TSTP Solution File: ALG260^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG260^1 : 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 : n021.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 17:57:48 EDT 2022
% Result : Theorem 188.43s 187.61s
% Output : Proof 188.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG260^1 : 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 : n021.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 03:53:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 188.43/187.61 % SZS status Theorem
% 188.43/187.61 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 188.43/187.61 % Inferences: 558
% 188.43/187.61 % SZS output start Proof
% 188.43/187.61 thf(def_axapp,definition,(axapp = (![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))))).
% 188.43/187.61 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))).
% 188.43/187.61 thf(def_axvarid,definition,(axvarid = (![X1:term]:(((sub @ X1) @ id) = X1)))).
% 188.43/187.61 thf(def_axabs,definition,(axabs = (![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))))).
% 188.43/187.61 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
% 188.43/187.61 thf(def_axidl,definition,(axidl = (![X1:subst]:(((comp @ id) @ X1) = X1)))).
% 188.43/187.61 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
% 188.43/187.61 thf(def_axassoc,definition,(axassoc = (![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))))).
% 188.43/187.61 thf(def_axmap,definition,(axmap = (![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))))).
% 188.43/187.61 thf(def_axidr,definition,(axidr = (![X1:subst]:(((comp @ X1) @ id) = X1)))).
% 188.43/187.61 thf(def_axvarshift,definition,(axvarshift = (((push @ one) @ sh) = id))).
% 188.43/187.61 thf(def_axscons,definition,(axscons = (![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)))).
% 188.43/187.61 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))).
% 188.43/187.61 thf(def_ulamvarsh,definition,(ulamvarsh = (![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))))).
% 188.43/187.61 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))).
% 188.43/187.61 thf(def_apinj1,definition,(apinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))))).
% 188.43/187.61 thf(def_apinj2,definition,(apinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))))).
% 188.43/187.61 thf(def_laminj,definition,(laminj = (![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))))).
% 188.43/187.61 thf(def_shinj,definition,(shinj = (![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))))).
% 188.43/187.61 thf(def_lamnotap,definition,(lamnotap = (![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))))).
% 188.43/187.61 thf(def_apnotvar,definition,(apnotvar = (![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))))).
% 188.43/187.61 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))).
% 188.43/187.61 thf(def_induction,definition,(induction = (![X1:term>$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))))))).
% 188.43/187.61 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))).
% 188.43/187.61 thf(def_induction2lem,definition,(induction2lem = (![X1:term>$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)))))))))).
% 188.43/187.61 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))))))).
% 188.43/187.61 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))))))))).
% 188.43/187.61 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))))))))).
% 188.43/187.61 thf(def_hoasap,definition,(hoasap = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(ap @ ((sub @ X2) @ X3))))))).
% 188.43/187.61 thf(def_hoaslam,definition,(hoaslam = (^[X1:subst]:(^[X2:subst>term>term]:(lam @ ((X2 @ sh) @ one)))))).
% 188.43/187.61 thf(def_hoasvar,definition,(hoasvar = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(var @ ((sub @ X2) @ X3))))))).
% 188.43/187.61 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)))))))).
% 188.43/187.61 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)))))))).
% 188.43/187.61 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))))))))))).
% 188.43/187.61 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)))))))))).
% 188.43/187.61 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))))))).
% 188.43/187.61 thf(def_hoaslamnotvar_gthm,definition,(hoaslamnotvar_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)))))))))))))))))))))))))))))))))).
% 188.43/187.61 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))))))))))))))))))))))))))))))))))))))).
% 188.43/187.61 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)))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 188.43/187.61 thf(ax1161, axiom, (p1|~(p3)), file('<stdin>', ax1161)).
% 188.43/187.61 thf(ax1163, axiom, ~(p1), file('<stdin>', ax1163)).
% 188.43/187.61 thf(ax1159, axiom, (p3|~(p5)), file('<stdin>', ax1159)).
% 188.43/187.61 thf(ax1157, axiom, (p5|~(p7)), file('<stdin>', ax1157)).
% 188.43/187.61 thf(ax1155, axiom, (p7|~(p9)), file('<stdin>', ax1155)).
% 188.43/187.61 thf(ax1153, axiom, (p9|~(p11)), file('<stdin>', ax1153)).
% 188.43/187.61 thf(ax1151, axiom, (p11|~(p13)), file('<stdin>', ax1151)).
% 188.43/187.61 thf(ax1149, axiom, (p13|~(p15)), file('<stdin>', ax1149)).
% 188.43/187.61 thf(ax1147, axiom, (p15|~(p17)), file('<stdin>', ax1147)).
% 188.43/187.61 thf(ax1145, axiom, (p17|~(p19)), file('<stdin>', ax1145)).
% 188.43/187.61 thf(ax1143, axiom, (p19|~(p21)), file('<stdin>', ax1143)).
% 188.43/187.61 thf(ax1141, axiom, (p21|~(p23)), file('<stdin>', ax1141)).
% 188.43/187.61 thf(ax1139, axiom, (p23|~(p25)), file('<stdin>', ax1139)).
% 188.43/187.61 thf(ax1137, axiom, (p25|~(p27)), file('<stdin>', ax1137)).
% 188.43/187.61 thf(ax1135, axiom, (p27|~(p29)), file('<stdin>', ax1135)).
% 188.43/187.61 thf(ax1133, axiom, (p29|~(p31)), file('<stdin>', ax1133)).
% 188.43/187.61 thf(ax1131, axiom, (p31|~(p33)), file('<stdin>', ax1131)).
% 188.43/187.61 thf(ax1129, axiom, (p33|~(p35)), file('<stdin>', ax1129)).
% 188.43/187.61 thf(ax1127, axiom, (p35|~(p37)), file('<stdin>', ax1127)).
% 188.43/187.61 thf(ax1125, axiom, (p37|~(p39)), file('<stdin>', ax1125)).
% 188.43/187.61 thf(ax1123, axiom, (p39|~(p41)), file('<stdin>', ax1123)).
% 188.43/187.61 thf(ax1121, axiom, (p41|~(p43)), file('<stdin>', ax1121)).
% 188.43/187.61 thf(ax1119, axiom, (p43|~(p45)), file('<stdin>', ax1119)).
% 188.43/187.61 thf(ax1117, axiom, (p45|~(p47)), file('<stdin>', ax1117)).
% 188.43/187.61 thf(ax1115, axiom, (p47|~(p49)), file('<stdin>', ax1115)).
% 188.43/187.61 thf(ax1113, axiom, (p49|~(p51)), file('<stdin>', ax1113)).
% 188.43/187.61 thf(ax1111, axiom, (p51|~(p53)), file('<stdin>', ax1111)).
% 188.43/187.61 thf(ax1109, axiom, (p53|~(p55)), file('<stdin>', ax1109)).
% 188.43/187.61 thf(ax1107, axiom, (p55|~(p57)), file('<stdin>', ax1107)).
% 188.43/187.61 thf(ax1105, axiom, (p57|~(p59)), file('<stdin>', ax1105)).
% 188.43/187.61 thf(ax1103, axiom, (p59|~(p61)), file('<stdin>', ax1103)).
% 188.43/187.61 thf(ax1101, axiom, (p61|~(p63)), file('<stdin>', ax1101)).
% 188.43/187.61 thf(ax1099, axiom, (p63|~(p65)), file('<stdin>', ax1099)).
% 188.43/187.61 thf(ax1098, axiom, (p65|~(p66)), file('<stdin>', ax1098)).
% 188.43/187.61 thf(nax53, axiom, (p53<=(~((~((![X248:subst, X247:subst, X249:subst]:(fcomp @ (fcomp @ X248 @ X247) @ X249)=(fcomp @ X248 @ (fcomp @ X247 @ X249))=>~(![X248:subst]:(fcomp @ fid @ X248)=(X248))))=>~(![X248:subst]:(fcomp @ X248 @ fid)=(X248))))=>(~((![X250:term, X247:subst, X249:subst]:(fsub @ (fsub @ X250 @ X247) @ X249)=(fsub @ X250 @ (fcomp @ X247 @ X249))=>~(![X250:term]:(fsub @ X250 @ fid)=(X250))))=>(![X250:term, X251:term, X252:term, X253:term]:((fap @ (fsub @ X250 @ fid) @ X252)=(fap @ (fsub @ X251 @ fid) @ X253)=>(X250)=(X251))=>(![X250:term, X251:term, X252:term, X253:term]:((fap @ (fsub @ X250 @ fid) @ X252)=(fap @ (fsub @ X251 @ fid) @ X253)=>(X252)=(X253))=>(![X254:subst > term > term]:(![X255:subst, X252:term, X256:subst]:(fsub @ (X254 @ X255 @ X252) @ X256)=(X254 @ (fcomp @ X255 @ X256) @ (fsub @ X252 @ X256))=>![X257:subst > term > term]:(![X258:subst, X259:term, X117:subst]:(fsub @ (X257 @ X258 @ X259) @ X117)=(X257 @ (fcomp @ X258 @ X117) @ (fsub @ X259 @ X117))=>((flam @ (X254 @ fsh @ fone))=(flam @ (X257 @ fsh @ fone))=>![X258:subst, X259:term]:(X254 @ X258 @ X259)=(X257 @ X258 @ X259))))=>(![X254:subst > term > term]:(![X260:subst, X261:term, X262:subst]:(fsub @ (X254 @ X260 @ X261) @ X262)=(X254 @ (fcomp @ X260 @ X262) @ (fsub @ X261 @ X262))=>![X263:term, X261:term]:~((flam @ (X254 @ fsh @ fone))=(fap @ (fsub @ X263 @ fid) @ X261)))=>![X254:subst > term > term]:(![X264:subst, X261:term, X262:subst]:(fsub @ (X254 @ X264 @ X261) @ X262)=(X254 @ (fcomp @ X264 @ X262) @ (fsub @ X261 @ X262))=>~(fvar @ (fsub @ (flam @ (X254 @ fsh @ fone)) @ fid)))))))))), file('<stdin>', nax53)).
% 188.43/187.61 thf(pax44, axiom, (p44=>![X265:term]:~(fvar @ (flam @ X265))), file('<stdin>', pax44)).
% 188.43/187.61 thf(ax1120, axiom, (p43|p44), file('<stdin>', ax1120)).
% 188.43/187.61 thf(pax68, axiom, (p68=>fvar @ (fsub @ (flam @ (f__0 @ fsh @ fone)) @ fid)), file('<stdin>', pax68)).
% 188.43/187.61 thf(ax1096, axiom, (p66|p68), file('<stdin>', ax1096)).
% 188.43/187.61 thf(c_0_39, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1161])).
% 188.43/187.61 thf(c_0_40, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1163])).
% 188.43/187.61 thf(c_0_41, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1159])).
% 188.43/187.61 thf(c_0_42, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_39])).
% 188.43/187.61 thf(c_0_43, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_40])).
% 188.43/187.61 thf(c_0_44, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax1157])).
% 188.43/187.61 thf(c_0_45, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_41])).
% 188.43/187.61 thf(c_0_46, plain, ~p3, inference(sr,[status(thm)],[c_0_42, c_0_43])).
% 188.43/187.61 thf(c_0_47, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax1155])).
% 188.43/187.61 thf(c_0_48, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_44])).
% 188.43/187.61 thf(c_0_49, plain, ~p5, inference(sr,[status(thm)],[c_0_45, c_0_46])).
% 188.43/187.61 thf(c_0_50, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax1153])).
% 188.43/187.61 thf(c_0_51, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_47])).
% 188.43/187.61 thf(c_0_52, plain, ~p7, inference(sr,[status(thm)],[c_0_48, c_0_49])).
% 188.43/187.61 thf(c_0_53, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax1151])).
% 188.43/187.61 thf(c_0_54, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_50])).
% 188.43/187.61 thf(c_0_55, plain, ~p9, inference(sr,[status(thm)],[c_0_51, c_0_52])).
% 188.43/187.61 thf(c_0_56, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax1149])).
% 188.43/187.61 thf(c_0_57, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_53])).
% 188.43/187.61 thf(c_0_58, plain, ~p11, inference(sr,[status(thm)],[c_0_54, c_0_55])).
% 188.43/187.61 thf(c_0_59, plain, (p15|~p17), inference(fof_simplification,[status(thm)],[ax1147])).
% 188.43/187.61 thf(c_0_60, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_56])).
% 188.43/187.61 thf(c_0_61, plain, ~p13, inference(sr,[status(thm)],[c_0_57, c_0_58])).
% 188.43/187.61 thf(c_0_62, plain, (p17|~p19), inference(fof_simplification,[status(thm)],[ax1145])).
% 188.43/187.61 thf(c_0_63, plain, (p15|~p17), inference(split_conjunct,[status(thm)],[c_0_59])).
% 188.43/187.61 thf(c_0_64, plain, ~p15, inference(sr,[status(thm)],[c_0_60, c_0_61])).
% 188.43/187.61 thf(c_0_65, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax1143])).
% 188.43/187.61 thf(c_0_66, plain, (p17|~p19), inference(split_conjunct,[status(thm)],[c_0_62])).
% 188.43/187.61 thf(c_0_67, plain, ~p17, inference(sr,[status(thm)],[c_0_63, c_0_64])).
% 188.43/187.61 thf(c_0_68, plain, (p21|~p23), inference(fof_simplification,[status(thm)],[ax1141])).
% 188.43/187.61 thf(c_0_69, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_65])).
% 188.43/187.61 thf(c_0_70, plain, ~p19, inference(sr,[status(thm)],[c_0_66, c_0_67])).
% 188.43/187.61 thf(c_0_71, plain, (p23|~p25), inference(fof_simplification,[status(thm)],[ax1139])).
% 188.43/187.61 thf(c_0_72, plain, (p21|~p23), inference(split_conjunct,[status(thm)],[c_0_68])).
% 188.43/187.61 thf(c_0_73, plain, ~p21, inference(sr,[status(thm)],[c_0_69, c_0_70])).
% 188.43/187.61 thf(c_0_74, plain, (p25|~p27), inference(fof_simplification,[status(thm)],[ax1137])).
% 188.43/187.61 thf(c_0_75, plain, (p23|~p25), inference(split_conjunct,[status(thm)],[c_0_71])).
% 188.43/187.61 thf(c_0_76, plain, ~p23, inference(sr,[status(thm)],[c_0_72, c_0_73])).
% 188.43/187.61 thf(c_0_77, plain, (p27|~p29), inference(fof_simplification,[status(thm)],[ax1135])).
% 188.43/187.61 thf(c_0_78, plain, (p25|~p27), inference(split_conjunct,[status(thm)],[c_0_74])).
% 188.43/187.61 thf(c_0_79, plain, ~p25, inference(sr,[status(thm)],[c_0_75, c_0_76])).
% 188.43/187.61 thf(c_0_80, plain, (p29|~p31), inference(fof_simplification,[status(thm)],[ax1133])).
% 188.43/187.61 thf(c_0_81, plain, (p27|~p29), inference(split_conjunct,[status(thm)],[c_0_77])).
% 188.43/187.61 thf(c_0_82, plain, ~p27, inference(sr,[status(thm)],[c_0_78, c_0_79])).
% 188.43/187.61 thf(c_0_83, plain, (p31|~p33), inference(fof_simplification,[status(thm)],[ax1131])).
% 188.43/187.61 thf(c_0_84, plain, (p29|~p31), inference(split_conjunct,[status(thm)],[c_0_80])).
% 188.43/187.61 thf(c_0_85, plain, ~p29, inference(sr,[status(thm)],[c_0_81, c_0_82])).
% 188.43/187.61 thf(c_0_86, plain, (p33|~p35), inference(fof_simplification,[status(thm)],[ax1129])).
% 188.43/187.61 thf(c_0_87, plain, (p31|~p33), inference(split_conjunct,[status(thm)],[c_0_83])).
% 188.43/187.61 thf(c_0_88, plain, ~p31, inference(sr,[status(thm)],[c_0_84, c_0_85])).
% 188.43/187.61 thf(c_0_89, plain, (p35|~p37), inference(fof_simplification,[status(thm)],[ax1127])).
% 188.43/187.61 thf(c_0_90, plain, (p33|~p35), inference(split_conjunct,[status(thm)],[c_0_86])).
% 188.43/187.61 thf(c_0_91, plain, ~p33, inference(sr,[status(thm)],[c_0_87, c_0_88])).
% 188.43/187.61 thf(c_0_92, plain, (p37|~p39), inference(fof_simplification,[status(thm)],[ax1125])).
% 188.43/187.61 thf(c_0_93, plain, (p35|~p37), inference(split_conjunct,[status(thm)],[c_0_89])).
% 188.43/187.61 thf(c_0_94, plain, ~p35, inference(sr,[status(thm)],[c_0_90, c_0_91])).
% 188.43/187.61 thf(c_0_95, plain, (p39|~p41), inference(fof_simplification,[status(thm)],[ax1123])).
% 188.43/187.61 thf(c_0_96, plain, (p37|~p39), inference(split_conjunct,[status(thm)],[c_0_92])).
% 188.43/187.61 thf(c_0_97, plain, ~p37, inference(sr,[status(thm)],[c_0_93, c_0_94])).
% 188.43/187.61 thf(c_0_98, plain, (p41|~p43), inference(fof_simplification,[status(thm)],[ax1121])).
% 188.43/187.61 thf(c_0_99, plain, (p39|~p41), inference(split_conjunct,[status(thm)],[c_0_95])).
% 188.43/187.61 thf(c_0_100, plain, ~p39, inference(sr,[status(thm)],[c_0_96, c_0_97])).
% 188.43/187.61 thf(c_0_101, plain, (p43|~p45), inference(fof_simplification,[status(thm)],[ax1119])).
% 188.43/187.61 thf(c_0_102, plain, (p41|~p43), inference(split_conjunct,[status(thm)],[c_0_98])).
% 188.43/187.61 thf(c_0_103, plain, ~p41, inference(sr,[status(thm)],[c_0_99, c_0_100])).
% 188.43/187.61 thf(c_0_104, plain, (p45|~p47), inference(fof_simplification,[status(thm)],[ax1117])).
% 188.43/187.61 thf(c_0_105, plain, (p43|~p45), inference(split_conjunct,[status(thm)],[c_0_101])).
% 188.43/187.61 thf(c_0_106, plain, ~p43, inference(sr,[status(thm)],[c_0_102, c_0_103])).
% 188.43/187.61 thf(c_0_107, plain, (p47|~p49), inference(fof_simplification,[status(thm)],[ax1115])).
% 188.43/187.61 thf(c_0_108, plain, (p45|~p47), inference(split_conjunct,[status(thm)],[c_0_104])).
% 188.43/187.61 thf(c_0_109, plain, ~p45, inference(sr,[status(thm)],[c_0_105, c_0_106])).
% 188.43/187.61 thf(c_0_110, plain, (p49|~p51), inference(fof_simplification,[status(thm)],[ax1113])).
% 188.43/187.61 thf(c_0_111, plain, (p47|~p49), inference(split_conjunct,[status(thm)],[c_0_107])).
% 188.43/187.61 thf(c_0_112, plain, ~p47, inference(sr,[status(thm)],[c_0_108, c_0_109])).
% 188.43/187.61 thf(c_0_113, plain, (p51|~p53), inference(fof_simplification,[status(thm)],[ax1111])).
% 188.43/187.61 thf(c_0_114, plain, (p49|~p51), inference(split_conjunct,[status(thm)],[c_0_110])).
% 188.43/187.61 thf(c_0_115, plain, ~p49, inference(sr,[status(thm)],[c_0_111, c_0_112])).
% 188.43/187.61 thf(c_0_116, plain, (p53|~p55), inference(fof_simplification,[status(thm)],[ax1109])).
% 188.43/187.61 thf(c_0_117, plain, (p51|~p53), inference(split_conjunct,[status(thm)],[c_0_113])).
% 188.43/187.61 thf(c_0_118, plain, ~p51, inference(sr,[status(thm)],[c_0_114, c_0_115])).
% 188.43/187.61 thf(c_0_119, plain, (p55|~p57), inference(fof_simplification,[status(thm)],[ax1107])).
% 188.43/187.61 thf(c_0_120, plain, (p53|~p55), inference(split_conjunct,[status(thm)],[c_0_116])).
% 188.43/187.61 thf(c_0_121, plain, ~p53, inference(sr,[status(thm)],[c_0_117, c_0_118])).
% 188.43/187.61 thf(c_0_122, plain, (p57|~p59), inference(fof_simplification,[status(thm)],[ax1105])).
% 188.43/187.61 thf(c_0_123, plain, (p55|~p57), inference(split_conjunct,[status(thm)],[c_0_119])).
% 188.43/187.61 thf(c_0_124, plain, ~p55, inference(sr,[status(thm)],[c_0_120, c_0_121])).
% 188.43/187.61 thf(c_0_125, plain, (p59|~p61), inference(fof_simplification,[status(thm)],[ax1103])).
% 188.43/187.61 thf(c_0_126, plain, (p57|~p59), inference(split_conjunct,[status(thm)],[c_0_122])).
% 188.43/187.61 thf(c_0_127, plain, ~p57, inference(sr,[status(thm)],[c_0_123, c_0_124])).
% 188.43/187.61 thf(c_0_128, plain, (p61|~p63), inference(fof_simplification,[status(thm)],[ax1101])).
% 188.43/187.61 thf(c_0_129, plain, (p59|~p61), inference(split_conjunct,[status(thm)],[c_0_125])).
% 188.43/187.61 thf(c_0_130, plain, ~p59, inference(sr,[status(thm)],[c_0_126, c_0_127])).
% 188.43/187.61 thf(c_0_131, plain, (p63|~p65), inference(fof_simplification,[status(thm)],[ax1099])).
% 188.43/187.61 thf(c_0_132, plain, (p61|~p63), inference(split_conjunct,[status(thm)],[c_0_128])).
% 188.43/187.61 thf(c_0_133, plain, ~p61, inference(sr,[status(thm)],[c_0_129, c_0_130])).
% 188.43/187.61 thf(c_0_134, plain, (p65|~p66), inference(fof_simplification,[status(thm)],[ax1098])).
% 188.43/187.61 thf(c_0_135, plain, (p63|~p65), inference(split_conjunct,[status(thm)],[c_0_131])).
% 188.43/187.61 thf(c_0_136, plain, ~p63, inference(sr,[status(thm)],[c_0_132, c_0_133])).
% 188.43/187.61 thf(c_0_137, plain, ![X1180:subst, X1181:subst, X1182:subst, X1183:subst, X1184:subst, X1185:term, X1186:subst, X1187:subst, X1188:term, X1189:term, X1190:term, X1191:term, X1192:term, X1193:term, X1194:term, X1195:term, X1196:term, X1197:subst > term > term, X1201:subst > term > term, X1205:subst, X1206:term, X1207:subst > term > term, X1211:term, X1212:term, X1214:subst, X1215:term, X1216:subst]:(((((fcomp @ (fcomp @ X1180 @ X1181) @ X1182)=(fcomp @ X1180 @ (fcomp @ X1181 @ X1182))|p53)&((fcomp @ fid @ X1183)=(X1183)|p53))&((fcomp @ X1184 @ fid)=(X1184)|p53))&((((fsub @ (fsub @ X1185 @ X1186) @ X1187)=(fsub @ X1185 @ (fcomp @ X1186 @ X1187))|p53)&((fsub @ X1188 @ fid)=(X1188)|p53))&(((fap @ (fsub @ X1189 @ fid) @ X1191)!=(fap @ (fsub @ X1190 @ fid) @ X1192)|(X1189)=(X1190)|p53)&(((fap @ (fsub @ X1193 @ fid) @ X1195)!=(fap @ (fsub @ X1194 @ fid) @ X1196)|(X1195)=(X1196)|p53)&(((fsub @ (X1197 @ (esk461_1 @ X1197) @ (esk462_1 @ X1197)) @ (esk463_1 @ X1197))!=(X1197 @ (fcomp @ (esk461_1 @ X1197) @ (esk463_1 @ X1197)) @ (fsub @ (esk462_1 @ X1197) @ (esk463_1 @ X1197)))|((fsub @ (X1201 @ (esk464_2 @ X1197 @ X1201) @ (esk465_2 @ X1197 @ X1201)) @ (esk466_2 @ X1197 @ X1201))!=(X1201 @ (fcomp @ (esk464_2 @ X1197 @ X1201) @ (esk466_2 @ X1197 @ X1201)) @ (fsub @ (esk465_2 @ X1197 @ X1201) @ (esk466_2 @ X1197 @ X1201)))|((flam @ (X1197 @ fsh @ fone))!=(flam @ (X1201 @ fsh @ fone))|(X1197 @ X1205 @ X1206)=(X1201 @ X1205 @ X1206)))|p53)&(((fsub @ (X1207 @ (esk467_1 @ X1207) @ (esk468_1 @ X1207)) @ (esk469_1 @ X1207))!=(X1207 @ (fcomp @ (esk467_1 @ X1207) @ (esk469_1 @ X1207)) @ (fsub @ (esk468_1 @ X1207) @ (esk469_1 @ X1207)))|(flam @ (X1207 @ fsh @ fone))!=(fap @ (fsub @ X1211 @ fid) @ X1212)|p53)&(((fsub @ (esk470_0 @ X1214 @ X1215) @ X1216)=(esk470_0 @ (fcomp @ X1214 @ X1216) @ (fsub @ X1215 @ X1216))|p53)&(fvar @ (fsub @ (flam @ (esk470_0 @ fsh @ fone)) @ fid)|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])])])])])])).
% 188.43/187.61 thf(c_0_138, plain, (p65|~p66), inference(split_conjunct,[status(thm)],[c_0_134])).
% 188.43/187.61 thf(c_0_139, plain, ~p65, inference(sr,[status(thm)],[c_0_135, c_0_136])).
% 188.43/187.61 thf(c_0_140, plain, ![X1217:term]:(~p44|~fvar @ (flam @ X1217)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax44])])])])).
% 188.43/187.61 thf(c_0_141, plain, (p43|p44), inference(split_conjunct,[status(thm)],[ax1120])).
% 188.43/187.61 thf(c_0_142, plain, (~p68|fvar @ (fsub @ (flam @ (f__0 @ fsh @ fone)) @ fid)), inference(fof_nnf,[status(thm)],[pax68])).
% 188.43/187.61 thf(c_0_143, plain, ![X2:term]:((fsub @ X2 @ fid)=(X2)|p53), inference(split_conjunct,[status(thm)],[c_0_137])).
% 188.43/187.61 thf(c_0_144, plain, (p66|p68), inference(split_conjunct,[status(thm)],[ax1096])).
% 188.43/187.61 thf(c_0_145, plain, ~p66, inference(sr,[status(thm)],[c_0_138, c_0_139])).
% 188.43/187.61 thf(c_0_146, plain, ![X2:term]:(~p44|~fvar @ (flam @ X2)), inference(split_conjunct,[status(thm)],[c_0_140])).
% 188.43/187.61 thf(c_0_147, plain, p44, inference(sr,[status(thm)],[c_0_141, c_0_106])).
% 188.43/187.61 thf(c_0_148, plain, (fvar @ (fsub @ (flam @ (f__0 @ fsh @ fone)) @ fid)|~p68), inference(split_conjunct,[status(thm)],[c_0_142])).
% 188.43/187.61 thf(c_0_149, plain, ![X2:term]:(fsub @ X2 @ fid)=(X2), inference(sr,[status(thm)],[c_0_143, c_0_121])).
% 188.43/187.61 thf(c_0_150, plain, p68, inference(sr,[status(thm)],[c_0_144, c_0_145])).
% 188.43/187.61 thf(c_0_151, plain, ![X2:term]:~fvar @ (flam @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146, c_0_147])])).
% 188.43/187.61 thf(c_0_152, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148, c_0_149]), c_0_150])]), c_0_151]), ['proof']).
% 188.43/187.61 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 188.43/187.61 thf(0,theorem,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => ((![X1:term>$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)))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 188.43/187.61 % SZS output end Proof
%------------------------------------------------------------------------------