TSTP Solution File: SCT162+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT162+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 14:11:23 EDT 2023
% Result : Theorem 1.67s 1.76s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 159
% Syntax : Number of formulae : 212 ( 30 unt; 143 typ; 0 def)
% Number of atoms : 154 ( 52 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 140 ( 55 ~; 57 |; 11 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 267 ( 115 >; 152 *; 0 +; 0 <<)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-6 aty)
% Number of functors : 108 ( 108 usr; 28 con; 0-6 aty)
% Number of variables : 149 ( 13 sgn; 79 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_24,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_25,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_26,type,
tc_HOL_Obool: $i ).
tff(decl_27,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_28,type,
c_member: $i > $i ).
tff(decl_29,type,
v_P____: $i ).
tff(decl_30,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_31,type,
hBOOL: $i > $o ).
tff(decl_32,type,
v_c____: $i ).
tff(decl_33,type,
v_d____: $i ).
tff(decl_34,type,
c_COMBC: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_If: $i > $i ).
tff(decl_36,type,
c_COMBB: ( $i * $i * $i * $i ) > $i ).
tff(decl_37,type,
tc_Nat_Onat: $i ).
tff(decl_38,type,
c_Orderings_Oord__class_Oless: $i > $i ).
tff(decl_39,type,
v_h____: $i ).
tff(decl_40,type,
v_Lab____: $i ).
tff(decl_41,type,
v_Lba____: $i ).
tff(decl_42,type,
c_Arrow__Order__Mirabelle_Odictator: ( $i * $i ) > $o ).
tff(decl_43,type,
v_n____: $i ).
tff(decl_44,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_45,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_46,type,
v_e____: $i ).
tff(decl_47,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_48,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
c_List_Odistinct: ( $i * $i ) > $o ).
tff(decl_50,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_51,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_52,type,
c_fequal: $i ).
tff(decl_53,type,
c_Product__Type_OPair: ( $i * $i ) > $i ).
tff(decl_54,type,
c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_55,type,
class_Orderings_Otop: $i > $o ).
tff(decl_56,type,
c_COMBK: ( $i * $i ) > $i ).
tff(decl_57,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
tff(decl_58,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
tff(decl_59,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
tff(decl_60,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_61,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_62,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_63,type,
class_Orderings_Oord: $i > $o ).
tff(decl_64,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
c_COMBI: $i > $i ).
tff(decl_66,type,
v_a____: $i ).
tff(decl_67,type,
v_b____: $i ).
tff(decl_68,type,
c_List_Omeasures: ( $i * $i ) > $i ).
tff(decl_69,type,
c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_70,type,
c_List_Osplice: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
c_Recdef_Osame__fst: ( $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
c_List_Olist_Olist__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(decl_74,type,
v_F: $i ).
tff(decl_75,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(decl_76,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_77,type,
c_Wellfounded_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_79,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(decl_80,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_81,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_82,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_83,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_84,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_85,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_86,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_87,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_88,type,
class_Groups_Oone: $i > $o ).
tff(decl_89,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_90,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_91,type,
c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_93,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(decl_94,type,
tc_Product__Type_Ounit: $i ).
tff(decl_95,type,
tc_Option_Ooption: $i > $i ).
tff(decl_96,type,
tc_sum: ( $i * $i ) > $i ).
tff(decl_97,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
tff(decl_98,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_Finite__Set_Ofolding__image__simple__idem: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_101,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_102,type,
c_Finite__Set_Ofolding__image__simple: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_103,type,
class_Groups_Ozero: $i > $o ).
tff(decl_104,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_105,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_106,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_107,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_108,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_109,type,
c_Nat_OSuc: $i ).
tff(decl_110,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_111,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_112,type,
c_List_Olist_Olist__size: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
c_Int_Oring__1__class_OInts: $i > $i ).
tff(decl_114,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_115,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_116,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_117,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_118,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk3_0: $i ).
tff(decl_124,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_127,type,
esk7_0: $i ).
tff(decl_128,type,
esk8_0: $i ).
tff(decl_129,type,
esk9_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_130,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_131,type,
esk11_0: $i ).
tff(decl_132,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
esk13_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_134,type,
esk14_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_135,type,
esk15_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
esk16_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_137,type,
esk17_0: $i ).
tff(decl_138,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_140,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk21_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_142,type,
esk22_1: $i > $i ).
tff(decl_143,type,
esk23_1: $i > $i ).
tff(decl_144,type,
esk24_1: $i > $i ).
tff(decl_145,type,
esk25_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk26_1: $i > $i ).
tff(decl_147,type,
esk27_1: $i > $i ).
tff(decl_148,type,
esk28_1: $i > $i ).
tff(decl_149,type,
esk29_1: $i > $i ).
tff(decl_150,type,
esk30_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_151,type,
esk31_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_152,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk33_1: $i > $i ).
tff(decl_154,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_155,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk36_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_157,type,
esk37_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_158,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_163,type,
esk43_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_164,type,
esk44_5: ( $i * $i * $i * $i * $i ) > $i ).
fof(fact_range__ex1__eq,axiom,
! [X21,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X28),X21),c_Set_Oimage(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
<=> ? [X3] :
( X21 = hAPP(X2,X3)
& ! [X80] :
( X21 = hAPP(X2,X80)
=> X80 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_range__eqI,axiom,
! [X28,X5,X20,X2,X21] :
( X21 = hAPP(X2,X20)
=> hBOOL(hAPP(hAPP(c_member(X5),X21),c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_inj__Suc,axiom,
! [X62] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X62),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_finite__code,axiom,
! [X7,X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_gr0__conv__Suc,axiom,
! [X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8))
<=> ? [X52] : X8 = hAPP(c_Nat_OSuc,X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Set_Oimage(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_finite__imageD,axiom,
! [X7,X2,X28,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X28,X5,X2,X7))
=> ( c_Fun_Oinj__on(X28,X5,X2,X7)
=> c_Finite__Set_Ofinite(X28,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(fact_inj__on__def,axiom,
! [X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> ! [X41] :
( hBOOL(hAPP(hAPP(c_member(X5),X41),X7))
=> ( hAPP(X2,X3) = hAPP(X2,X41)
=> X3 = X41 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_zero__less__Suc,axiom,
! [X13] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_UNIV__I,axiom,
! [X20,X5] : hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_Suc__lessD,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),X13))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_lessI,axiom,
! [X13] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_less__Suc__eq__le,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X8)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_le__0__eq,axiom,
! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X8 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_Zero__not__Suc,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(c_0_16,plain,
! [X1423,X1424,X1425,X1426,X1428,X1429] :
( ( X1423 = hAPP(X1424,esk36_4(X1423,X1424,X1425,X1426))
| ~ hBOOL(hAPP(hAPP(c_member(X1425),X1423),c_Set_Oimage(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool))) )
& ( X1423 != hAPP(X1424,X1428)
| X1428 = esk36_4(X1423,X1424,X1425,X1426)
| ~ hBOOL(hAPP(hAPP(c_member(X1425),X1423),c_Set_Oimage(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool))) )
& ( X1423 = hAPP(X1424,esk37_5(X1423,X1424,X1425,X1426,X1429))
| X1423 != hAPP(X1424,X1429)
| hBOOL(hAPP(hAPP(c_member(X1425),X1423),c_Set_Oimage(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool))) )
& ( esk37_5(X1423,X1424,X1425,X1426,X1429) != X1429
| X1423 != hAPP(X1424,X1429)
| hBOOL(hAPP(hAPP(c_member(X1425),X1423),c_Set_Oimage(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1426,X1425,X1424,c_Orderings_Otop__class_Otop(tc_fun(X1426,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__ex1__eq])])])])]) ).
fof(c_0_17,plain,
! [X1580,X1581,X1582,X1583,X1584] :
( X1584 != hAPP(X1583,X1582)
| hBOOL(hAPP(hAPP(c_member(X1581),X1584),c_Set_Oimage(X1580,X1581,X1583,c_Orderings_Otop__class_Otop(tc_fun(X1580,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
cnf(c_0_18,plain,
( X3 = esk36_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| X1 != hAPP(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X1305] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1305),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(c_0_21,plain,
! [X988,X989] :
( ~ class_Finite__Set_Ofinite(X989)
| c_Finite__Set_Ofinite(X989,X988) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
cnf(c_0_22,plain,
( X1 = esk36_4(X2,X3,X4,X5)
| X2 != hAPP(X3,X1)
| ~ c_Fun_Oinj__on(X5,X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(csr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X1313,X1315,X1316] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1313))
| X1313 = hAPP(c_Nat_OSuc,esk33_1(X1313)) )
& ( X1315 != hAPP(c_Nat_OSuc,X1316)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1315)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).
fof(c_0_25,plain,
! [X1607,X1608] :
( ~ c_Finite__Set_Ofinite(X1608,c_Orderings_Otop__class_Otop(tc_fun(X1608,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1608,X1608,X1607,c_Orderings_Otop__class_Otop(tc_fun(X1608,tc_HOL_Obool)))
| c_Set_Oimage(X1608,X1608,X1607,c_Orderings_Otop__class_Otop(tc_fun(X1608,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1608,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(c_0_26,plain,
! [X1441,X1442,X1443,X1444] :
( ~ c_Finite__Set_Ofinite(X1444,c_Set_Oimage(X1443,X1444,X1442,X1441))
| ~ c_Fun_Oinj__on(X1443,X1444,X1442,X1441)
| c_Finite__Set_Ofinite(X1443,X1441) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
cnf(c_0_27,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
cnf(c_0_29,plain,
( X1 = esk36_4(X2,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_30,plain,
! [X319,X320,X321,X322,X323,X324,X325,X326,X327,X328] :
( ( ~ c_Fun_Oinj__on(X322,X321,X320,X319)
| ~ hBOOL(hAPP(hAPP(c_member(X322),X323),X319))
| ~ hBOOL(hAPP(hAPP(c_member(X322),X324),X319))
| hAPP(X320,X323) != hAPP(X320,X324)
| X323 = X324 )
& ( hBOOL(hAPP(hAPP(c_member(X328),esk5_4(X325,X326,X327,X328)),X325))
| c_Fun_Oinj__on(X328,X327,X326,X325) )
& ( hBOOL(hAPP(hAPP(c_member(X328),esk6_4(X325,X326,X327,X328)),X325))
| c_Fun_Oinj__on(X328,X327,X326,X325) )
& ( hAPP(X326,esk5_4(X325,X326,X327,X328)) = hAPP(X326,esk6_4(X325,X326,X327,X328))
| c_Fun_Oinj__on(X328,X327,X326,X325) )
& ( esk5_4(X325,X326,X327,X328) != esk6_4(X325,X326,X327,X328)
| c_Fun_Oinj__on(X328,X327,X326,X325) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__def])])])])])]) ).
cnf(c_0_31,plain,
( X1 = hAPP(c_Nat_OSuc,esk33_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X1250] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1250))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
cnf(c_0_33,plain,
( c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_34,plain,
! [X118,X119] : hBOOL(hAPP(hAPP(c_member(X119),X118),c_Orderings_Otop__class_Otop(tc_fun(X119,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
cnf(c_0_35,plain,
( c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
esk36_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = X1,
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( hAPP(X1,esk5_4(X2,X1,X3,X4)) = hAPP(X1,esk6_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk5_4(X1,X2,X3,X4) != esk6_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
( esk36_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk33_1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31])]) ).
cnf(c_0_41,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( X1 = hAPP(X2,esk36_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_43,plain,
( c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_44,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_45,plain,
! [X1284,X1285] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1285)),X1284))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1285),X1284)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(c_0_46,plain,
! [X1247] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1247),hAPP(c_Nat_OSuc,X1247))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
cnf(c_0_47,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_48,plain,
c_Fun_Oinj__on(X1,X2,c_Nat_OSuc,X3),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_37]),c_0_39]) ).
cnf(c_0_49,plain,
esk33_1(hAPP(c_Nat_OSuc,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_40]),c_0_41])]) ).
cnf(c_0_50,plain,
( hAPP(c_Nat_OSuc,esk36_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)) = X1
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_23]),c_0_44])]) ).
fof(c_0_51,plain,
! [X1341,X1342] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1342),hAPP(c_Nat_OSuc,X1341)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1342),X1341)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1342),X1341))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1342),hAPP(c_Nat_OSuc,X1341))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
cnf(c_0_52,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
( esk36_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk33_1(X1)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_54])]) ).
cnf(c_0_59,plain,
esk36_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk33_1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54])]) ).
fof(c_0_60,plain,
! [X1172] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1172),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X1172 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1172),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).
cnf(c_0_61,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
hAPP(c_Nat_OSuc,esk33_1(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_58]),c_0_59]),c_0_23]),c_0_44])]) ).
cnf(c_0_63,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk33_1(X1)),X1)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_65,plain,
! [X1251] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1251),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_66,plain,
esk33_1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_68,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_66]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SCT162+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 15:53:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.67/1.76 % Version : CSE_E---1.5
% 1.67/1.76 % Problem : theBenchmark.p
% 1.67/1.76 % Proof found
% 1.67/1.76 % SZS status Theorem for theBenchmark.p
% 1.67/1.76 % SZS output start Proof
% See solution above
% 1.67/1.77 % Total time : 1.155000 s
% 1.67/1.77 % SZS output end Proof
% 1.67/1.77 % Total time : 1.179000 s
%------------------------------------------------------------------------------