%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL771-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n019.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 11:12:41 AM UTC 2026
% Result : Unsatisfiable 8.96s 3.01s
% Output : CNFRefutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 80 ( 80 usr; 10 con; 0-5 aty)
% Number of variables : 4 ( 4 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_List_Olistrelp > c_ListOrder_Ostep1 > c_fequal > c_Type_Otyping > c_List_Olistsp > c_List_Olist__ex > c_HOL_Oord__class_Oless > c_List_Onull > c_List_Olinorder__class_Osorted > hBOOL > class_Ring__and__Field_Oordered__idom > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Lattices_Olower__semilattice > class_Lattices_Olattice > c_Map_Omap__upds > c_List_Osko__List__Xappend__eq__Cons__conv__1__1 > c_List_Osko__List__XCons__eq__append__conv__1__1 > c_List_Olist_Olist__rec > c_List_Olist_Olist__case > c_List_Ofoldr > c_List_Ofoldl > c_Lambda_OdB_OdB__rec > c_Lambda_OdB_OdB__case > c_COMBB > c_List_Omap > c_List_Olist__update > c_List_Ofiltermap > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_COMBC > c_List_Osublist > c_List_Osko__List__Xin__listsp__conv__set__1__1 > c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 > c_List_Osko__List__XCons__eq__filter__iff__1__3 > c_List_Orotate > c_List_Oreplicate > c_List_Oremove1 > c_List_Olist_OCons > c_List_Ofilter > c_List_Oappend > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lattices_Olower__semilattice__class_Oinf > c_Lambda_Osubstn > c_Lambda_Osubst > c_Lambda_Oliftn > v_sko__List__Xlistsp__Xinducts__2 > v_sko__List__Xlistsp__Xinducts__1 > v_sko__List__Xlistsp__Xinduct__2 > v_sko__List__Xlistsp__Xinduct__1 > v_sko__List__Xlistsp__Xcases__2 > v_sko__List__Xlistsp__Xcases__1 > tc_fun > hAPP > c_Transitive__Closure_Ortranclp > c_Nat_Osize__class_Osize > c_List_Orotate1 > c_List_Orev > c_List_Oremdups > c_List_Olast > c_List_Obutlast > c_Lambda_Olift > #nlpp > v_sko__List__Xzip__Xinduct__2 > v_sko__List__Xzip__Xinduct__1 > v_sko__List__Xtake__Xinduct__2 > v_sko__List__Xtake__Xinduct__1 > v_sko__List__Xremove1__Xinduct__2 > v_sko__List__Xremove1__Xinduct__1 > v_sko__List__Xmap__Xinduct__2 > v_sko__List__Xmap__Xinduct__1 > v_sko__List__Xlistset__Xinduct__2 > v_sko__List__Xlistset__Xinduct__1 > v_sko__List__Xlist__Xinduct__2 > v_sko__List__Xlist__Xinduct__1 > v_sko__List__XdropWhile__Xinduct__2 > v_sko__List__XdropWhile__Xinduct__1 > v_sko__List__Xdistinct__Xinduct__2 > v_sko__List__Xdistinct__Xinduct__1 > v_sko__List__Xconcat__Xinduct__2 > v_sko__List__Xconcat__Xinduct__1 > tc_List_Olist > c_Suc > c_List_Olist_ONil > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > v_rs > v_i > tc_nat > tc_bool > tc_Lambda_OdB > t_b > t_a > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(c_List_Ofiltermap,type,
c_List_Ofiltermap: ( $i * $i * $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
tff(v_sko__List__Xlistsp__Xcases__1,type,
v_sko__List__Xlistsp__Xcases__1: ( $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
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(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(v_sko__List__Xlistsp__Xinducts__1,type,
v_sko__List__Xlistsp__Xinducts__1: ( $i * $i ) > $i ).
tff(c_List_Onull,type,
c_List_Onull: ( $i * $i ) > $o ).
tff(c_List_Ofilter,type,
c_List_Ofilter: ( $i * $i * $i ) > $i ).
tff(v_sko__List__Xremove1__Xinduct__1,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(c_List_Orev,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(v_i,type,
v_i: $i ).
tff(v_sko__List__Xconcat__Xinduct__1,type,
v_sko__List__Xconcat__Xinduct__1: $i > $i ).
tff(c_Map_Omap__upds,type,
c_Map_Omap__upds: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__List__Xmap__Xinduct__1,type,
v_sko__List__Xmap__Xinduct__1: $i > $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
tff(c_List_Obutlast,type,
c_List_Obutlast: ( $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(v_sko__List__Xdistinct__Xinduct__2,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
tff(v_sko__List__Xlistset__Xinduct__2,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
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(c_COMBB,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Olistsp,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(c_Lambda_Osubst,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(v_sko__List__Xtake__Xinduct__1,type,
v_sko__List__Xtake__Xinduct__1: $i > $i ).
tff(c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).
tff(c_List_Oreplicate,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
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_sko__List__XdropWhile__Xinduct__2,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
tff(c_List_Ofoldr,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Osko__List__XCons__eq__filter__iff__1__3,type,
c_List_Osko__List__XCons__eq__filter__iff__1__3: ( $i * $i * $i ) > $i ).
tff(c_List_Osko__List__Xin__listsp__conv__set__1__1,type,
c_List_Osko__List__Xin__listsp__conv__set__1__1: ( $i * $i * $i ) > $i ).
tff(c_List_Olist__ex,type,
c_List_Olist__ex: ( $i * $i * $i ) > $o ).
tff(c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_List_Oremdups,type,
c_List_Oremdups: ( $i * $i ) > $i ).
tff(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: ( $i * $i ) > $o ).
tff(tc_List_Olist,type,
tc_List_Olist: $i > $i ).
tff(v_sko__List__Xlistsp__Xinducts__2,type,
v_sko__List__Xlistsp__Xinducts__2: ( $i * $i ) > $i ).
tff(v_sko__List__Xlistset__Xinduct__1,type,
v_sko__List__Xlistset__Xinduct__1: $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(c_List_Olist__update,type,
c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(v_rs,type,
v_rs: $i ).
tff(c_List_Oremove1,type,
c_List_Oremove1: ( $i * $i * $i ) > $i ).
tff(v_sko__List__XdropWhile__Xinduct__1,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
tff(v_sko__List__Xlistsp__Xinduct__2,type,
v_sko__List__Xlistsp__Xinduct__2: ( $i * $i ) > $i ).
tff(v_sko__List__Xtake__Xinduct__2,type,
v_sko__List__Xtake__Xinduct__2: $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(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
tff(c_List_Osko__List__Xfilter__eq__Cons__iff__1__3,type,
c_List_Osko__List__Xfilter__eq__Cons__iff__1__3: ( $i * $i * $i ) > $i ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_List_Olist_Olist__case,type,
c_List_Olist_Olist__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Osko__List__XCons__eq__append__conv__1__1,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
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_List_Orotate,type,
c_List_Orotate: ( $i * $i * $i ) > $i ).
tff(c_List_Osublist,type,
c_List_Osublist: ( $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(v_sko__List__Xconcat__Xinduct__2,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $o ).
tff(v_sko__List__Xremove1__Xinduct__2,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
tff(v_sko__List__Xzip__Xinduct__1,type,
v_sko__List__Xzip__Xinduct__1: $i > $i ).
tff(v_sko__List__Xlistsp__Xcases__2,type,
v_sko__List__Xlistsp__Xcases__2: ( $i * $i ) > $i ).
tff(c_List_Osko__List__Xappend__eq__Cons__conv__1__1,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__List__Xlistsp__Xinduct__1,type,
v_sko__List__Xlistsp__Xinduct__1: ( $i * $i ) > $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(v_sko__List__Xlist__Xinduct__2,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
tff(v_sko__List__Xzip__Xinduct__2,type,
v_sko__List__Xzip__Xinduct__2: $i > $i ).
tff(c_List_Olist_OCons,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_List_Orotate1,type,
c_List_Orotate1: ( $i * $i ) > $i ).
tff(v_sko__List__Xdistinct__Xinduct__1,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
tff(c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(c_List_Olist_Olist__rec,type,
c_List_Olist_Olist__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__List__Xlist__Xinduct__1,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(v_sko__List__Xmap__Xinduct__2,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
tff(c_List_Olast,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Olistrelp,type,
c_List_Olistrelp: ( $i * $i * $i * $i ) > $o ).
tff(c_List_Omap,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(f_1826,axiom,
! [V_A,T_a] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file(unknown,unknown) ).
tff(f_1837,axiom,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
file(unknown,unknown) ).
tff(c_810,plain,
! [V_A_1286,T_a_1287] : c_List_Olistsp(V_A_1286,c_List_Olist_ONil(T_a_1287),T_a_1287),
inference(cnfTransformation,[status(thm)],[f_1826]) ).
tff(c_822,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(cnfTransformation,[status(thm)],[f_1837]) ).
tff(c_860,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL771-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 20:15:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 8.96/3.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.96/3.02
% 8.96/3.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------