TSTP Solution File: SCT163+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT163+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 : 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 : Thu Aug 31 14:11:23 EDT 2023
% Result : Theorem 1.92s 2.22s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 161
% Syntax : Number of formulae : 206 ( 24 unt; 148 typ; 0 def)
% Number of atoms : 136 ( 53 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 130 ( 52 ~; 53 |; 10 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 275 ( 118 >; 157 *; 0 +; 0 <<)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-6 aty)
% Number of functors : 113 ( 113 usr; 30 con; 0-6 aty)
% Number of variables : 139 ( 13 sgn; 72 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_c____: $i ).
tff(decl_24,type,
v_d____: $i ).
tff(decl_25,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_26,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_27,type,
c_member: $i > $i ).
tff(decl_28,type,
c_Product__Type_OPair: ( $i * $i ) > $i ).
tff(decl_29,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
tff(decl_30,type,
hBOOL: $i > $o ).
tff(decl_31,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
tff(decl_32,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_33,type,
tc_HOL_Obool: $i ).
tff(decl_34,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_35,type,
v_P____: $i ).
tff(decl_36,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_37,type,
tc_Nat_Onat: $i ).
tff(decl_38,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_39,type,
v_h____: $i ).
tff(decl_40,type,
c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
v_n____: $i ).
tff(decl_42,type,
v_e____: $i ).
tff(decl_43,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_44,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
c_List_Odistinct: ( $i * $i ) > $o ).
tff(decl_46,type,
c_If: $i > $i ).
tff(decl_47,type,
c_COMBB: ( $i * $i * $i * $i ) > $i ).
tff(decl_48,type,
c_COMBC: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
c_Orderings_Oord__class_Oless: $i > $i ).
tff(decl_50,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
c_fequal: $i ).
tff(decl_52,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
tff(decl_53,type,
c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_54,type,
c_Recdef_Osame__fst: ( $i * $i * $i * $i ) > $i ).
tff(decl_55,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(decl_56,type,
c_Nitpick_Orefl_H: ( $i * $i ) > $o ).
tff(decl_57,type,
c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_59,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_60,type,
c_Wellfounded_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
class_Orderings_Otop: $i > $o ).
tff(decl_62,type,
v_Lab____: $i ).
tff(decl_63,type,
v_Lba____: $i ).
tff(decl_64,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_65,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_66,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_67,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_68,type,
class_Orderings_Oord: $i > $o ).
tff(decl_69,type,
c_COMBK: ( $i * $i ) > $i ).
tff(decl_70,type,
c_COMBI: $i > $i ).
tff(decl_71,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
v_b____: $i ).
tff(decl_73,type,
v_a____: $i ).
tff(decl_74,type,
c_List_Omeasures: ( $i * $i ) > $i ).
tff(decl_75,type,
c_Arrow__Order__Mirabelle_Odictator: ( $i * $i ) > $o ).
tff(decl_76,type,
c_List_Osplice: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(decl_78,type,
v_F: $i ).
tff(decl_79,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(decl_80,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_81,type,
c_List_Olist_Olist__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_83,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_84,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_85,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_86,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_87,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_88,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_89,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_90,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_91,type,
class_Groups_Oone: $i > $o ).
tff(decl_92,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_93,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_94,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_95,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(decl_96,type,
tc_Product__Type_Ounit: $i ).
tff(decl_97,type,
tc_sum: ( $i * $i ) > $i ).
tff(decl_98,type,
tc_Option_Ooption: $i > $i ).
tff(decl_99,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
tff(decl_100,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_103,type,
c_Finite__Set_Ofolding__image__simple: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_104,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_105,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_106,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_107,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_108,type,
class_Groups_Ozero: $i > $o ).
tff(decl_109,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_110,type,
c_Nat_OSuc: $i ).
tff(decl_111,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_112,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_113,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_114,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_115,type,
c_List_Olist_Olist__size: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
c_Int_Oring__1__class_OInts: $i > $i ).
tff(decl_117,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_118,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_119,type,
c_Finite__Set_Ofold__image: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_120,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
c_fFalse: $i ).
tff(decl_123,type,
c_Nat_Onat_Onat__case: ( $i * $i * $i * $i ) > $i ).
tff(decl_124,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk3_0: $i ).
tff(decl_127,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_129,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_130,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_131,type,
esk8_0: $i ).
tff(decl_132,type,
esk9_0: $i ).
tff(decl_133,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_134,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk12_0: $i ).
tff(decl_136,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_137,type,
esk14_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_138,type,
esk15_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_139,type,
esk16_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_140,type,
esk17_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_141,type,
esk18_0: $i ).
tff(decl_142,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk22_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk23_1: $i > $i ).
tff(decl_147,type,
esk24_1: $i > $i ).
tff(decl_148,type,
esk25_1: $i > $i ).
tff(decl_149,type,
esk26_1: $i > $i ).
tff(decl_150,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_151,type,
esk28_1: $i > $i ).
tff(decl_152,type,
esk29_1: $i > $i ).
tff(decl_153,type,
esk30_1: $i > $i ).
tff(decl_154,type,
esk31_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_155,type,
esk32_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_156,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk34_1: $i > $i ).
tff(decl_158,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_165,type,
esk42_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_166,type,
esk43_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_167,type,
esk44_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_168,type,
esk45_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_169,type,
esk46_0: $i ).
fof(fact_range__ex1__eq,axiom,
! [X18,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X18),c_Set_Oimage(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))))
<=> ? [X3] :
( X18 = hAPP(X2,X3)
& ! [X84] :
( X18 = hAPP(X2,X84)
=> X84 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_range__eqI,axiom,
! [X13,X9,X7,X2,X18] :
( X18 = hAPP(X2,X7)
=> hBOOL(hAPP(hAPP(c_member(X9),X18),c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,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_nat_Oinject,axiom,
! [X74,X75] :
( hAPP(c_Nat_OSuc,X75) = hAPP(c_Nat_OSuc,X74)
<=> X75 = X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_gr0__conv__Suc,axiom,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
<=> ? [X53] : X20 = hAPP(c_Nat_OSuc,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Set_Oimage(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_finite,axiom,
! [X11,X9] :
( class_Finite__Set_Ofinite(X9)
=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_UNIV__I,axiom,
! [X7,X9] : hBOOL(hAPP(hAPP(c_member(X9),X7),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_finite__imageD,axiom,
! [X11,X2,X13,X9] :
( c_Finite__Set_Ofinite(X9,c_Set_Oimage(X13,X9,X2,X11))
=> ( c_Fun_Oinj__on(X13,X9,X2,X11)
=> c_Finite__Set_Ofinite(X13,X11) ) ),
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,
! [X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X9),X3),X11))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X9),X43),X11))
=> ( hAPP(X2,X3) = hAPP(X2,X43)
=> X3 = X43 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_less__zeroE,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_lessI,axiom,
! [X17] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(c_0_13,plain,
! [X1621,X1622,X1623,X1624,X1626,X1627] :
( ( X1621 = hAPP(X1622,esk44_4(X1621,X1622,X1623,X1624))
| ~ hBOOL(hAPP(hAPP(c_member(X1623),X1621),c_Set_Oimage(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool))) )
& ( X1621 != hAPP(X1622,X1626)
| X1626 = esk44_4(X1621,X1622,X1623,X1624)
| ~ hBOOL(hAPP(hAPP(c_member(X1623),X1621),c_Set_Oimage(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool))) )
& ( X1621 = hAPP(X1622,esk45_5(X1621,X1622,X1623,X1624,X1627))
| X1621 != hAPP(X1622,X1627)
| hBOOL(hAPP(hAPP(c_member(X1623),X1621),c_Set_Oimage(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool))) )
& ( esk45_5(X1621,X1622,X1623,X1624,X1627) != X1627
| X1621 != hAPP(X1622,X1627)
| hBOOL(hAPP(hAPP(c_member(X1623),X1621),c_Set_Oimage(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1624,X1623,X1622,c_Orderings_Otop__class_Otop(tc_fun(X1624,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_14,plain,
! [X1583,X1584,X1585,X1586,X1587] :
( X1587 != hAPP(X1586,X1585)
| hBOOL(hAPP(hAPP(c_member(X1584),X1587),c_Set_Oimage(X1583,X1584,X1586,c_Orderings_Otop__class_Otop(tc_fun(X1583,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
cnf(c_0_15,plain,
( X3 = esk44_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_13]) ).
cnf(c_0_16,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_14]) ).
fof(c_0_17,plain,
! [X1280] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1280),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(c_0_18,plain,
! [X1276,X1277] :
( ( hAPP(c_Nat_OSuc,X1277) != hAPP(c_Nat_OSuc,X1276)
| X1277 = X1276 )
& ( X1277 != X1276
| hAPP(c_Nat_OSuc,X1277) = hAPP(c_Nat_OSuc,X1276) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(c_0_19,plain,
! [X1288,X1290,X1291] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1288))
| X1288 = hAPP(c_Nat_OSuc,esk34_1(X1288)) )
& ( X1290 != hAPP(c_Nat_OSuc,X1291)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1290)) ) ),
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_20,plain,
! [X1608,X1609] :
( ~ c_Finite__Set_Ofinite(X1609,c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1609,X1609,X1608,c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool)))
| c_Set_Oimage(X1609,X1609,X1608,c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
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])]) ).
cnf(c_0_22,plain,
( X1 = esk44_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_15,c_0_16]) ).
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_17]) ).
cnf(c_0_24,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( X1 = hAPP(c_Nat_OSuc,esk34_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_19]) ).
cnf(c_0_26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,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_20]) ).
fof(c_0_28,plain,
! [X132,X133] : hBOOL(hAPP(hAPP(c_member(X133),X132),c_Orderings_Otop__class_Otop(tc_fun(X133,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(c_0_29,plain,
! [X1448,X1449,X1450,X1451] :
( ~ c_Finite__Set_Ofinite(X1451,c_Set_Oimage(X1450,X1451,X1449,X1448))
| ~ c_Fun_Oinj__on(X1450,X1451,X1449,X1448)
| c_Finite__Set_Ofinite(X1450,X1448) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
cnf(c_0_30,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
cnf(c_0_32,plain,
( X1 = esk44_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_33,plain,
! [X346,X347,X348,X349,X350,X351,X352,X353,X354,X355] :
( ( ~ c_Fun_Oinj__on(X349,X348,X347,X346)
| ~ hBOOL(hAPP(hAPP(c_member(X349),X350),X346))
| ~ hBOOL(hAPP(hAPP(c_member(X349),X351),X346))
| hAPP(X347,X350) != hAPP(X347,X351)
| X350 = X351 )
& ( hBOOL(hAPP(hAPP(c_member(X355),esk5_4(X352,X353,X354,X355)),X352))
| c_Fun_Oinj__on(X355,X354,X353,X352) )
& ( hBOOL(hAPP(hAPP(c_member(X355),esk6_4(X352,X353,X354,X355)),X352))
| c_Fun_Oinj__on(X355,X354,X353,X352) )
& ( hAPP(X353,esk5_4(X352,X353,X354,X355)) = hAPP(X353,esk6_4(X352,X353,X354,X355))
| c_Fun_Oinj__on(X355,X354,X353,X352) )
& ( esk5_4(X352,X353,X354,X355) != esk6_4(X352,X353,X354,X355)
| c_Fun_Oinj__on(X355,X354,X353,X352) ) ),
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_34,plain,
( esk34_1(X1) = X2
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_35,plain,
( X1 = hAPP(X2,esk44_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_13]) ).
cnf(c_0_36,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_27,c_0_23]) ).
cnf(c_0_37,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_28]) ).
cnf(c_0_38,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_29]) ).
cnf(c_0_39,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
esk44_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = X1,
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_41,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_33]) ).
cnf(c_0_42,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_33]) ).
cnf(c_0_43,plain,
esk34_1(hAPP(c_Nat_OSuc,X1)) = X1,
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( hAPP(c_Nat_OSuc,esk44_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_35,c_0_36]),c_0_23]),c_0_37])]) ).
cnf(c_0_45,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,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_40,c_0_41]),c_0_40]),c_0_42]) ).
cnf(c_0_47,plain,
( esk44_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk34_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_43,c_0_44]) ).
cnf(c_0_48,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_49,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(c_0_50,plain,
! [X1224] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1224),hAPP(c_Nat_OSuc,X1224))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
cnf(c_0_51,plain,
esk44_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk34_1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
fof(c_0_52,plain,
! [X1119] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1119),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[c_0_49]) ).
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_50]) ).
cnf(c_0_54,plain,
hAPP(c_Nat_OSuc,esk34_1(X1)) = X1,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_48])]),c_0_51]) ).
cnf(c_0_55,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_1(X1)),X1)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
$false,
inference(spm,[status(thm)],[c_0_55,c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT163+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 16:39:23 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.56 start to proof: theBenchmark
% 1.92/2.22 % Version : CSE_E---1.5
% 1.92/2.22 % Problem : theBenchmark.p
% 1.92/2.22 % Proof found
% 1.92/2.22 % SZS status Theorem for theBenchmark.p
% 1.92/2.22 % SZS output start Proof
% See solution above
% 2.15/2.23 % Total time : 1.647000 s
% 2.15/2.23 % SZS output end Proof
% 2.15/2.23 % Total time : 1.661000 s
%------------------------------------------------------------------------------