TSTP Solution File: LCL847-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL847-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 : Thu Aug 31 06:59:57 EDT 2023
% Result : Unsatisfiable 28.99s 29.12s
% Output : CNFRefutation 28.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 127
% Syntax : Number of formulae : 146 ( 19 unt; 116 typ; 0 def)
% Number of atoms : 41 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 213 ( 104 >; 109 *; 0 +; 0 <<)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-4 aty)
% Number of functors : 79 ( 79 usr; 12 con; 0-5 aty)
% Number of variables : 78 ( 14 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_nat: $i ).
tff(decl_23,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_24,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
tc_List_Olist: $i > $i ).
tff(decl_26,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_27,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_28,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_List_Onth: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(decl_31,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_32,type,
c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
c_List_OtakeWhile: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
hBOOL: $i > $o ).
tff(decl_35,type,
c_List_Obutlast: ( $i * $i ) > $i ).
tff(decl_36,type,
c_List_Otake: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
c_List_Odrop: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(decl_39,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_42,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_44,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_45,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_46,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_47,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_49,type,
c_List_Olist_Olist__size: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(decl_51,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_52,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_53,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_55,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_56,type,
class_Int_Onumber: $i > $o ).
tff(decl_57,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_58,type,
c_Lambda_Osubst: $i ).
tff(decl_59,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_60,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
c_Lambda_Olift: $i ).
tff(decl_62,type,
c_List_Ofilter: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
c_Map_Omap__upds: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
c_List_Olinorder__class_Osorted: ( $i * $i ) > $o ).
tff(decl_65,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_66,type,
c_Lambda_OdB_OApp: $i ).
tff(decl_67,type,
tc_Lambda_OdB: $i ).
tff(decl_68,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_70,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_71,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_73,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_74,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_76,type,
c_List_Oremdups: ( $i * $i ) > $i ).
tff(decl_77,type,
c_List_Oremove1: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
c_List_Orotate: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_80,type,
c_List_Olistsum: ( $i * $i ) > $i ).
tff(decl_81,type,
c_List_Osko__List__Xlistsum__map__filter__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
c_List_Olength__unique: ( $i * $i ) > $i ).
tff(decl_83,type,
c_List_Olinorder__class_Oinsort__key: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_84,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_85,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(decl_87,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_89,type,
c_Lambda_Obeta: ( $i * $i ) > $o ).
tff(decl_90,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(decl_91,type,
c_List_Osublist: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
v_sko__List__Xconcat__Xinduct__1: $i > $i ).
tff(decl_93,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
tff(decl_94,type,
t_a: $i ).
tff(decl_95,type,
v_sko__List__Xtake__Xinduct__1: $i > $i ).
tff(decl_96,type,
v_sko__List__Xtake__Xinduct__2: $i > $i ).
tff(decl_97,type,
v_sko__List__Xmap__Xinduct__1: $i > $i ).
tff(decl_98,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
tff(decl_99,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
tff(decl_100,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
tff(decl_101,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
tff(decl_102,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
tff(decl_103,type,
v_sko__List__Xlistset__Xinduct__1: $i > $i ).
tff(decl_104,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
tff(decl_105,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
tff(decl_106,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
tff(decl_107,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
tff(decl_108,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
tff(decl_109,type,
c_List_Osko__List__Xin__listsp__conv__set__1__1: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
c_InductTermi_OIT: $i ).
tff(decl_111,type,
tc_bool: $i ).
tff(decl_112,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_113,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_114,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_115,type,
class_Power_Opower: $i > $o ).
tff(decl_116,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_117,type,
t_b: $i ).
tff(decl_118,type,
c_List_Olist_Olist__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_List_Olist_Olist__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_120,type,
c_List_Osplice: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
c_List_Olistrelp: ( $i * $i * $i * $i ) > $o ).
tff(decl_122,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_123,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_124,type,
c_List_Ofiltermap: ( $i * $i * $i * $i ) > $i ).
tff(decl_125,type,
v_s____: $i ).
tff(decl_126,type,
v_sko__List__Xlistsp__Xcases__1: ( $i * $i ) > $i ).
tff(decl_127,type,
v_sko__List__Xlistsp__Xcases__2: ( $i * $i ) > $i ).
tff(decl_128,type,
v_sko__List__Xlistsp__Xinduct__1: ( $i * $i ) > $i ).
tff(decl_129,type,
v_sko__List__Xlistsp__Xinduct__2: ( $i * $i ) > $i ).
tff(decl_130,type,
v_sko__List__Xlistsp__Xinducts__1: ( $i * $i ) > $i ).
tff(decl_131,type,
v_sko__List__Xlistsp__Xinducts__2: ( $i * $i ) > $i ).
tff(decl_132,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_133,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_134,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_135,type,
v_ta____: $i ).
tff(decl_136,type,
tc_Int_Oint: $i ).
tff(decl_137,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_set__takeWhileD_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,c_List_Oset(c_List_OtakeWhile(X1,X3,X4),X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
cnf(cls_in__listsp__conv__set_1,axiom,
( c_List_Olistsp(X1,X2,X3)
| c_in(c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3),c_List_Oset(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_1) ).
cnf(cls_in__listsp__conv__set_2,axiom,
( c_List_Olistsp(X1,X2,X3)
| ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
cnf(cls_takeWhile_Osimps_I2_J_0,axiom,
( c_List_OtakeWhile(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_OtakeWhile(X1,X3,X4),X4)
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
cnf(cls_App_I4_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
cnf(cls_takeWhile_Osimps_I1_J_0,axiom,
c_List_OtakeWhile(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
cnf(cls_lifts__IT_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
cnf(cls_map__eq__Cons__conv_3,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_11,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,c_List_Oset(c_List_OtakeWhile(X1,X3,X4),X4),X4) ),
cls_set__takeWhileD_1 ).
cnf(c_0_12,axiom,
( c_List_Olistsp(X1,X2,X3)
| c_in(c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3),c_List_Oset(X2,X3),X3) ),
cls_in__listsp__conv__set_1 ).
cnf(c_0_13,axiom,
( c_List_Olistsp(X1,X2,X3)
| ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3))) ),
cls_in__listsp__conv__set_2 ).
cnf(c_0_14,plain,
( c_List_Olistsp(X1,c_List_OtakeWhile(X2,X3,X4),X4)
| hBOOL(hAPP(X2,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,c_List_OtakeWhile(X2,X3,X4),X4))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
( c_List_OtakeWhile(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_OtakeWhile(X1,X3,X4),X4)
| ~ hBOOL(hAPP(X1,X2)) ),
cls_takeWhile_Osimps_I2_J_0 ).
cnf(c_0_16,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
cls_App_I4_J_0 ).
cnf(c_0_17,plain,
c_List_Olistsp(X1,c_List_OtakeWhile(X1,X2,X3),X3),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
c_List_OtakeWhile(c_InductTermi_OIT,c_List_Olist_OCons(v_ta____,X1,X2),X2) = c_List_Olist_OCons(v_ta____,c_List_OtakeWhile(c_InductTermi_OIT,X1,X2),X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(v_ta____,c_List_OtakeWhile(c_InductTermi_OIT,X1,X2),X2),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
c_List_OtakeWhile(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
cls_takeWhile_Osimps_I1_J_0 ).
cnf(c_0_21,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
cls_lifts__IT_0 ).
cnf(c_0_22,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(v_ta____,c_List_Olist_ONil(X1),X1),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
cls_map__eq__Cons__conv_3 ).
cnf(c_0_24,axiom,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
cls_Nil__is__map__conv_1 ).
cnf(c_0_25,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_ta____,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3,X4) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Olist_ONil(X4),X4),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
cls_COMBC__def_0 ).
cnf(c_0_28,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
cls_conjecture_0 ).
cnf(c_0_29,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL847-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 07:22:21 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 28.99/29.12 % Version : CSE_E---1.5
% 28.99/29.12 % Problem : theBenchmark.p
% 28.99/29.12 % Proof found
% 28.99/29.12 % SZS status Theorem for theBenchmark.p
% 28.99/29.12 % SZS output start Proof
% See solution above
% 28.99/29.12 % Total time : 28.518000 s
% 28.99/29.12 % SZS output end Proof
% 28.99/29.12 % Total time : 28.537000 s
%------------------------------------------------------------------------------