[c_0_225])).
% 187.70/187.13 thf(c_0_265, plain, ~p57, inference(sr,[status(thm)],[c_0_226, c_0_227])).
% 187.70/187.13 thf(c_0_266, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_228, c_0_229, c_0_230, c_0_231, c_0_232, c_0_233, c_0_234, c_0_235, c_0_236, c_0_237, c_0_238, c_0_239, c_0_240, c_0_241, c_0_242, c_0_243, c_0_244, c_0_245, c_0_246, c_0_247, c_0_248, c_0_249, c_0_250, c_0_251, c_0_252, c_0_253, c_0_254, c_0_255, c_0_256, c_0_257, c_0_258, c_0_259, c_0_260, c_0_261, c_0_262, c_0_263, c_0_264, c_0_265]), ['proof']).
% 187.70/187.13 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 187.70/187.13 thf(0,theorem,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => ((![X1:term>$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))))))))) => ((![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]:(~(((lam @ ((X1 @ sh) @ one)) = ((ap @ ((sub @ 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)))))) => (~((var @ ((sub @ (lam @ ((X1 @ sh) @ one))) @ id)))))) => ((![X1:term]:(![X2:term]:(~((var @ ((sub @ ((ap @ ((sub @ X1) @ id)) @ X2)) @ id)))))) => (![X1:subst>term>subst>$o]:(![X2:term>$o]:((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ X3) @ X4) @ ((comp @ X6) @ X5)) => (((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5)))))) => ((![X3:subst]:(![X4:term]:(![X5:subst]:(![X6:subst]:((((X1 @ ((comp @ X3) @ X6)) @ ((sub @ X4) @ X6)) @ X5) => (((X1 @ X3) @ X4) @ ((comp @ X6) @ X5))))))) => ((![X3:term]:(![X4:term]:((((X1 @ id) @ X3) @ id) => ((((X1 @ id) @ X4) @ id) => (((X1 @ id) @ ((ap @ ((sub @ X3) @ id)) @ X4)) @ id))))) => ((![X3:term]:((X2 @ X3) = (((X1 @ id) @ X3) @ id))) => (![X3:term]:(![X4:term]:((X2 @ X3) => ((X2 @ X4) => (X2 @ ((ap @ X3) @ X4)))))))))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 187.70/187.13 % SZS output end Proof
%------------------------------------------------------------------------------