%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:12:48 AM UTC 2026
% Result : Unsatisfiable 95.96s 66.94s
% Output : CNFRefutation 95.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 44 ( 43 usr; 1 prp; 0-4 aty)
% Number of functors : 74 ( 74 usr; 16 con; 0-6 aty)
% Number of variables : 4 ( 4 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_lessequals > c_fequal > c_Type_Otypings > c_Type_Otyping > c_OrderedGroup_Omonoid__add > c_List_Olistsp > c_HOL_Oord__class_Oless > c_OrderedGroup_Osemigroup__add > hBOOL > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Osemigroup__add > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > c_COMBB > c_List_Osko__List__Xmap__ext__1__1 > c_List_Osko__List__Xmap__eq__conv__1__1 > c_List_Osko__List__Xmap__cong__1__1 > c_List_Ofoldl > c_Lambda_OdB_OdB__rec > c_Lambda_OdB_OdB__case > c_Fun_Ocomp > c_COMBC > c_Type_Osko__Type__Xvar__app__types__1__1 > c_Type_Osko__Type__Xvar__app__typesE__1__1 > c_Type_Osko__Type__Xlist__app__typeE__1__1 > c_Type_Osko__Type__Xlist__app__typeD__1__1 > c_Type_Oshift > c_Nat_Osemiring__1__class_Oof__nat__aux > c_List_Omap > c_List_Olist__update > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_Power_Opower__class_Opower > c_List_Otake > c_List_Olist_OCons > c_List_Oappend > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lambda_Osubstn > c_Lambda_Oliftn > c_HOL_Ominus__class_Ominus > tc_fun > hAPP > c_Type_Otype_OFun > c_Transitive__Closure_Ortranclp > c_Nat_Osize__class_Osize > c_Nat_Osemiring__1__class_Oof__nat > c_List_Orev > c_Int_Onumber__class_Onumber__of > #nlpp > v_sko__InductTermi__XIT__Xcases__6 > v_sko__InductTermi__XIT__Xcases__5 > v_sko__InductTermi__XIT__Xcases__4 > v_sko__InductTermi__XIT__Xcases__3 > v_sko__InductTermi__XIT__Xcases__2 > v_sko__InductTermi__XIT__Xcases__1 > c_Suc > c_List_Olist_ONil > c_ListApplication_Osko__ListApplication__Xlem__1__4 > c_ListApplication_Osko__ListApplication__Xlem__1__3 > c_ListApplication_Osko__ListApplication__Xlem__1__2 > c_ListApplication_Osko__ListApplication__Xlem__1__1 > c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 > c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 > c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 > c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 > c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 > c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 > c_Lambda_OdB_OdB__size > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oplus__class_Oplus > c_HOL_Oone__class_Oone > v_ua______ > v_u____ > v_n____ > v_i____ > v_as____ > tc_nat > tc_bool > tc_Type_Otype > tc_Lambda_OdB > tc_Int_Oint > t_a > c_Lambda_Osubst > c_Lambda_Olift > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Oappend,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(tc_Type_Otype,type,
tc_Type_Otype: $i ).
tff(c_Lambda_Oliftn,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(c_Lambda_OdB_OdB__case,type,
c_Lambda_OdB_OdB__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(c_Fun_Ocomp,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Nat_Osemiring__1__class_Oof__nat__aux,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(c_List_Osko__List__Xmap__cong__1__1,type,
c_List_Osko__List__Xmap__cong__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Orev,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2: $i > $i ).
tff(v_sko__InductTermi__XIT__Xcases__4,type,
v_sko__InductTermi__XIT__Xcases__4: $i > $i ).
tff(c_Type_Otype_OFun,type,
c_Type_Otype_OFun: ( $i * $i ) > $i ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
tff(t_a,type,
t_a: $i ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(c_List_Ofoldl,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(v_sko__InductTermi__XIT__Xcases__1,type,
v_sko__InductTermi__XIT__Xcases__1: $i > $i ).
tff(c_List_Olistsp,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
tff(v_sko__InductTermi__XIT__Xcases__2,type,
v_sko__InductTermi__XIT__Xcases__2: $i > $i ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__Xlem__1__2,type,
c_ListApplication_Osko__ListApplication__Xlem__1__2: $i > $i ).
tff(c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4: $i > $i ).
tff(c_ListApplication_Osko__ListApplication__Xlem__1__4,type,
c_ListApplication_Osko__ListApplication__Xlem__1__4: $i > $i ).
tff(c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).
tff(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).
tff(c_ListApplication_Osko__ListApplication__Xlem__1__3,type,
c_ListApplication_Osko__ListApplication__Xlem__1__3: $i > $i ).
tff(v_sko__InductTermi__XIT__Xcases__5,type,
v_sko__InductTermi__XIT__Xcases__5: $i > $i ).
tff(v_ua______,type,
v_ua______: $i ).
tff(c_Lambda_Osubst,type,
c_Lambda_Osubst: $i ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_Type_Oshift,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(v_n____,type,
v_n____: $i ).
tff(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Olist__update,type,
c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_List_Osko__List__Xmap__eq__conv__1__1,type,
c_List_Osko__List__Xmap__eq__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__Xlem__1__1,type,
c_ListApplication_Osko__ListApplication__Xlem__1__1: $i > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
tff(c_OrderedGroup_Omonoid__add,type,
c_OrderedGroup_Omonoid__add: ( $i * $i * $i ) > $o ).
tff(tc_bool,type,
tc_bool: $i ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2: $i > $i ).
tff(c_Type_Otypings,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(c_Lambda_Osubstn,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(c_Lambda_OdB_OdB__rec,type,
c_Lambda_OdB_OdB__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_COMBB,type,
c_COMBB: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $o ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1: $i > $i ).
tff(v_sko__InductTermi__XIT__Xcases__3,type,
v_sko__InductTermi__XIT__Xcases__3: $i > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(c_List_Olist_OCons,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_List_Osko__List__Xmap__ext__1__1,type,
c_List_Osko__List__Xmap__ext__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__InductTermi__XIT__Xcases__6,type,
v_sko__InductTermi__XIT__Xcases__6: $i > $i ).
tff(v_i____,type,
v_i____: $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(v_as____,type,
v_as____: $i ).
tff(c_List_Otake,type,
c_List_Otake: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1: $i > $i ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(v_u____,type,
v_u____: $i ).
tff(c_Lambda_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $i > $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
tff(c_Lambda_Olift,type,
c_Lambda_Olift: $i ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(c_OrderedGroup_Osemigroup__add,type,
c_OrderedGroup_Osemigroup__add: ( $i * $i ) > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(c_List_Omap,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(f_3303,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file(unknown,unknown) ).
tff(f_3216,axiom,
! [V_n,V_rs] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ),
file(unknown,unknown) ).
tff(f_3305,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file(unknown,unknown) ).
tff(c_1174,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(cnfTransformation,[status(thm)],[f_3303]) ).
tff(c_1126,plain,
! [V_rs_1677,V_n_1676] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs_1677,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n_1676),V_rs_1677,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnfTransformation,[status(thm)],[f_3216]) ).
tff(c_1176,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnfTransformation,[status(thm)],[f_3305]) ).
tff(c_139584,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(resolution,[status(thm)],[c_1126,c_1176]) ).
tff(c_139588,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1174,c_139584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 23:24:12 UTC 2026
% 0.09/0.35 % CPUTime :
% 95.96/66.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 95.96/66.95
% 95.96/66.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------