%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL748-1 : 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 : 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 11:12:38 AM UTC 2026
% Result : Unsatisfiable 40.80s 21.87s
% Output : CNFRefutation 40.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_HOL_Oord__class_Oless > c_Lambda_Obeta > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__comm__semiring__strict > 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_Ring__and__Field_Ocomm__semiring > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > 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__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Int_Onumber__ring > c_InductTermi_OIT > c_Lambda_Osubstn > c_Lambda_Osubst > c_Lambda_Oliftn > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Osko__Lambda__Xbeta__cases__2__1 > c_Lambda_Olift > c_Lambda_OdB_OApp > #nlpp > c_Suc > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_r > v_ia > tc_nat
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Lambda_Oliftn,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i > $o ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
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(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_Lambda_Obeta,type,
c_Lambda_Obeta: ( $i * $i ) > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_Lambda_Osubst,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
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_Suc,type,
c_Suc: $i > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
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(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__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_Lambda_Osubstn,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(v_r,type,
v_r: $i ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
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(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(v_ia,type,
v_ia: $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
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(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_2004,axiom,
! [V_i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)),
file(unknown,unknown) ).
tff(f_1868,axiom,
! [V_n] : ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file(unknown,unknown) ).
tff(f_1965,axiom,
! [V_s,V_k] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
file(unknown,unknown) ).
tff(f_1989,axiom,
! [V_r] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
file(unknown,unknown) ).
tff(f_2006,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
file(unknown,unknown) ).
tff(c_688,plain,
! [V_i_925] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i_925)),
inference(cnfTransformation,[status(thm)],[f_2004]) ).
tff(c_614,plain,
! [V_n_833] : ( c_HOL_Oplus__class_Oplus(V_n_833,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(V_n_833) ),
inference(cnfTransformation,[status(thm)],[f_1868]) ).
tff(c_664,plain,
! [V_s_899,V_k_900] : ( c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s_899,c_HOL_Oplus__class_Oplus(V_k_900,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s_899),V_k_900) ),
inference(cnfTransformation,[status(thm)],[f_1965]) ).
tff(c_3523,plain,
! [V_s_1088,V_k_1089] : ( c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s_1088,c_Suc(V_k_1089))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s_1088),V_k_1089) ),
inference(demodulation,[status(thm),theory(equality)],[c_614,c_664]) ).
tff(c_678,plain,
! [V_r_916] :
( ~ c_InductTermi_OIT(V_r_916)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r_916)) ),
inference(cnfTransformation,[status(thm)],[f_1989]) ).
tff(c_77433,plain,
! [V_s_2109,V_k_2110] :
( ~ c_InductTermi_OIT(c_Lambda_Olift(V_s_2109,c_Suc(V_k_2110)))
| c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s_2109),V_k_2110)) ),
inference(superposition,[status(thm),theory(equality)],[c_3523,c_678]) ).
tff(c_690,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
inference(cnfTransformation,[status(thm)],[f_2006]) ).
tff(c_77436,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(v_r,c_Suc(v_ia))),
inference(resolution,[status(thm)],[c_77433,c_690]) ).
tff(c_77458,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_688,c_77436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL748-1 : 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
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 09:07:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 40.80/21.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.80/21.88
% 40.80/21.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------