TSTP Solution File: LCL839-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL839-1 : TPTP v8.1.2. 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 : n004.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 : Tue Aug 22 10:49:09 EDT 2023
% Result : Unsatisfiable 16.36s 5.65s
% Output : CNFRefutation 16.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 89
% Syntax : Number of formulae : 96 ( 7 unt; 85 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 : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 63 >; 59 *; 0 +; 0 <<)
% Number of predicates : 33 ( 32 usr; 2 prp; 0-4 aty)
% Number of functors : 53 ( 53 usr; 21 con; 0-5 aty)
% Number of variables : 11 (; 11 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_Wellfounded_Oaccp > c_Type_Otypings > c_Type_Otyping > c_List_Olistsp > c_HOL_Oord__class_Oless > hBOOL > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > 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_Opordered__ab__group__add > 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_Nat_Osemiring__char__0 > class_Int_Onumber__ring > c_List_Ofoldr > c_List_Ofoldl > c_Type_Osko__Type__Xvar__app__types__1__1 > c_Type_Osko__Type__Xvar__app__typesE__1__1 > c_Type_Osko__Type__Xtyping__elims__2__1 > c_Type_Osko__Type__Xlist__app__typeE__1__1 > c_Type_Osko__Type__Xlist__app__typeD__1__1 > c_Type_Oshift > c_Type_Osko__Type__Xtyping__elims__3__2 > c_Type_Osko__Type__Xtyping__elims__3__1 > c_Predicate_Oconversep > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lambda_Osubst > c_HOL_Ominus__class_Ominus > tc_fun > hAPP > c_Type_Osko__Type__Xabs__typeE__1__2 > c_Type_Osko__Type__Xabs__typeE__1__1 > c_Transitive__Closure_Ortranclp > c_Nat_Osize__class_Osize > c_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Olift > #nlpp > c_fequal > c_Type_Otype_Otype__size > c_Suc > c_List_Olist_ONil > c_Lambda_OdB_OdB__size > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oplus__class_Oplus > c_HOL_Oone__class_Oone > v_ua______ > v_u____ > v_thesis____ > v_r____ > v_ia______ > v_i____ > v_ea______ > v_e____ > v_as____ > v_a____ > v_Ua____ > v_T____ > v_T_Ha______ > v_T_H____ > tc_nat > tc_bool > tc_Type_Otype > tc_Lambda_OdB > c_Type_Otype_OFun > 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(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $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_Type_Osko__Type__Xtyping__elims__3__2,type,
c_Type_Osko__Type__Xtyping__elims__3__2: ( $i * $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: $i > $i ).
tff(c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(tc_Type_Otype,type,
tc_Type_Otype: $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(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(v_T_Ha______,type,
v_T_Ha______: $i ).
tff(v_thesis____,type,
v_thesis____: $o ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $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(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(c_Lambda_Osubst,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(v_ia______,type,
v_ia______: $i ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(v_Ua____,type,
v_Ua____: $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_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_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).
tff(v_ea______,type,
v_ea______: $i ).
tff(c_List_Ofoldr,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_ua______,type,
v_ua______: $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(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
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(tc_fun,type,
tc_fun: ( $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(tc_bool,type,
tc_bool: $i ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_Type_Otypings,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
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_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $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_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $o ).
tff(c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
tff(c_Type_Osko__Type__Xabs__typeE__1__2,type,
c_Type_Osko__Type__Xabs__typeE__1__2: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
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_as____,type,
v_as____: $i ).
tff(v_a____,type,
v_a____: $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_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Type_Osko__Type__Xabs__typeE__1__1,type,
c_Type_Osko__Type__Xabs__typeE__1__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Type_Osko__Type__Xtyping__elims__3__1,type,
c_Type_Osko__Type__Xtyping__elims__3__1: ( $i * $i * $i ) > $i ).
tff(v_u____,type,
v_u____: $i ).
tff(c_Type_Otype_Otype__size,type,
c_Type_Otype_Otype__size: $i > $i ).
tff(v_r____,type,
v_r____: $i ).
tff(c_Lambda_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $i > $i ).
tff(c_Predicate_Oconversep,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
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_1882,axiom,
~ v_thesis____,
file(unknown,unknown) ).
tff(f_1887,axiom,
! [V_x] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_x) ),
file(unknown,unknown) ).
tff(f_1880,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
file(unknown,unknown) ).
tff(f_754,axiom,
! [V_e,V_u,V_T,V_t] :
( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
| ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ),
file(unknown,unknown) ).
tff(c_730,plain,
~ v_thesis____,
inference(cnfTransformation,[status(thm)],[f_1882]) ).
tff(c_732,plain,
! [V_x_964] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_x_964)
| v_thesis____ ),
inference(cnfTransformation,[status(thm)],[f_1887]) ).
tff(c_779,plain,
! [V_x_964] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_x_964),
inference(negUnitSimplification,[status(thm)],[c_730,c_732]) ).
tff(c_728,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
inference(cnfTransformation,[status(thm)],[f_1880]) ).
tff(c_26166,plain,
! [V_e_1695,V_t_1696,V_u_1697,V_T_1698] :
( ~ c_Type_Otyping(V_e_1695,hAPP(hAPP(c_Lambda_OdB_OApp,V_t_1696),V_u_1697),V_T_1698)
| c_Type_Otyping(V_e_1695,V_u_1697,c_Type_Osko__Type__Xtyping__elims__2__1(V_T_1698,V_e_1695,V_t_1696,V_u_1697)) ),
inference(cnfTransformation,[status(thm)],[f_754]) ).
tff(c_26168,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)),
inference(resolution,[status(thm)],[c_728,c_26166]) ).
tff(c_26172,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_779,c_26168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL839-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % 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
% 0.12/0.35 % Computer : n004.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Aug 3 13:42:11 EDT 2023
% 0.12/0.35 % CPUTime :
% 16.36/5.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.36/5.65
% 16.36/5.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.36/5.68
% 16.36/5.68 Inference rules
% 16.36/5.68 ----------------------
% 16.36/5.68 #Ref : 29
% 16.36/5.68 #Sup : 5715
% 16.36/5.68 #Fact : 8
% 16.36/5.68 #Define : 0
% 16.36/5.68 #Split : 3
% 16.36/5.68 #Chain : 0
% 16.36/5.68 #Close : 0
% 16.36/5.68
% 16.36/5.68 Ordering : KBO
% 16.36/5.68
% 16.36/5.68 Simplification rules
% 16.36/5.68 ----------------------
% 16.36/5.68 #Subsume : 2372
% 16.36/5.68 #Demod : 2793
% 16.36/5.68 #Tautology : 1535
% 16.36/5.68 #SimpNegUnit : 304
% 16.36/5.68 #BackRed : 10
% 16.36/5.68
% 16.36/5.68 #Partial instantiations: 0
% 16.36/5.68 #Strategies tried : 1
% 16.36/5.68
% 16.36/5.68 Timing (in seconds)
% 16.36/5.68 ----------------------
% 16.36/5.68 Preprocessing : 1.14
% 16.36/5.69 Parsing : 0.61
% 16.36/5.69 CNF conversion : 0.10
% 16.36/5.69 Main loop : 3.42
% 16.36/5.69 Inferencing : 0.81
% 16.36/5.69 Reduction : 1.52
% 16.36/5.69 Demodulation : 1.12
% 16.36/5.69 BG Simplification : 0.12
% 16.36/5.69 Subsumption : 0.78
% 16.36/5.69 Abstraction : 0.08
% 16.36/5.69 MUC search : 0.00
% 16.36/5.69 Cooper : 0.00
% 16.36/5.69 Total : 4.60
% 16.36/5.69 Index Insertion : 0.00
% 16.36/5.69 Index Deletion : 0.00
% 16.36/5.69 Index Matching : 0.00
% 16.36/5.69 BG Taut test : 0.00
%------------------------------------------------------------------------------