TSTP Solution File: ALG261^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG261^1 : 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 : n032.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 187.57s 187.04s
% Output : Proof 187.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG261^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.00/0.08 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Wed Jun 8 08:07:21 EDT 2022
% 0.07/0.27 % CPUTime :
% 187.57/187.04 % SZS status Theorem
% 187.57/187.04 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 187.57/187.04 % Inferences: 19457
% 187.57/187.04 % SZS output start Proof
% 187.57/187.04 thf(def_axapp,definition,(axapp = (![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))))).
% 187.57/187.04 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))).
% 187.57/187.04 thf(def_axvarid,definition,(axvarid = (![X1:term]:(((sub @ X1) @ id) = X1)))).
% 187.57/187.04 thf(def_axabs,definition,(axabs = (![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))))).
% 187.57/187.04 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
% 187.57/187.04 thf(def_axidl,definition,(axidl = (![X1:subst]:(((comp @ id) @ X1) = X1)))).
% 187.57/187.04 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
% 187.57/187.04 thf(def_axassoc,definition,(axassoc = (![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))))).
% 187.57/187.04 thf(def_axmap,definition,(axmap = (![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))))).
% 187.57/187.04 thf(def_axidr,definition,(axidr = (![X1:subst]:(((comp @ X1) @ id) = X1)))).
% 187.57/187.04 thf(def_axvarshift,definition,(axvarshift = (((push @ one) @ sh) = id))).
% 187.57/187.04 thf(def_axscons,definition,(axscons = (![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)))).
% 187.57/187.04 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))).
% 187.57/187.04 thf(def_ulamvarsh,definition,(ulamvarsh = (![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))))).
% 187.57/187.04 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))).
% 187.57/187.04 thf(def_apinj1,definition,(apinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))))).
% 187.57/187.04 thf(def_apinj2,definition,(apinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))))).
% 187.57/187.04 thf(def_laminj,definition,(laminj = (![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))))).
% 187.57/187.04 thf(def_shinj,definition,(shinj = (![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))))).
% 187.57/187.04 thf(def_lamnotap,definition,(lamnotap = (![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))))).
% 187.57/187.04 thf(def_apnotvar,definition,(apnotvar = (![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))))).
% 187.57/187.04 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))).
% 187.57/187.04 thf(def_induction,definition,(induction = (![X1:term>$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))))))).
% 187.57/187.04 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))).
% 187.57/187.04 thf(def_induction2lem,definition,(induction2lem = (![X1:term>$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)))))))))).
% 187.57/187.04 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))))))).
% 187.57/187.04 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))))))))).
% 187.57/187.04 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))))))))).
% 187.57/187.04 thf(def_hoasap,definition,(hoasap = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(ap @ ((sub @ X2) @ X3))))))).
% 187.57/187.04 thf(def_hoaslam,definition,(hoaslam = (^[X1:subst]:(^[X2:subst>term>term]:(lam @ ((X2 @ sh) @ one)))))).
% 187.57/187.04 thf(def_hoasvar,definition,(hoasvar = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(var @ ((sub @ X2) @ X3))))))).
% 187.57/187.04 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)))))))).
% 187.57/187.04 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)))))))).
% 187.57/187.04 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))))))))))).
% 187.57/187.04 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)))))))))).
% 187.57/187.04 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))))))).
% 187.57/187.04 thf(def_hoasapnotvar,definition,(hoasapnotvar = (![X1:term]:(![X2:term]:(~((((hoasvar @ id) @ ((((hoasap @ id) @ X1) @ id) @ X2)) @ id))))))).
% 187.57/187.04 thf(def_hoasapnotvar_gthm,definition,(hoasapnotvar_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))))))))))))))))))))))))))))))))))).
% 187.57/187.04 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)))))))))))))))))))))))))))))))))))))))).
% 187.57/187.04 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))))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 187.57/187.04 thf(ax1913, axiom, (p1|~(p3)), file('<stdin>', ax1913)).
% 187.57/187.04 thf(ax1915, axiom, ~(p1), file('<stdin>', ax1915)).
% 187.57/187.04 thf(ax1911, axiom, (p3|~(p5)), file('<stdin>', ax1911)).
% 187.57/187.04 thf(ax1909, axiom, (p5|~(p7)), file('<stdin>', ax1909)).
% 187.57/187.04 thf(ax1907, axiom, (p7|~(p9)), file('<stdin>', ax1907)).
% 187.57/187.04 thf(ax1905, axiom, (p9|~(p11)), file('<stdin>', ax1905)).
% 187.57/187.04 thf(ax1903, axiom, (p11|~(p13)), file('<stdin>', ax1903)).
% 187.57/187.04 thf(ax1901, axiom, (p13|~(p15)), file('<stdin>', ax1901)).
% 187.57/187.04 thf(ax1899, axiom, (p15|~(p17)), file('<stdin>', ax1899)).
% 187.57/187.04 thf(ax1897, axiom, (p17|~(p19)), file('<stdin>', ax1897)).
% 187.57/187.04 thf(ax1895, axiom, (p19|~(p21)), file('<stdin>', ax1895)).
% 187.57/187.04 thf(ax1893, axiom, (p21|~(p23)), file('<stdin>', ax1893)).
% 187.57/187.04 thf(ax1891, axiom, (p23|~(p25)), file('<stdin>', ax1891)).
% 187.57/187.04 thf(ax1889, axiom, (p25|~(p27)), file('<stdin>', ax1889)).
% 187.57/187.04 thf(ax1887, axiom, (p27|~(p29)), file('<stdin>', ax1887)).
% 187.57/187.04 thf(ax1885, axiom, (p29|~(p31)), file('<stdin>', ax1885)).
% 187.57/187.04 thf(ax1883, axiom, (p31|~(p33)), file('<stdin>', ax1883)).
% 187.57/187.04 thf(ax1881, axiom, (p33|~(p35)), file('<stdin>', ax1881)).
% 187.57/187.04 thf(ax1879, axiom, (p35|~(p37)), file('<stdin>', ax1879)).
% 187.57/187.04 thf(ax1877, axiom, (p37|~(p39)), file('<stdin>', ax1877)).
% 187.57/187.04 thf(ax1875, axiom, (p39|~(p41)), file('<stdin>', ax1875)).
% 187.57/187.04 thf(ax1873, axiom, (p41|~(p43)), file('<stdin>', ax1873)).
% 187.57/187.04 thf(ax1871, axiom, (p43|~(p45)), file('<stdin>', ax1871)).
% 187.57/187.04 thf(ax1869, axiom, (p45|~(p47)), file('<stdin>', ax1869)).
% 187.57/187.04 thf(ax1867, axiom, (p47|~(p49)), file('<stdin>', ax1867)).
% 187.57/187.04 thf(ax1805, axiom, (~(p114)|p113), file('<stdin>', ax1805)).
% 187.57/187.04 thf(ax1865, axiom, (p49|~(p51)), file('<stdin>', ax1865)).
% 187.57/187.04 thf(ax1537, axiom, (~(p113)|p369), file('<stdin>', ax1537)).
% 187.57/187.04 thf(ax1806, axiom, p114, file('<stdin>', ax1806)).
% 187.57/187.04 thf(ax1863, axiom, (p51|~(p53)), file('<stdin>', ax1863)).
% 187.57/187.04 thf(ax888, axiom, (~(p75)|p1016), file('<stdin>', ax888)).
% 187.57/187.04 thf(ax1536, axiom, (~(p369)|p53|p368), file('<stdin>', ax1536)).
% 187.57/187.04 thf(ax1800, axiom, (~(p6)|p109), file('<stdin>', ax1800)).
% 187.57/187.04 thf(ax1910, axiom, (p5|p6), file('<stdin>', ax1910)).
% 187.57/187.04 thf(ax887, axiom, (~(p1016)|p1017), file('<stdin>', ax887)).
% 187.57/187.04 thf(ax1843, axiom, p75, file('<stdin>', ax1843)).
% 187.57/187.04 thf(pax367, axiom, (p367=>((fsub @ fone @ fid)=(fone)=>~((~((~((![X121:subst, X122:subst, X123:subst]:(fcomp @ (fcomp @ X121 @ X122) @ X123)=(fcomp @ X121 @ (fcomp @ X122 @ X123))=>~(![X121:subst]:(fcomp @ fid @ X121)=(X121))))=>~(![X121:subst]:(fcomp @ X121 @ fid)=(X121))))=>(~((![X124:term, X122:subst, X123:subst]:(fsub @ (fsub @ X124 @ X122) @ X123)=(fsub @ X124 @ (fcomp @ X122 @ X123))=>~(![X124:term]:(fsub @ X124 @ fid)=(X124))))=>(![X124:term, X125:term, X126:term, X115:term]:((fap @ (fsub @ X124 @ fid) @ X126)=(fap @ (fsub @ X125 @ fid) @ X115)=>(X124)=(X125))=>(![X124:term, X125:term, X126:term, X115:term]:((fap @ (fsub @ X124 @ fid) @ X126)=(fap @ (fsub @ X125 @ fid) @ X115)=>(X126)=(X115))=>(![X127:subst > term > term]:(![X128:subst, X126:term, X129:subst]:(fsub @ (X127 @ X128 @ X126) @ X129)=(X127 @ (fcomp @ X128 @ X129) @ (fsub @ X126 @ X129))=>![X130:subst > term > term]:(![X131:subst, X132:term, X116:subst]:(fsub @ (X130 @ X131 @ X132) @ X116)=(X130 @ (fcomp @ X131 @ X116) @ (fsub @ X132 @ X116))=>((flam @ (X127 @ fsh @ fone))=(flam @ (X130 @ fsh @ fone))=>![X131:subst, X132:term]:(X127 @ X131 @ X132)=(X130 @ X131 @ X132))))=>(![X127:subst > term > term]:(![X133:subst, X134:term, X135:subst]:(fsub @ (X127 @ X133 @ X134) @ X135)=(X127 @ (fcomp @ X133 @ X135) @ (fsub @ X134 @ X135))=>![X136:term, X134:term]:~((flam @ (X127 @ fsh @ fone))=(fap @ (fsub @ X136 @ fid) @ X134)))=>(![X127:subst > term > term]:(![X137:subst, X134:term, X135:subst]:(fsub @ (X127 @ X137 @ X134) @ X135)=(X127 @ (fcomp @ X137 @ X135) @ (fsub @ X134 @ X135))=>~(fvar @ (fsub @ (flam @ (X127 @ fsh @ (fsub @ fone @ fid))) @ fid)))=>![X138:term, X139:term]:~(fvar @ (fsub @ (fap @ (fsub @ X138 @ fid) @ X139) @ fid)))))))))))), file('<stdin>', pax367)).
% 187.57/187.04 thf(ax1535, axiom, (~(p368)|p367), file('<stdin>', ax1535)).
% 187.57/187.04 thf(ax886, axiom, (~(p1017)|~(p109)|p1015), file('<stdin>', ax886)).
% 187.57/187.04 thf(pax1015, axiom, (p1015=>(fone)=(fsub @ fone @ fid)), file('<stdin>', pax1015)).
% 187.57/187.04 thf(pax6, axiom, (p6=>![X3768:term]:(fsub @ X3768 @ fid)=(X3768)), file('<stdin>', pax6)).
% 187.57/187.04 thf(pax42, axiom, (p42=>![X3758:term, X3759:term]:~(fvar @ (fap @ X3758 @ X3759))), file('<stdin>', pax42)).
% 187.57/187.04 thf(ax1874, axiom, (p41|p42), file('<stdin>', ax1874)).
% 187.57/187.04 thf(c_0_43, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1913])).
% 187.57/187.04 thf(c_0_44, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1915])).
% 187.57/187.04 thf(c_0_45, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1911])).
% 187.57/187.04 thf(c_0_46, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_43])).
% 187.57/187.04 thf(c_0_47, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_44])).
% 187.57/187.04 thf(c_0_48, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax1909])).
% 187.57/187.04 thf(c_0_49, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_45])).
% 187.57/187.04 thf(c_0_50, plain, ~p3, inference(sr,[status(thm)],[c_0_46, c_0_47])).
% 187.57/187.04 thf(c_0_51, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax1907])).
% 187.57/187.04 thf(c_0_52, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_48])).
% 187.57/187.04 thf(c_0_53, plain, ~p5, inference(sr,[status(thm)],[c_0_49, c_0_50])).
% 187.57/187.04 thf(c_0_54, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax1905])).
% 187.57/187.04 thf(c_0_55, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_51])).
% 187.57/187.04 thf(c_0_56, plain, ~p7, inference(sr,[status(thm)],[c_0_52, c_0_53])).
% 187.57/187.04 thf(c_0_57, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax1903])).
% 187.57/187.04 thf(c_0_58, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_54])).
% 187.57/187.04 thf(c_0_59, plain, ~p9, inference(sr,[status(thm)],[c_0_55, c_0_56])).
% 187.57/187.04 thf(c_0_60, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax1901])).
% 187.57/187.04 thf(c_0_61, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_57])).
% 187.57/187.04 thf(c_0_62, plain, ~p11, inference(sr,[status(thm)],[c_0_58, c_0_59])).
% 187.57/187.04 thf(c_0_63, plain, (p15|~p17), inference(fof_simplification,[status(thm)],[ax1899])).
% 187.57/187.04 thf(c_0_64, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_60])).
% 187.57/187.04 thf(c_0_65, plain, ~p13, inference(sr,[status(thm)],[c_0_61, c_0_62])).
% 187.57/187.04 thf(c_0_66, plain, (p17|~p19), inference(fof_simplification,[status(thm)],[ax1897])).
% 187.57/187.04 thf(c_0_67, plain, (p15|~p17), inference(split_conjunct,[status(thm)],[c_0_63])).
% 187.57/187.04 thf(c_0_68, plain, ~p15, inference(sr,[status(thm)],[c_0_64, c_0_65])).
% 187.57/187.04 thf(c_0_69, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax1895])).
% 187.57/187.04 thf(c_0_70, plain, (p17|~p19), inference(split_conjunct,[status(thm)],[c_0_66])).
% 187.57/187.04 thf(c_0_71, plain, ~p17, inference(sr,[status(thm)],[c_0_67, c_0_68])).
% 187.57/187.04 thf(c_0_72, plain, (p21|~p23), inference(fof_simplification,[status(thm)],[ax1893])).
% 187.57/187.04 thf(c_0_73, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_69])).
% 187.57/187.04 thf(c_0_74, plain, ~p19, inference(sr,[status(thm)],[c_0_70, c_0_71])).
% 187.57/187.04 thf(c_0_75, plain, (p23|~p25), inference(fof_simplification,[status(thm)],[ax1891])).
% 187.57/187.04 thf(c_0_76, plain, (p21|~p23), inference(split_conjunct,[status(thm)],[c_0_72])).
% 187.57/187.04 thf(c_0_77, plain, ~p21, inference(sr,[status(thm)],[c_0_73, c_0_74])).
% 187.57/187.04 thf(c_0_78, plain, (p25|~p27), inference(fof_simplification,[status(thm)],[ax1889])).
% 187.57/187.04 thf(c_0_79, plain, (p23|~p25), inference(split_conjunct,[status(thm)],[c_0_75])).
% 187.57/187.04 thf(c_0_80, plain, ~p23, inference(sr,[status(thm)],[c_0_76, c_0_77])).
% 187.57/187.04 thf(c_0_81, plain, (p27|~p29), inference(fof_simplification,[status(thm)],[ax1887])).
% 187.57/187.04 thf(c_0_82, plain, (p25|~p27), inference(split_conjunct,[status(thm)],[c_0_78])).
% 187.57/187.04 thf(c_0_83, plain, ~p25, inference(sr,[status(thm)],[c_0_79, c_0_80])).
% 187.57/187.04 thf(c_0_84, plain, (p29|~p31), inference(fof_simplification,[status(thm)],[ax1885])).
% 187.57/187.04 thf(c_0_85, plain, (p27|~p29), inference(split_conjunct,[status(thm)],[c_0_81])).
% 187.57/187.04 thf(c_0_86, plain, ~p27, inference(sr,[status(thm)],[c_0_82, c_0_83])).
% 187.57/187.04 thf(c_0_87, plain, (p31|~p33), inference(fof_simplification,[status(thm)],[ax1883])).
% 187.57/187.04 thf(c_0_88, plain, (p29|~p31), inference(split_conjunct,[status(thm)],[c_0_84])).
% 187.57/187.04 thf(c_0_89, plain, ~p29, inference(sr,[status(thm)],[c_0_85, c_0_86])).
% 187.57/187.04 thf(c_0_90, plain, (p33|~p35), inference(fof_simplification,[status(thm)],[ax1881])).
% 187.57/187.04 thf(c_0_91, plain, (p31|~p33), inference(split_conjunct,[status(thm)],[c_0_87])).
% 187.57/187.04 thf(c_0_92, plain, ~p31, inference(sr,[status(thm)],[c_0_88, c_0_89])).
% 187.57/187.04 thf(c_0_93, plain, (p35|~p37), inference(fof_simplification,[status(thm)],[ax1879])).
% 187.57/187.04 thf(c_0_94, plain, (p33|~p35), inference(split_conjunct,[status(thm)],[c_0_90])).
% 187.57/187.04 thf(c_0_95, plain, ~p33, inference(sr,[status(thm)],[c_0_91, c_0_92])).
% 187.57/187.04 thf(c_0_96, plain, (p37|~p39), inference(fof_simplification,[status(thm)],[ax1877])).
% 187.57/187.04 thf(c_0_97, plain, (p35|~p37), inference(split_conjunct,[status(thm)],[c_0_93])).
% 187.57/187.04 thf(c_0_98, plain, ~p35, inference(sr,[status(thm)],[c_0_94, c_0_95])).
% 187.57/187.04 thf(c_0_99, plain, (p39|~p41), inference(fof_simplification,[status(thm)],[ax1875])).
% 187.57/187.04 thf(c_0_100, plain, (p37|~p39), inference(split_conjunct,[status(thm)],[c_0_96])).
% 187.57/187.04 thf(c_0_101, plain, ~p37, inference(sr,[status(thm)],[c_0_97, c_0_98])).
% 187.57/187.04 thf(c_0_102, plain, (p41|~p43), inference(fof_simplification,[status(thm)],[ax1873])).
% 187.57/187.04 thf(c_0_103, plain, (p39|~p41), inference(split_conjunct,[status(thm)],[c_0_99])).
% 187.57/187.04 thf(c_0_104, plain, ~p39, inference(sr,[status(thm)],[c_0_100, c_0_101])).
% 187.57/187.04 thf(c_0_105, plain, (p43|~p45), inference(fof_simplification,[status(thm)],[ax1871])).
% 187.57/187.04 thf(c_0_106, plain, (p41|~p43), inference(split_conjunct,[status(thm)],[c_0_102])).
% 187.57/187.04 thf(c_0_107, plain, ~p41, inference(sr,[status(thm)],[c_0_103, c_0_104])).
% 187.57/187.04 thf(c_0_108, plain, (p45|~p47), inference(fof_simplification,[status(thm)],[ax1869])).
% 187.57/187.04 thf(c_0_109, plain, (p43|~p45), inference(split_conjunct,[status(thm)],[c_0_105])).
% 187.57/187.04 thf(c_0_110, plain, ~p43, inference(sr,[status(thm)],[c_0_106, c_0_107])).
% 187.57/187.04 thf(c_0_111, plain, (p47|~p49), inference(fof_simplification,[status(thm)],[ax1867])).
% 187.57/187.04 thf(c_0_112, plain, (p45|~p47), inference(split_conjunct,[status(thm)],[c_0_108])).
% 187.57/187.04 thf(c_0_113, plain, ~p45, inference(sr,[status(thm)],[c_0_109, c_0_110])).
% 187.57/187.04 thf(c_0_114, plain, (~p114|p113), inference(fof_simplification,[status(thm)],[ax1805])).
% 187.57/187.04 thf(c_0_115, plain, (p49|~p51), inference(fof_simplification,[status(thm)],[ax1865])).
% 187.57/187.04 thf(c_0_116, plain, (p47|~p49), inference(split_conjunct,[status(thm)],[c_0_111])).
% 187.57/187.04 thf(c_0_117, plain, ~p47, inference(sr,[status(thm)],[c_0_112, c_0_113])).
% 187.57/187.04 thf(c_0_118, plain, (~p113|p369), inference(fof_simplification,[status(thm)],[ax1537])).
% 187.57/187.04 thf(c_0_119, plain, (p113|~p114), inference(split_conjunct,[status(thm)],[c_0_114])).
% 187.57/187.04 thf(c_0_120, plain, p114, inference(split_conjunct,[status(thm)],[ax1806])).
% 187.57/187.04 thf(c_0_121, plain, (p51|~p53), inference(fof_simplification,[status(thm)],[ax1863])).
% 187.57/187.04 thf(c_0_122, plain, (p49|~p51), inference(split_conjunct,[status(thm)],[c_0_115])).
% 187.57/187.04 thf(c_0_123, plain, ~p49, inference(sr,[status(thm)],[c_0_116, c_0_117])).
% 187.57/187.04 thf(c_0_124, plain, (~p75|p1016), inference(fof_simplification,[status(thm)],[ax888])).
% 187.57/187.04 thf(c_0_125, plain, (epred3_0<=>~((~((~((![X121:subst, X122:subst, X123:subst]:(fcomp @ (fcomp @ X121 @ X122) @ X123)=(fcomp @ X121 @ (fcomp @ X122 @ X123))=>~(![X121:subst]:(fcomp @ fid @ X121)=(X121))))=>~(![X121:subst]:(fcomp @ X121 @ fid)=(X121))))=>(~((![X124:term, X122:subst, X123:subst]:(fsub @ (fsub @ X124 @ X122) @ X123)=(fsub @ X124 @ (fcomp @ X122 @ X123))=>~(![X124:term]:(fsub @ X124 @ fid)=(X124))))=>(![X124:term, X125:term, X126:term, X115:term]:((fap @ (fsub @ X124 @ fid) @ X126)=(fap @ (fsub @ X125 @ fid) @ X115)=>(X124)=(X125))=>(![X124:term, X125:term, X126:term, X115:term]:((fap @ (fsub @ X124 @ fid) @ X126)=(fap @ (fsub @ X125 @ fid) @ X115)=>(X126)=(X115))=>(![X127:subst > term > term]:(![X128:subst, X126:term, X129:subst]:(fsub @ (X127 @ X128 @ X126) @ X129)=(X127 @ (fcomp @ X128 @ X129) @ (fsub @ X126 @ X129))=>![X130:subst > term > term]:(![X131:subst, X132:term, X116:subst]:(fsub @ (X130 @ X131 @ X132) @ X116)=(X130 @ (fcomp @ X131 @ X116) @ (fsub @ X132 @ X116))=>((flam @ (X127 @ fsh @ fone))=(flam @ (X130 @ fsh @ fone))=>![X131:subst, X132:term]:(X127 @ X131 @ X132)=(X130 @ X131 @ X132))))=>(![X127:subst > term > term]:(![X133:subst, X134:term, X135:subst]:(fsub @ (X127 @ X133 @ X134) @ X135)=(X127 @ (fcomp @ X133 @ X135) @ (fsub @ X134 @ X135))=>![X136:term, X134:term]:~((flam @ (X127 @ fsh @ fone))=(fap @ (fsub @ X136 @ fid) @ X134)))=>(![X127:subst > term > term]:(![X137:subst, X134:term, X135:subst]:(fsub @ (X127 @ X137 @ X134) @ X135)=(X127 @ (fcomp @ X137 @ X135) @ (fsub @ X134 @ X135))=>~(fvar @ (fsub @ (flam @ (X127 @ fsh @ (fsub @ fone @ fid))) @ fid)))=>![X138:term, X139:term]:~(fvar @ (fsub @ (fap @ (fsub @ X138 @ fid) @ X139) @ fid))))))))))), introduced(definition)).
% 187.57/187.04 thf(c_0_126, plain, (~p369|p53|p368), inference(fof_simplification,[status(thm)],[ax1536])).
% 187.57/187.04 thf(c_0_127, plain, (p369|~p113), inference(split_conjunct,[status(thm)],[c_0_118])).
% 187.57/187.04 thf(c_0_128, plain, p113, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119, c_0_120])])).
% 187.57/187.04 thf(c_0_129, plain, (p51|~p53), inference(split_conjunct,[status(thm)],[c_0_121])).
% 187.57/187.04 thf(c_0_130, plain, ~p51, inference(sr,[status(thm)],[c_0_122, c_0_123])).
% 187.57/187.04 thf(c_0_131, plain, (~p6|p109), inference(fof_simplification,[status(thm)],[ax1800])).
% 187.57/187.04 thf(c_0_132, plain, (p5|p6), inference(split_conjunct,[status(thm)],[ax1910])).
% 187.57/187.04 thf(c_0_133, plain, (~p1016|p1017), inference(fof_simplification,[status(thm)],[ax887])).
% 187.57/187.04 thf(c_0_134, plain, (p1016|~p75), inference(split_conjunct,[status(thm)],[c_0_124])).
% 187.57/187.04 thf(c_0_135, plain, p75, inference(split_conjunct,[status(thm)],[ax1843])).
% 187.57/187.04 thf(c_0_136, axiom, (p367=>((fsub @ fone @ fid)=(fone)=>epred3_0)), inference(apply_def,[status(thm)],[pax367, c_0_125])).
% 187.57/187.04 thf(c_0_137, plain, (~p368|p367), inference(fof_simplification,[status(thm)],[ax1535])).
% 187.57/187.04 thf(c_0_138, plain, (p53|p368|~p369), inference(split_conjunct,[status(thm)],[c_0_126])).
% 187.57/187.04 thf(c_0_139, plain, p369, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127, c_0_128])])).
% 187.57/187.04 thf(c_0_140, plain, ~p53, inference(sr,[status(thm)],[c_0_129, c_0_130])).
% 187.57/187.04 thf(c_0_141, plain, (~p1017|~p109|p1015), inference(fof_simplification,[status(thm)],[ax886])).
% 187.57/187.04 thf(c_0_142, plain, (p109|~p6), inference(split_conjunct,[status(thm)],[c_0_131])).
% 187.57/187.04 thf(c_0_143, plain, p6, inference(sr,[status(thm)],[c_0_132, c_0_53])).
% 187.57/187.04 thf(c_0_144, plain, (p1017|~p1016), inference(split_conjunct,[status(thm)],[c_0_133])).
% 187.57/187.04 thf(c_0_145, plain, p1016, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134, c_0_135])])).
% 187.57/187.04 thf(c_0_146, plain, (~p367|((fsub @ fone @ fid)!=(fone)|epred3_0)), inference(fof_nnf,[status(thm)],[c_0_136])).
% 187.57/187.04 thf(c_0_147, plain, (p367|~p368), inference(split_conjunct,[status(thm)],[c_0_137])).
% 187.57/187.04 thf(c_0_148, plain, p368, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138, c_0_139])]), c_0_140])).
% 187.57/187.04 thf(c_0_149, plain, (~p1015|(fone)=(fsub @ fone @ fid)), inference(fof_nnf,[status(thm)],[pax1015])).
% 187.57/187.04 thf(c_0_150, plain, (p1015|~p1017|~p109), inference(split_conjunct,[status(thm)],[c_0_141])).
% 187.57/187.04 thf(c_0_151, plain, p109, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142, c_0_143])])).
% 187.57/187.04 thf(c_0_152, plain, p1017, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144, c_0_145])])).
% 187.57/187.04 thf(c_0_153, plain, (epred3_0=>~((~((~((![X121:subst, X122:subst, X123:subst]:(fcomp @ (fcomp @ X121 @ X122) @ X123)=(fcomp @ X121 @ (fcomp @ X122 @ X123))=>~(![X121:subst]:(fcomp @ fid @ X121)=(X121))))=>~(![X121:subst]:(fcomp @ X121 @ fid)=(X121))))=>(~((![X124:term, X122:subst, X123:subst]:(fsub @ (fsub @ X124 @ X122) @ X123)=(fsub @ X124 @ (fcomp @ X122 @ X123))=>~(![X124:term]:(fsub @ X124 @ fid)=(X124))))=>(![X124:term, X125:term, X126:term, X115:term]:((fap @ (fsub @ X124 @ fid) @ X126)=(fap @ (fsub @ X125 @ fid) @ X115)=>(X124)=(X125))=>(![X124:term, X125:term, X126:term, X115:term]:((fap @ (fsub @ X124 @ fid) @ X126)=(fap @ (fsub @ X125 @ fid) @ X115)=>(X126)=(X115))=>(![X127:subst > term > term]:(![X128:subst, X126:term, X129:subst]:(fsub @ (X127 @ X128 @ X126) @ X129)=(X127 @ (fcomp @ X128 @ X129) @ (fsub @ X126 @ X129))=>![X130:subst > term > term]:(![X131:subst, X132:term, X116:subst]:(fsub @ (X130 @ X131 @ X132) @ X116)=(X130 @ (fcomp @ X131 @ X116) @ (fsub @ X132 @ X116))=>((flam @ (X127 @ fsh @ fone))=(flam @ (X130 @ fsh @ fone))=>![X131:subst, X132:term]:(X127 @ X131 @ X132)=(X130 @ X131 @ X132))))=>(![X127:subst > term > term]:(![X133:subst, X134:term, X135:subst]:(fsub @ (X127 @ X133 @ X134) @ X135)=(X127 @ (fcomp @ X133 @ X135) @ (fsub @ X134 @ X135))=>![X136:term, X134:term]:~((flam @ (X127 @ fsh @ fone))=(fap @ (fsub @ X136 @ fid) @ X134)))=>(![X127:subst > term > term]:(![X137:subst, X134:term, X135:subst]:(fsub @ (X127 @ X137 @ X134) @ X135)=(X127 @ (fcomp @ X137 @ X135) @ (fsub @ X134 @ X135))=>~(fvar @ (fsub @ (flam @ (X127 @ fsh @ (fsub @ fone @ fid))) @ fid)))=>![X138:term, X139:term]:~(fvar @ (fsub @ (fap @ (fsub @ X138 @ fid) @ X139) @ fid))))))))))), inference(split_equiv,[status(thm)],[c_0_125])).
% 187.57/187.04 thf(c_0_154, plain, ![X10768:term]:(~p6|(fsub @ X10768 @ fid)=(X10768)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])])).
% 187.57/187.04 thf(c_0_155, plain, (epred3_0|~p367|(fsub @ fone @ fid)!=(fone)), inference(split_conjunct,[status(thm)],[c_0_146])).
% 187.57/187.04 thf(c_0_156, plain, p367, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147, c_0_148])])).
% 187.57/187.04 thf(c_0_157, plain, ((fone)=(fsub @ fone @ fid)|~p1015), inference(split_conjunct,[status(thm)],[c_0_149])).
% 187.57/187.04 thf(c_0_158, plain, p1015, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150, c_0_151]), c_0_152])])).
% 187.57/187.04 thf(c_0_159, plain, ![X10700:term, X10701:term]:(~p42|~fvar @ (fap @ X10700 @ X10701)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax42])])])])).
% 187.57/187.04 thf(c_0_160, plain, (p41|p42), inference(split_conjunct,[status(thm)],[ax1874])).
% 187.57/187.04 thf(c_0_161, plain, ![X10860:subst, X10861:subst, X10862:subst, X10863:subst, X10864:subst, X10865:term, X10866:subst, X10867:subst, X10868:term, X10869:term, X10870:term, X10871:term, X10872:term, X10873:term, X10874:term, X10875:term, X10876:term, X10877:subst > term > term, X10881:subst > term > term, X10885:subst, X10886:term, X10887:subst > term > term, X10891:term, X10892:term, X10893:subst > term > term]:(((((fcomp @ (fcomp @ X10860 @ X10861) @ X10862)=(fcomp @ X10860 @ (fcomp @ X10861 @ X10862))|~epred3_0)&((fcomp @ fid @ X10863)=(X10863)|~epred3_0))&((fcomp @ X10864 @ fid)=(X10864)|~epred3_0))&((((fsub @ (fsub @ X10865 @ X10866) @ X10867)=(fsub @ X10865 @ (fcomp @ X10866 @ X10867))|~epred3_0)&((fsub @ X10868 @ fid)=(X10868)|~epred3_0))&(((fap @ (fsub @ X10869 @ fid) @ X10871)!=(fap @ (fsub @ X10870 @ fid) @ X10872)|(X10869)=(X10870)|~epred3_0)&(((fap @ (fsub @ X10873 @ fid) @ X10875)!=(fap @ (fsub @ X10874 @ fid) @ X10876)|(X10875)=(X10876)|~epred3_0)&(((fsub @ (X10877 @ (esk3636_1 @ X10877) @ (esk3637_1 @ X10877)) @ (esk3638_1 @ X10877))!=(X10877 @ (fcomp @ (esk3636_1 @ X10877) @ (esk3638_1 @ X10877)) @ (fsub @ (esk3637_1 @ X10877) @ (esk3638_1 @ X10877)))|((fsub @ (X10881 @ (esk3639_2 @ X10877 @ X10881) @ (esk3640_2 @ X10877 @ X10881)) @ (esk3641_2 @ X10877 @ X10881))!=(X10881 @ (fcomp @ (esk3639_2 @ X10877 @ X10881) @ (esk3641_2 @ X10877 @ X10881)) @ (fsub @ (esk3640_2 @ X10877 @ X10881) @ (esk3641_2 @ X10877 @ X10881)))|((flam @ (X10877 @ fsh @ fone))!=(flam @ (X10881 @ fsh @ fone))|(X10877 @ X10885 @ X10886)=(X10881 @ X10885 @ X10886)))|~epred3_0)&(((fsub @ (X10887 @ (esk3642_1 @ X10887) @ (esk3643_1 @ X10887)) @ (esk3644_1 @ X10887))!=(X10887 @ (fcomp @ (esk3642_1 @ X10887) @ (esk3644_1 @ X10887)) @ (fsub @ (esk3643_1 @ X10887) @ (esk3644_1 @ X10887)))|(flam @ (X10887 @ fsh @ fone))!=(fap @ (fsub @ X10891 @ fid) @ X10892)|~epred3_0)&(((fsub @ (X10893 @ (esk3645_1 @ X10893) @ (esk3646_1 @ X10893)) @ (esk3647_1 @ X10893))!=(X10893 @ (fcomp @ (esk3645_1 @ X10893) @ (esk3647_1 @ X10893)) @ (fsub @ (esk3646_1 @ X10893) @ (esk3647_1 @ X10893)))|~fvar @ (fsub @ (flam @ (X10893 @ fsh @ (fsub @ fone @ fid))) @ fid)|~epred3_0)&(fvar @ (fsub @ (fap @ (fsub @ esk3648_0 @ fid) @ esk3649_0) @ fid)|~epred3_0)))))))), 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)],[c_0_153])])])])])])).
% 187.57/187.04 thf(c_0_162, plain, ![X1:term]:((fsub @ X1 @ fid)=(X1)|~p6), inference(split_conjunct,[status(thm)],[c_0_154])).
% 187.57/187.04 thf(c_0_163, plain, (epred3_0|(fsub @ fone @ fid)!=(fone)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155, c_0_156])])).
% 187.57/187.04 thf(c_0_164, plain, (fsub @ fone @ fid)=(fone), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157, c_0_158])])).
% 187.57/187.04 thf(c_0_165, plain, ![X1:term, X5:term]:(~p42|~fvar @ (fap @ X1 @ X5)), inference(split_conjunct,[status(thm)],[c_0_159])).
% 187.57/187.04 thf(c_0_166, plain, p42, inference(sr,[status(thm)],[c_0_160, c_0_107])).
% 187.57/187.04 thf(c_0_167, plain, (fvar @ (fsub @ (fap @ (fsub @ esk3648_0 @ fid) @ esk3649_0) @ fid)|~epred3_0), inference(split_conjunct,[status(thm)],[c_0_161])).
% 187.57/187.04 thf(c_0_168, plain, ![X1:term]:(fsub @ X1 @ fid)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162, c_0_143])])).
% 187.57/187.04 thf(c_0_169, plain, epred3_0, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163, c_0_164])])).
% 187.57/187.04 thf(c_0_170, plain, ![X1:term, X5:term]:~fvar @ (fap @ X1 @ X5), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165, c_0_166])])).
% 187.57/187.04 thf(c_0_171, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_167, c_0_168]), c_0_168]), c_0_169])]), c_0_170]), ['proof']).
% 187.57/187.04 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 187.57/187.04 thf(0,theorem,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => ((![X1:term>$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))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 187.57/187.04 % SZS output end Proof
%------------------------------------------------------------------------------