%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SCT042-1 : TPTP v9.0.0. 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 08:34:18 PM UTC 2025
% Result : Unsatisfiable 41.38s 25.79s
% Output : CNFRefutation 41.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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; 2 prp; 0-3 aty)
% Number of functors : 48 ( 48 usr; 8 con; 0-5 aty)
% Number of variables : 7 ( 7 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_List_Omember > c_HOL_Oord__class_Oless > c_List_Onull > c_List_Olinorder__class_Osorted > c_List_Odistinct > class_Ring__and__Field_Ozero__neq__one > 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_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_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > class_HOL_Oord > class_Divides_Osemiring__div > class_Divides_Oring__div > c_List_Osko__List__Xappend__eq__Cons__conv__1__1 > c_List_Osko__List__XCons__eq__append__conv__1__1 > c_List_Olist__update > c_Power_Opower__class_Opower > c_Orderings_Oord__class_Omin > c_List_Otake > c_List_Osplice > c_List_Orotate > c_List_Oreplicate > c_List_OremoveAll > c_List_Oremove1 > c_List_Olist__inter > c_List_Olist_OCons > c_List_Odrop > c_List_Oappend > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Divides_Odiv__class_Omod > v_sko__CHAINED__1 > v_sko__Arrow__Order__Mirabelle__Xthird__alt__1 > c_Nat_Osize__class_Osize > c_List_Otl > c_List_Osko__List__Xneq__Nil__conv__1__2 > c_List_Osko__List__Xneq__Nil__conv__1__1 > c_List_Osko__List__Xlist__Xnchotomy__1__2 > c_List_Osko__List__Xlist__Xnchotomy__1__1 > c_List_Osko__List__Xlist__Xexhaust__1__2 > c_List_Osko__List__Xlist__Xexhaust__1__1 > c_List_Orotate1 > c_List_Orev > c_List_Oremdups > c_List_Olast > c_List_Ohd > c_List_Obutlast > c_Int_Onumber__class_Onumber__of > #nlpp > tc_List_Olist > c_Suc > c_List_Olist_ONil > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_thesis____ > v_sko__Arrow__Order__Mirabelle__Xalt3__3 > v_sko__Arrow__Order__Mirabelle__Xalt3__2 > v_sko__Arrow__Order__Mirabelle__Xalt3__1 > v_b____ > v_a____ > tc_nat > tc_Int_Oint > tc_Arrow__Order__Mirabelle_Oalt
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_List_Olist__inter,type,
c_List_Olist__inter: ( $i * $i * $i ) > $i ).
tff(c_List_Osko__List__Xlist__Xnchotomy__1__1,type,
c_List_Osko__List__Xlist__Xnchotomy__1__1: ( $i * $i ) > $i ).
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_List_Omember,type,
c_List_Omember: ( $i * $i * $i ) > $o ).
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_List_Odistinct,type,
c_List_Odistinct: ( $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_List_Osko__List__Xlist__Xexhaust__1__2,type,
c_List_Osko__List__Xlist__Xexhaust__1__2: ( $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_List_Onull,type,
c_List_Onull: ( $i * $i ) > $o ).
tff(v_sko__Arrow__Order__Mirabelle__Xalt3__3,type,
v_sko__Arrow__Order__Mirabelle__Xalt3__3: $i ).
tff(class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(c_List_Orev,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1,type,
v_sko__Arrow__Order__Mirabelle__Xthird__alt__1: ( $i * $i ) > $i ).
tff(v_thesis____,type,
v_thesis____: $o ).
tff(c_List_Obutlast,type,
c_List_Obutlast: ( $i * $i ) > $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(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
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__Arrow__Order__Mirabelle__Xalt3__1,type,
v_sko__Arrow__Order__Mirabelle__Xalt3__1: $i ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_List_Otl,type,
c_List_Otl: ( $i * $i ) > $i ).
tff(c_List_Oreplicate,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(v_sko__CHAINED__1,type,
v_sko__CHAINED__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_List_Oremdups,type,
c_List_Oremdups: ( $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).
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(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
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_List_Olist__update,type,
c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(c_List_Oremove1,type,
c_List_Oremove1: ( $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(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
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(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_List_Osplice,type,
c_List_Osplice: ( $i * $i * $i ) > $i ).
tff(c_List_Orotate,type,
c_List_Orotate: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $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(v_sko__Arrow__Order__Mirabelle__Xalt3__2,type,
v_sko__Arrow__Order__Mirabelle__Xalt3__2: $i ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_List_Osko__List__Xneq__Nil__conv__1__1,type,
c_List_Osko__List__Xneq__Nil__conv__1__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_List_OremoveAll,type,
c_List_OremoveAll: ( $i * $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(c_List_Odrop,type,
c_List_Odrop: ( $i * $i * $i ) > $i ).
tff(v_b____,type,
v_b____: $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(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff(c_List_Ohd,type,
c_List_Ohd: ( $i * $i ) > $i ).
tff(c_List_Orotate1,type,
c_List_Orotate1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(v_a____,type,
v_a____: $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(tc_Arrow__Order__Mirabelle_Oalt,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_List_Osko__List__Xlist__Xnchotomy__1__2,type,
c_List_Osko__List__Xlist__Xnchotomy__1__2: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_List_Osko__List__Xneq__Nil__conv__1__2,type,
c_List_Osko__List__Xneq__Nil__conv__1__2: ( $i * $i ) > $i ).
tff(c_List_Olast,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(c_List_Osko__List__Xlist__Xexhaust__1__1,type,
c_List_Osko__List__Xlist__Xexhaust__1__1: ( $i * $i ) > $i ).
tff(f_3329,axiom,
v_a____ != v_b____,
file(unknown,unknown) ).
tff(f_3327,axiom,
! [V_a,V_b] :
( c_List_Odistinct(c_List_Olist_OCons(V_a,c_List_Olist_OCons(V_b,c_List_Olist_OCons(v_sko__CHAINED__1(V_a,V_b),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_3331,axiom,
~ v_thesis____,
file(unknown,unknown) ).
tff(f_3336,axiom,
! [V_x] :
( v_thesis____
| ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Olist_OCons(V_x,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file(unknown,unknown) ).
tff(c_1216,plain,
v_b____ != v_a____,
inference(cnfTransformation,[status(thm)],[f_3329]) ).
tff(c_104896,plain,
! [V_b_3657,V_a_3658] :
( ( V_b_3657 = V_a_3658 )
| c_List_Odistinct(c_List_Olist_OCons(V_a_3658,c_List_Olist_OCons(V_b_3657,c_List_Olist_OCons(v_sko__CHAINED__1(V_a_3658,V_b_3657),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(cnfTransformation,[status(thm)],[f_3327]) ).
tff(c_1218,plain,
~ v_thesis____,
inference(cnfTransformation,[status(thm)],[f_3331]) ).
tff(c_1220,plain,
! [V_x_1719] :
( ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Olist_OCons(V_x_1719,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_thesis____ ),
inference(cnfTransformation,[status(thm)],[f_3336]) ).
tff(c_1333,plain,
! [V_x_1719] : ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Olist_OCons(V_x_1719,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
inference(negUnitSimplification,[status(thm)],[c_1218,c_1220]) ).
tff(c_104900,plain,
v_b____ = v_a____,
inference(resolution,[status(thm)],[c_104896,c_1333]) ).
tff(c_104912,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1216,c_104900]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT042-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.13 % 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
% 0.13/0.32 % Computer : n016.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Apr 8 19:07:38 EDT 2025
% 0.13/0.33 % CPUTime :
% 41.38/25.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.38/25.80
% 41.38/25.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------