%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL784-1 : 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 : n018.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 11:12:43 AM UTC 2026
% Result : Unsatisfiable 9.15s 3.52s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 30 ( 28 usr; 1 prp; 0-4 aty)
% Number of functors : 63 ( 63 usr; 22 con; 0-5 aty)
% Number of variables : 7 ( 7 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > 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_Oordered__semidom > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > 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_Omonoid__add > class_OrderedGroup_Olordered__ab__group__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_Int_Onumber__ring > c_List_Ofoldr > c_List_Ofoldl > c_Lambda_OdB_OdB__rec > c_Lambda_OdB_OdB__case > 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_List_Omap > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_List_Olist_OCons > c_List_Oappend > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lambda_Osubstn > c_Lambda_Oliftn > tc_fun > hAPP > c_Transitive__Closure_Ortranclp > #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_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_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oplus__class_Oplus > v_ua______ > v_u____ > v_rs____ > v_n____ > v_ia______ > v_i____ > v_ea______ > v_e____ > v_T____ > v_T_Ha______ > v_T_H____ > tc_nat > tc_bool > tc_Type_Otype > tc_Lambda_OdB > t_a > c_Type_Otype_OFun > c_Lambda_Osubst > c_Lambda_Olift > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT
%Foreground sorts:
%Background operators:
%Foreground operators:
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_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(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(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_T_Ha______,type,
v_T_Ha______: $i ).
tff(v_sko__InductTermi__XIT__Xcases__4,type,
v_sko__InductTermi__XIT__Xcases__4: $i > $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
tff(t_a,type,
t_a: $i ).
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(v_rs____,type,
v_rs____: $i ).
tff(v_ia______,type,
v_ia______: $i ).
tff(v_sko__InductTermi__XIT__Xcases__2,type,
v_sko__InductTermi__XIT__Xcases__2: $i > $i ).
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(v_ea______,type,
v_ea______: $i ).
tff(c_ListApplication_Osko__ListApplication__Xlem__1__3,type,
c_ListApplication_Osko__ListApplication__Xlem__1__3: $i > $i ).
tff(c_List_Ofoldr,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $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(v_e____,type,
v_e____: $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_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $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(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(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_fequal,type,
c_fequal: ( $i * $i * $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_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
tff(c_List_Olist_OCons,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(v_sko__InductTermi__XIT__Xcases__6,type,
v_sko__InductTermi__XIT__Xcases__6: $i > $i ).
tff(v_T____,type,
v_T____: $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_T_H____,type,
v_T_H____: $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(v_u____,type,
v_u____: $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
tff(c_Lambda_Olift,type,
c_Lambda_Olift: $i ).
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_1532,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file(unknown,unknown) ).
tff(f_1231,axiom,
! [V_k,V_u] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
file(unknown,unknown) ).
tff(f_1530,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file(unknown,unknown) ).
tff(f_1432,axiom,
! [V_m] : ( c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
file(unknown,unknown) ).
tff(f_1531,axiom,
v_n____ = v_i____,
file(unknown,unknown) ).
tff(f_1534,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file(unknown,unknown) ).
tff(c_592,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(cnfTransformation,[status(thm)],[f_1532]) ).
tff(c_442,plain,
! [V_k_744,V_u_745] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k_744)),V_u_745),V_k_744) = V_u_745 ),
inference(cnfTransformation,[status(thm)],[f_1231]) ).
tff(c_588,plain,
c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____,
inference(cnfTransformation,[status(thm)],[f_1530]) ).
tff(c_532,plain,
! [V_m_878] : ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m_878),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(V_m_878) ),
inference(cnfTransformation,[status(thm)],[f_1432]) ).
tff(c_644,plain,
! [V_m_878] : ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m_878),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(V_m_878) ),
inference(demodulation,[status(thm),theory(equality)],[c_588,c_532]) ).
tff(c_590,plain,
v_n____ = v_i____,
inference(cnfTransformation,[status(thm)],[f_1531]) ).
tff(c_594,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(cnfTransformation,[status(thm)],[f_1534]) ).
tff(c_635,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(demodulation,[status(thm),theory(equality)],[c_590,c_594]) ).
tff(c_645,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____))),
inference(demodulation,[status(thm),theory(equality)],[c_644,c_635]) ).
tff(c_656,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(demodulation,[status(thm),theory(equality)],[c_442,c_645]) ).
tff(c_658,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_592,c_656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % 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
% 0.12/0.36 % Computer : n018.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 4 23:15:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 9.15/3.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.15/3.53
% 9.15/3.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------