TSTP Solution File: ALG253^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG253^1 : 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 : n024.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 17:57:45 EDT 2022
% Result : Theorem 154.55s 154.71s
% Output : Proof 154.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG253^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 8 06:24:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 154.55/154.71 % SZS status Theorem
% 154.55/154.71 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 154.55/154.71 % Inferences: 43
% 154.55/154.71 % SZS output start Proof
% 154.55/154.71 thf(def_axapp,definition,(axapp = (![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))))).
% 154.55/154.71 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))).
% 154.55/154.71 thf(def_axvarid,definition,(axvarid = (![X1:term]:(((sub @ X1) @ id) = X1)))).
% 154.55/154.71 thf(def_axabs,definition,(axabs = (![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))))).
% 154.55/154.71 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
% 154.55/154.71 thf(def_axidl,definition,(axidl = (![X1:subst]:(((comp @ id) @ X1) = X1)))).
% 154.55/154.71 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
% 154.55/154.71 thf(def_axassoc,definition,(axassoc = (![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))))).
% 154.55/154.71 thf(def_axmap,definition,(axmap = (![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))))).
% 154.55/154.71 thf(def_axidr,definition,(axidr = (![X1:subst]:(((comp @ X1) @ id) = X1)))).
% 154.55/154.71 thf(def_axvarshift,definition,(axvarshift = (((push @ one) @ sh) = id))).
% 154.55/154.71 thf(def_axscons,definition,(axscons = (![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)))).
% 154.55/154.71 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))).
% 154.55/154.71 thf(def_ulamvarsh,definition,(ulamvarsh = (![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))))).
% 154.55/154.71 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))).
% 154.55/154.71 thf(def_apinj1,definition,(apinj1 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X1 = X2)))))))).
% 154.55/154.71 thf(def_apinj2,definition,(apinj2 = (![X1:term]:(![X2:term]:(![X3:term]:(![X4:term]:((((ap @ X1) @ X3) = ((ap @ X2) @ X4)) => (X3 = X4)))))))).
% 154.55/154.71 thf(def_laminj,definition,(laminj = (![X1:term]:(![X2:term]:(((lam @ X1) = (lam @ X2)) => (X1 = X2)))))).
% 154.55/154.71 thf(def_shinj,definition,(shinj = (![X1:term]:(![X2:term]:((((sub @ X1) @ sh) = ((sub @ X2) @ sh)) => (X1 = X2)))))).
% 154.55/154.71 thf(def_lamnotap,definition,(lamnotap = (![X1:term]:(![X2:term]:(![X3:term]:(~(((lam @ X1) = ((ap @ X2) @ X3))))))))).
% 154.55/154.71 thf(def_apnotvar,definition,(apnotvar = (![X1:term]:(![X2:term]:(~((var @ ((ap @ X1) @ X2)))))))).
% 154.55/154.71 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))).
% 154.55/154.71 thf(def_induction,definition,(induction = (![X1:term>$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))))))).
% 154.55/154.71 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))).
% 154.55/154.71 thf(def_induction2lem,definition,(induction2lem = (![X1:term>$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)))))))))).
% 154.55/154.71 thf(def_induction2,definition,(induction2 = (![X1:term>$o]:((![X2:term]:((var @ X2) => (X1 @ X2))) => ((![X2:term]:(![X3:term]:((X1 @ X2) => ((X1 @ X3) => (X1 @ ((ap @ X2) @ X3)))))) => ((![X2:term]:((![X3:term]:((X1 @ X3) => (X1 @ ((sub @ X2) @ ((push @ X3) @ id))))) => (X1 @ (lam @ X2)))) => ((!!) @ X1))))))).
% 154.55/154.71 thf(def_induction2_gthm,definition,(induction2_gthm = (axapp => (axvarcons => (axvarid => (axabs => (axclos => (axidl => (axshiftcons => (axassoc => (axmap => (axidr => (axvarshift => (axscons => (ulamvar1 => (ulamvarsh => (ulamvarind => (apinj1 => (apinj2 => (laminj => (shinj => (lamnotap => (apnotvar => (lamnotvar => (induction => (pushprop => (induction2lem => induction2))))))))))))))))))))))))))).
% 154.55/154.71 thf(thm,conjecture,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => ((![X1:term>$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))))))))))))))))))))))))))))))).
% 154.55/154.71 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)))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 154.55/154.71 thf(ax71, axiom, (p1|~(p3)), file('<stdin>', ax71)).
% 154.55/154.71 thf(ax73, axiom, ~(p1), file('<stdin>', ax73)).
% 154.55/154.71 thf(ax69, axiom, (p3|~(p5)), file('<stdin>', ax69)).
% 154.55/154.71 thf(ax67, axiom, (p5|~(p7)), file('<stdin>', ax67)).
% 154.55/154.71 thf(ax65, axiom, (p7|~(p9)), file('<stdin>', ax65)).
% 154.55/154.71 thf(ax63, axiom, (p9|~(p11)), file('<stdin>', ax63)).
% 154.55/154.71 thf(ax61, axiom, (p11|~(p13)), file('<stdin>', ax61)).
% 154.55/154.71 thf(ax59, axiom, (p13|~(p15)), file('<stdin>', ax59)).
% 154.55/154.71 thf(ax57, axiom, (p15|~(p17)), file('<stdin>', ax57)).
% 154.55/154.71 thf(ax55, axiom, (p17|~(p19)), file('<stdin>', ax55)).
% 154.55/154.71 thf(ax53, axiom, (p19|~(p21)), file('<stdin>', ax53)).
% 154.55/154.71 thf(ax51, axiom, (p21|~(p23)), file('<stdin>', ax51)).
% 154.55/154.71 thf(ax49, axiom, (p23|~(p25)), file('<stdin>', ax49)).
% 154.55/154.71 thf(ax47, axiom, (p25|~(p27)), file('<stdin>', ax47)).
% 154.55/154.71 thf(ax45, axiom, (p27|~(p29)), file('<stdin>', ax45)).
% 154.55/154.71 thf(ax43, axiom, (p29|~(p31)), file('<stdin>', ax43)).
% 154.55/154.71 thf(ax41, axiom, (p31|~(p33)), file('<stdin>', ax41)).
% 154.55/154.71 thf(ax39, axiom, (p33|~(p35)), file('<stdin>', ax39)).
% 154.55/154.71 thf(ax37, axiom, (p35|~(p37)), file('<stdin>', ax37)).
% 154.55/154.71 thf(ax35, axiom, (p37|~(p39)), file('<stdin>', ax35)).
% 154.55/154.71 thf(ax33, axiom, (p39|~(p41)), file('<stdin>', ax33)).
% 154.55/154.71 thf(ax31, axiom, (p41|~(p43)), file('<stdin>', ax31)).
% 154.55/154.71 thf(ax29, axiom, (p43|~(p45)), file('<stdin>', ax29)).
% 154.55/154.71 thf(ax27, axiom, (p45|~(p47)), file('<stdin>', ax27)).
% 154.55/154.71 thf(ax25, axiom, (p47|~(p49)), file('<stdin>', ax25)).
% 154.55/154.71 thf(ax23, axiom, (p49|~(p51)), file('<stdin>', ax23)).
% 154.55/154.71 thf(ax18, axiom, (p54|~(p56)), file('<stdin>', ax18)).
% 154.55/154.71 thf(ax22, axiom, (p51|~(p52)), file('<stdin>', ax22)).
% 154.55/154.71 thf(ax20, axiom, (p52|~(p54)), file('<stdin>', ax20)).
% 154.55/154.71 thf(ax17, axiom, (p56|p57), file('<stdin>', ax17)).
% 154.55/154.71 thf(ax5, axiom, (~(p50)|p69), file('<stdin>', ax5)).
% 154.55/154.71 thf(ax24, axiom, (p49|p50), file('<stdin>', ax24)).
% 154.55/154.71 thf(ax7, axiom, (~(p68)|~(p57)|p67), file('<stdin>', ax7)).
% 154.55/154.71 thf(ax6, axiom, (~(p69)|~(p55)|p68), file('<stdin>', ax6)).
% 154.55/154.71 thf(ax19, axiom, (p54|p55), file('<stdin>', ax19)).
% 154.55/154.71 thf(ax16, axiom, (p56|~(p58)), file('<stdin>', ax16)).
% 154.55/154.71 thf(ax15, axiom, (p58|~(p59)), file('<stdin>', ax15)).
% 154.55/154.71 thf(pax67, axiom, (p67=>![X1:term, X18:subst]:(![X4:term]:(fvar @ X4=>f__0 @ (fsub @ X4 @ X18))=>f__0 @ (fsub @ X1 @ X18))), file('<stdin>', pax67)).
% 154.55/154.71 thf(pax6, axiom, (p6=>![X28:term]:(fsub @ X28 @ fid)=(X28)), file('<stdin>', pax6)).
% 154.55/154.71 thf(ax68, axiom, (p5|p6), file('<stdin>', ax68)).
% 154.55/154.71 thf(pax53, axiom, (p53=>![X1:term]:(fvar @ X1=>f__0 @ X1)), file('<stdin>', pax53)).
% 154.55/154.71 thf(ax21, axiom, (p52|p53), file('<stdin>', ax21)).
% 154.55/154.71 thf(nax59, axiom, (p59<=f__0 @ f__1), file('<stdin>', nax59)).
% 154.55/154.71 thf(c_0_43, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax71])).
% 154.55/154.71 thf(c_0_44, plain, ~p1, inference(fof_simplification,[status(thm)],[ax73])).
% 154.55/154.71 thf(c_0_45, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax69])).
% 154.55/154.71 thf(c_0_46, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_43])).
% 154.55/154.71 thf(c_0_47, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_44])).
% 154.55/154.71 thf(c_0_48, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax67])).
% 154.55/154.71 thf(c_0_49, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_45])).
% 154.55/154.71 thf(c_0_50, plain, ~p3, inference(sr,[status(thm)],[c_0_46, c_0_47])).
% 154.55/154.71 thf(c_0_51, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax65])).
% 154.55/154.71 thf(c_0_52, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_48])).
% 154.55/154.71 thf(c_0_53, plain, ~p5, inference(sr,[status(thm)],[c_0_49, c_0_50])).
% 154.55/154.71 thf(c_0_54, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax63])).
% 154.55/154.71 thf(c_0_55, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_51])).
% 154.55/154.71 thf(c_0_56, plain, ~p7, inference(sr,[status(thm)],[c_0_52, c_0_53])).
% 154.55/154.71 thf(c_0_57, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax61])).
% 154.55/154.71 thf(c_0_58, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_54])).
% 154.55/154.71 thf(c_0_59, plain, ~p9, inference(sr,[status(thm)],[c_0_55, c_0_56])).
% 154.55/154.71 thf(c_0_60, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax59])).
% 154.55/154.71 thf(c_0_61, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_57])).
% 154.55/154.71 thf(c_0_62, plain, ~p11, inference(sr,[status(thm)],[c_0_58, c_0_59])).
% 154.55/154.71 thf(c_0_63, plain, (p15|~p17), inference(fof_simplification,[status(thm)],[ax57])).
% 154.55/154.71 thf(c_0_64, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_60])).
% 154.55/154.71 thf(c_0_65, plain, ~p13, inference(sr,[status(thm)],[c_0_61, c_0_62])).
% 154.55/154.71 thf(c_0_66, plain, (p17|~p19), inference(fof_simplification,[status(thm)],[ax55])).
% 154.55/154.71 thf(c_0_67, plain, (p15|~p17), inference(split_conjunct,[status(thm)],[c_0_63])).
% 154.55/154.71 thf(c_0_68, plain, ~p15, inference(sr,[status(thm)],[c_0_64, c_0_65])).
% 154.55/154.71 thf(c_0_69, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax53])).
% 154.55/154.71 thf(c_0_70, plain, (p17|~p19), inference(split_conjunct,[status(thm)],[c_0_66])).
% 154.55/154.71 thf(c_0_71, plain, ~p17, inference(sr,[status(thm)],[c_0_67, c_0_68])).
% 154.55/154.71 thf(c_0_72, plain, (p21|~p23), inference(fof_simplification,[status(thm)],[ax51])).
% 154.55/154.71 thf(c_0_73, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_69])).
% 154.55/154.71 thf(c_0_74, plain, ~p19, inference(sr,[status(thm)],[c_0_70, c_0_71])).
% 154.55/154.71 thf(c_0_75, plain, (p23|~p25), inference(fof_simplification,[status(thm)],[ax49])).
% 154.55/154.71 thf(c_0_76, plain, (p21|~p23), inference(split_conjunct,[status(thm)],[c_0_72])).
% 154.55/154.71 thf(c_0_77, plain, ~p21, inference(sr,[status(thm)],[c_0_73, c_0_74])).
% 154.55/154.71 thf(c_0_78, plain, (p25|~p27), inference(fof_simplification,[status(thm)],[ax47])).
% 154.55/154.71 thf(c_0_79, plain, (p23|~p25), inference(split_conjunct,[status(thm)],[c_0_75])).
% 154.55/154.71 thf(c_0_80, plain, ~p23, inference(sr,[status(thm)],[c_0_76, c_0_77])).
% 154.55/154.71 thf(c_0_81, plain, (p27|~p29), inference(fof_simplification,[status(thm)],[ax45])).
% 154.55/154.71 thf(c_0_82, plain, (p25|~p27), inference(split_conjunct,[status(thm)],[c_0_78])).
% 154.55/154.71 thf(c_0_83, plain, ~p25, inference(sr,[status(thm)],[c_0_79, c_0_80])).
% 154.55/154.71 thf(c_0_84, plain, (p29|~p31), inference(fof_simplification,[status(thm)],[ax43])).
% 154.55/154.71 thf(c_0_85, plain, (p27|~p29), inference(split_conjunct,[status(thm)],[c_0_81])).
% 154.55/154.71 thf(c_0_86, plain, ~p27, inference(sr,[status(thm)],[c_0_82, c_0_83])).
% 154.55/154.71 thf(c_0_87, plain, (p31|~p33), inference(fof_simplification,[status(thm)],[ax41])).
% 154.55/154.71 thf(c_0_88, plain, (p29|~p31), inference(split_conjunct,[status(thm)],[c_0_84])).
% 154.55/154.71 thf(c_0_89, plain, ~p29, inference(sr,[status(thm)],[c_0_85, c_0_86])).
% 154.55/154.71 thf(c_0_90, plain, (p33|~p35), inference(fof_simplification,[status(thm)],[ax39])).
% 154.55/154.71 thf(c_0_91, plain, (p31|~p33), inference(split_conjunct,[status(thm)],[c_0_87])).
% 154.55/154.71 thf(c_0_92, plain, ~p31, inference(sr,[status(thm)],[c_0_88, c_0_89])).
% 154.55/154.71 thf(c_0_93, plain, (p35|~p37), inference(fof_simplification,[status(thm)],[ax37])).
% 154.55/154.71 thf(c_0_94, plain, (p33|~p35), inference(split_conjunct,[status(thm)],[c_0_90])).
% 154.55/154.71 thf(c_0_95, plain, ~p33, inference(sr,[status(thm)],[c_0_91, c_0_92])).
% 154.55/154.71 thf(c_0_96, plain, (p37|~p39), inference(fof_simplification,[status(thm)],[ax35])).
% 154.55/154.71 thf(c_0_97, plain, (p35|~p37), inference(split_conjunct,[status(thm)],[c_0_93])).
% 154.55/154.71 thf(c_0_98, plain, ~p35, inference(sr,[status(thm)],[c_0_94, c_0_95])).
% 154.55/154.71 thf(c_0_99, plain, (p39|~p41), inference(fof_simplification,[status(thm)],[ax33])).
% 154.55/154.71 thf(c_0_100, plain, (p37|~p39), inference(split_conjunct,[status(thm)],[c_0_96])).
% 154.55/154.71 thf(c_0_101, plain, ~p37, inference(sr,[status(thm)],[c_0_97, c_0_98])).
% 154.55/154.71 thf(c_0_102, plain, (p41|~p43), inference(fof_simplification,[status(thm)],[ax31])).
% 154.55/154.71 thf(c_0_103, plain, (p39|~p41), inference(split_conjunct,[status(thm)],[c_0_99])).
% 154.55/154.71 thf(c_0_104, plain, ~p39, inference(sr,[status(thm)],[c_0_100, c_0_101])).
% 154.55/154.71 thf(c_0_105, plain, (p43|~p45), inference(fof_simplification,[status(thm)],[ax29])).
% 154.55/154.71 thf(c_0_106, plain, (p41|~p43), inference(split_conjunct,[status(thm)],[c_0_102])).
% 154.55/154.71 thf(c_0_107, plain, ~p41, inference(sr,[status(thm)],[c_0_103, c_0_104])).
% 154.55/154.71 thf(c_0_108, plain, (p45|~p47), inference(fof_simplification,[status(thm)],[ax27])).
% 154.55/154.71 thf(c_0_109, plain, (p43|~p45), inference(split_conjunct,[status(thm)],[c_0_105])).
% 154.55/154.71 thf(c_0_110, plain, ~p43, inference(sr,[status(thm)],[c_0_106, c_0_107])).
% 154.55/154.71 thf(c_0_111, plain, (p47|~p49), inference(fof_simplification,[status(thm)],[ax25])).
% 154.55/154.71 thf(c_0_112, plain, (p45|~p47), inference(split_conjunct,[status(thm)],[c_0_108])).
% 154.55/154.71 thf(c_0_113, plain, ~p45, inference(sr,[status(thm)],[c_0_109, c_0_110])).
% 154.55/154.71 thf(c_0_114, plain, (p49|~p51), inference(fof_simplification,[status(thm)],[ax23])).
% 154.55/154.71 thf(c_0_115, plain, (p47|~p49), inference(split_conjunct,[status(thm)],[c_0_111])).
% 154.55/154.71 thf(c_0_116, plain, ~p47, inference(sr,[status(thm)],[c_0_112, c_0_113])).
% 154.55/154.71 thf(c_0_117, plain, (p54|~p56), inference(fof_simplification,[status(thm)],[ax18])).
% 154.55/154.71 thf(c_0_118, plain, (p51|~p52), inference(fof_simplification,[status(thm)],[ax22])).
% 154.55/154.71 thf(c_0_119, plain, (p49|~p51), inference(split_conjunct,[status(thm)],[c_0_114])).
% 154.55/154.71 thf(c_0_120, plain, ~p49, inference(sr,[status(thm)],[c_0_115, c_0_116])).
% 154.55/154.71 thf(c_0_121, plain, (p52|~p54), inference(fof_simplification,[status(thm)],[ax20])).
% 154.55/154.71 thf(c_0_122, plain, (p54|~p56), inference(split_conjunct,[status(thm)],[c_0_117])).
% 154.55/154.71 thf(c_0_123, plain, (p56|p57), inference(split_conjunct,[status(thm)],[ax17])).
% 154.55/154.71 thf(c_0_124, plain, (p51|~p52), inference(split_conjunct,[status(thm)],[c_0_118])).
% 154.55/154.71 thf(c_0_125, plain, ~p51, inference(sr,[status(thm)],[c_0_119, c_0_120])).
% 154.55/154.71 thf(c_0_126, plain, (~p50|p69), inference(fof_simplification,[status(thm)],[ax5])).
% 154.55/154.71 thf(c_0_127, plain, (p49|p50), inference(split_conjunct,[status(thm)],[ax24])).
% 154.55/154.71 thf(c_0_128, plain, (~p68|~p57|p67), inference(fof_simplification,[status(thm)],[ax7])).
% 154.55/154.71 thf(c_0_129, plain, (p52|~p54), inference(split_conjunct,[status(thm)],[c_0_121])).
% 154.55/154.71 thf(c_0_130, plain, (p57|p54), inference(spm,[status(thm)],[c_0_122, c_0_123])).
% 154.55/154.71 thf(c_0_131, plain, ~p52, inference(sr,[status(thm)],[c_0_124, c_0_125])).
% 154.55/154.71 thf(c_0_132, plain, (~p69|~p55|p68), inference(fof_simplification,[status(thm)],[ax6])).
% 154.55/154.71 thf(c_0_133, plain, (p54|p55), inference(split_conjunct,[status(thm)],[ax19])).
% 154.55/154.71 thf(c_0_134, plain, (p69|~p50), inference(split_conjunct,[status(thm)],[c_0_126])).
% 154.55/154.71 thf(c_0_135, plain, p50, inference(sr,[status(thm)],[c_0_127, c_0_120])).
% 154.55/154.71 thf(c_0_136, plain, (p56|~p58), inference(fof_simplification,[status(thm)],[ax16])).
% 154.55/154.71 thf(c_0_137, plain, (p58|~p59), inference(fof_simplification,[status(thm)],[ax15])).
% 154.55/154.71 thf(c_0_138, plain, (p67|~p68|~p57), inference(split_conjunct,[status(thm)],[c_0_128])).
% 154.55/154.71 thf(c_0_139, plain, p57, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130]), c_0_131])).
% 154.55/154.71 thf(c_0_140, plain, (p68|~p69|~p55), inference(split_conjunct,[status(thm)],[c_0_132])).
% 154.55/154.71 thf(c_0_141, plain, p55, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_133]), c_0_131])).
% 154.55/154.71 thf(c_0_142, plain, p69, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134, c_0_135])])).
% 154.55/154.71 thf(c_0_143, plain, (p56|~p58), inference(split_conjunct,[status(thm)],[c_0_136])).
% 154.55/154.71 thf(c_0_144, plain, (p58|~p59), inference(split_conjunct,[status(thm)],[c_0_137])).
% 154.55/154.71 thf(c_0_145, plain, ![X60:term, X61:subst]:((fvar @ (esk16_2 @ X60 @ X61)|f__0 @ (fsub @ X60 @ X61)|~p67)&(~f__0 @ (fsub @ (esk16_2 @ X60 @ X61) @ X61)|f__0 @ (fsub @ X60 @ X61)|~p67)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax67])])])])])).
% 154.55/154.71 thf(c_0_146, plain, (p67|~p68), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138, c_0_139])])).
% 154.55/154.71 thf(c_0_147, plain, p68, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140, c_0_141]), c_0_142])])).
% 154.55/154.71 thf(c_0_148, plain, ![X154:term]:(~p6|(fsub @ X154 @ fid)=(X154)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])])).
% 154.55/154.71 thf(c_0_149, plain, (p5|p6), inference(split_conjunct,[status(thm)],[ax68])).
% 154.55/154.71 thf(c_0_150, plain, ![X82:term]:(~p53|(~fvar @ X82|f__0 @ X82)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax53])])])).
% 154.55/154.71 thf(c_0_151, plain, (p52|p53), inference(split_conjunct,[status(thm)],[ax21])).
% 154.55/154.71 thf(c_0_152, plain, (p56|~p59), inference(spm,[status(thm)],[c_0_143, c_0_144])).
% 154.55/154.71 thf(c_0_153, plain, ![X1:term, X3:subst]:(f__0 @ (fsub @ X1 @ X3)|~f__0 @ (fsub @ (esk16_2 @ X1 @ X3) @ X3)|~p67), inference(split_conjunct,[status(thm)],[c_0_145])).
% 154.55/154.71 thf(c_0_154, plain, p67, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146, c_0_147])])).
% 154.55/154.71 thf(c_0_155, plain, ![X1:term]:((fsub @ X1 @ fid)=(X1)|~p6), inference(split_conjunct,[status(thm)],[c_0_148])).
% 154.55/154.71 thf(c_0_156, plain, p6, inference(sr,[status(thm)],[c_0_149, c_0_53])).
% 154.55/154.71 thf(c_0_157, plain, ![X1:term]:(f__0 @ X1|~p53|~fvar @ X1), inference(split_conjunct,[status(thm)],[c_0_150])).
% 154.55/154.71 thf(c_0_158, plain, p53, inference(sr,[status(thm)],[c_0_151, c_0_131])).
% 154.55/154.71 thf(c_0_159, plain, ![X1:term, X3:subst]:(fvar @ (esk16_2 @ X1 @ X3)|f__0 @ (fsub @ X1 @ X3)|~p67), inference(split_conjunct,[status(thm)],[c_0_145])).
% 154.55/154.71 thf(c_0_160, plain, (~f__0 @ f__1|p59), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax59])])).
% 154.55/154.71 thf(c_0_161, plain, (p54|~p59), inference(spm,[status(thm)],[c_0_122, c_0_152])).
% 154.55/154.71 thf(c_0_162, plain, ![X1:term, X3:subst]:(f__0 @ (fsub @ X1 @ X3)|~f__0 @ (fsub @ (esk16_2 @ X1 @ X3) @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153, c_0_154])])).
% 154.55/154.71 thf(c_0_163, plain, ![X1:term]:(fsub @ X1 @ fid)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155, c_0_156])])).
% 154.55/154.71 thf(c_0_164, plain, ![X1:term]:(f__0 @ X1|~fvar @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157, c_0_158])])).
% 154.55/154.71 thf(c_0_165, plain, ![X1:term, X3:subst]:(fvar @ (esk16_2 @ X1 @ X3)|f__0 @ (fsub @ X1 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159, c_0_154])])).
% 154.55/154.71 thf(c_0_166, plain, (p59|~f__0 @ f__1), inference(split_conjunct,[status(thm)],[c_0_160])).
% 154.55/154.71 thf(c_0_167, plain, ~p59, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_161]), c_0_131])).
% 154.55/154.71 thf(c_0_168, plain, ![X1:term]:(f__0 @ X1|~f__0 @ (esk16_2 @ X1 @ fid)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_163]), c_0_163])).
% 154.55/154.71 thf(c_0_169, plain, ![X1:term, X3:subst]:(f__0 @ (fsub @ X1 @ X3)|f__0 @ (esk16_2 @ X1 @ X3)), inference(spm,[status(thm)],[c_0_164, c_0_165])).
% 154.55/154.71 thf(c_0_170, plain, ~f__0 @ f__1, inference(sr,[status(thm)],[c_0_166, c_0_167])).
% 154.55/154.71 thf(c_0_171, plain, ![X1:term]:f__0 @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_169]), c_0_163])])).
% 154.55/154.71 thf(c_0_172, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170, c_0_171])]), ['proof']).
% 154.55/154.71 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 154.55/154.71 thf(0,theorem,((![X1:term]:(![X2:term]:(![X3:subst]:(((sub @ ((ap @ X1) @ X2)) @ X3) = ((ap @ ((sub @ X1) @ X3)) @ ((sub @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(![X2:subst]:(((sub @ (lam @ X1)) @ X2) = (lam @ ((sub @ X1) @ ((push @ one) @ ((comp @ X2) @ sh))))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ id) @ X1) = X1)) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => ((![X1:subst]:(![X2:subst]:(![X3:subst]:(((comp @ ((comp @ X1) @ X2)) @ X3) = ((comp @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(![X3:subst]:(((comp @ ((push @ X1) @ X2)) @ X3) = ((push @ ((sub @ X1) @ X3)) @ ((comp @ X2) @ X3)))))) => ((![X1:subst]:(((comp @ X1) @ id) = X1)) => ((((push @ one) @ sh) = id) => ((![X1:subst]:(((push @ ((sub @ one) @ X1)) @ ((comp @ sh) @ X1)) = X1)) => ((var @ one) => ((![X1:term]:((var @ X1) => (var @ ((sub @ X1) @ sh)))) => ((![X1:term>$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)))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 154.55/154.71 % SZS output end Proof
%------------------------------------------------------------------------------