%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL856-1 : 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 : n026.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 11:12:54 AM UTC 2026
% Result : Unsatisfiable 9.72s 3.82s
% Output : CNFRefutation 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 11 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 38 ( 38 usr; 11 con; 0-5 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_Wellfounded_Oaccp > c_Type_Otyping > c_List_Olistsp > c_Wellfounded_OwfP > hBOOL > class_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > c_Predicate_Opred__comp > c_List_Ofoldl > c_Type_Oshift > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_Predicate_Oconversep > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_Lambda_Osubst > c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 > c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 > v_sko__Wellfounded__Xaccp__Xinducts__1 > v_sko__Wellfounded__Xaccp__Xinduct__1 > tc_fun > hAPP > c_Type_Otype_OFun > c_Transitive__Closure_Otranclp > c_Transitive__Closure_Ortranclp > c_Lambda_Olift > #nlpp > c_fequal > c_List_Olist_ONil > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > v_t > v_e > v_T > tc_nat > tc_bool > tc_Type_Otype > tc_Lambda_OdB > t_a > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(v_sko__Wellfounded__Xaccp__Xinducts__1,type,
v_sko__Wellfounded__Xaccp__Xinducts__1: ( $i * $i ) > $i ).
tff(c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
tff(c_Predicate_Opred__comp,type,
c_Predicate_Opred__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: $i > $i ).
tff(tc_Type_Otype,type,
tc_Type_Otype: $i ).
tff(c_Transitive__Closure_Otranclp,type,
c_Transitive__Closure_Otranclp: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1: ( $i * $i * $i ) > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(v_e,type,
v_e: $i ).
tff(c_Type_Otype_OFun,type,
c_Type_Otype_OFun: ( $i * $i ) > $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
tff(t_a,type,
t_a: $i ).
tff(c_List_Ofoldl,type,
c_List_Ofoldl: ( $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(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(v_sko__Wellfounded__Xaccp__Xinduct__1,type,
v_sko__Wellfounded__Xaccp__Xinduct__1: ( $i * $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_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_Type_Oshift,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(tc_nat,type,
tc_nat: $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(tc_bool,type,
tc_bool: $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1: ( $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $o ).
tff(class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: ( $i * $i ) > $o ).
tff(c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(v_T,type,
v_T: $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1: ( $i * $i * $i ) > $i ).
tff(c_Predicate_Oconversep,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(v_t,type,
v_t: $i ).
tff(f_911,axiom,
c_Type_Otyping(v_e,v_t,v_T),
file(unknown,unknown) ).
tff(f_905,axiom,
! [V_t,V_e,V_T] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
file(unknown,unknown) ).
tff(f_708,axiom,
! [V_t] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ),
file(unknown,unknown) ).
tff(f_913,axiom,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
file(unknown,unknown) ).
tff(c_344,plain,
c_Type_Otyping(v_e,v_t,v_T),
inference(cnfTransformation,[status(thm)],[f_911]) ).
tff(c_516,plain,
! [V_e_670,V_t_671,V_T_672] :
( ~ c_Type_Otyping(V_e_670,V_t_671,V_T_672)
| hBOOL(hAPP(c_InductTermi_OIT,V_t_671)) ),
inference(cnfTransformation,[status(thm)],[f_905]) ).
tff(c_523,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(resolution,[status(thm)],[c_344,c_516]) ).
tff(c_1198,plain,
! [V_t_753] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t_753))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t_753,tc_Lambda_OdB) ),
inference(cnfTransformation,[status(thm)],[f_708]) ).
tff(c_346,plain,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
inference(cnfTransformation,[status(thm)],[f_913]) ).
tff(c_1201,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(resolution,[status(thm)],[c_1198,c_346]) ).
tff(c_1205,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_523,c_1201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL856-1 : 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
% 0.10/0.36 % Computer : n026.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 : Sat Sep 5 03:21:25 UTC 2026
% 0.15/0.36 % CPUTime :
% 9.72/3.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.72/3.83
% 9.72/3.83 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------