TSTP Solution File: SCT166+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT166+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 14:11:24 EDT 2023
% Result : Theorem 1.90s 1.97s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 150
% Syntax : Number of formulae : 180 ( 17 unt; 140 typ; 0 def)
% Number of atoms : 106 ( 28 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 109 ( 43 ~; 43 |; 10 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 258 ( 110 >; 148 *; 0 +; 0 <<)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-6 aty)
% Number of functors : 106 ( 106 usr; 30 con; 0-6 aty)
% Number of variables : 111 ( 10 sgn; 62 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_a____: $i ).
tff(decl_24,type,
v_b____: $i ).
tff(decl_25,type,
v_c____: $i ).
tff(decl_26,type,
v_d____: $i ).
tff(decl_27,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_28,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_29,type,
c_member: $i > $i ).
tff(decl_30,type,
c_Product__Type_OPair: ( $i * $i ) > $i ).
tff(decl_31,type,
v_Lab____: $i ).
tff(decl_32,type,
hBOOL: $i > $o ).
tff(decl_33,type,
v_Lba____: $i ).
tff(decl_34,type,
v_P____: $i ).
tff(decl_35,type,
tc_Nat_Onat: $i ).
tff(decl_36,type,
c_Orderings_Oord__class_Oless: $i > $i ).
tff(decl_37,type,
v_h____: $i ).
tff(decl_38,type,
v_n____: $i ).
tff(decl_39,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
tff(decl_40,type,
v_e____: $i ).
tff(decl_41,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
tff(decl_42,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
tff(decl_43,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_44,type,
tc_HOL_Obool: $i ).
tff(decl_45,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_46,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_47,type,
c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_48,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(decl_49,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_50,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_51,type,
v_F: $i ).
tff(decl_52,type,
c_If: $i > $i ).
tff(decl_53,type,
c_COMBB: ( $i * $i * $i * $i ) > $i ).
tff(decl_54,type,
c_COMBC: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
c_fequal: $i ).
tff(decl_57,type,
c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_58,type,
c_Recdef_Osame__fst: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_60,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(decl_61,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(decl_62,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_63,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_64,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_65,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_66,type,
c_Wellfounded_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
c_COMBK: ( $i * $i ) > $i ).
tff(decl_68,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_71,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_72,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_73,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_74,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_75,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_76,type,
class_Groups_Oone: $i > $o ).
tff(decl_77,type,
c_COMBI: $i > $i ).
tff(decl_78,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_79,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_80,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_81,type,
c_Arrow__Order__Mirabelle_Odictator: ( $i * $i ) > $o ).
tff(decl_82,type,
c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
class_Orderings_Oord: $i > $o ).
tff(decl_84,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_85,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_86,type,
class_Orderings_Otop: $i > $o ).
tff(decl_87,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_88,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(decl_89,type,
tc_Product__Type_Ounit: $i ).
tff(decl_90,type,
tc_Option_Ooption: $i > $i ).
tff(decl_91,type,
tc_sum: ( $i * $i ) > $i ).
tff(decl_92,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
tff(decl_93,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_96,type,
c_Finite__Set_Ofolding__image__simple: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_97,type,
c_Finite__Set_Ofolding__image__simple__idem: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_98,type,
class_Groups_Ozero: $i > $o ).
tff(decl_99,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_100,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_101,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_102,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_103,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_104,type,
c_Nat_OSuc: $i ).
tff(decl_105,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_106,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_107,type,
c_Int_Oring__1__class_OInts: $i > $i ).
tff(decl_108,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_109,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_110,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_111,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_112,type,
c_Finite__Set_Ofold__image: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_113,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_114,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
c_fFalse: $i ).
tff(decl_116,type,
c_Nat_Onat_Onat__case: ( $i * $i * $i * $i ) > $i ).
tff(decl_117,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
esk3_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_120,type,
esk4_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
esk5_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_122,type,
esk6_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_123,type,
esk7_0: $i ).
tff(decl_124,type,
esk8_0: $i ).
tff(decl_125,type,
esk9_0: $i ).
tff(decl_126,type,
esk10_0: $i ).
tff(decl_127,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_128,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_129,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_130,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_131,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk16_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk19_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
esk20_1: $i > $i ).
tff(decl_137,type,
esk21_1: $i > $i ).
tff(decl_138,type,
esk22_1: $i > $i ).
tff(decl_139,type,
esk23_1: $i > $i ).
tff(decl_140,type,
esk24_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_141,type,
esk25_1: $i > $i ).
tff(decl_142,type,
esk26_1: $i > $i ).
tff(decl_143,type,
esk27_1: $i > $i ).
tff(decl_144,type,
esk28_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_145,type,
esk29_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk30_1: $i > $i ).
tff(decl_147,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk34_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_151,type,
esk35_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_152,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk37_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_154,type,
esk38_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_155,type,
esk39_0: $i ).
tff(decl_156,type,
esk40_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_157,type,
esk41_1: $i > $i ).
tff(decl_158,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk43_1: $i > $i ).
tff(decl_160,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk45_0: $i ).
fof(fact_range__ex1__eq,axiom,
! [X22,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X14),X22),c_Set_Oimage(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
<=> ? [X3] :
( X22 = hAPP(X2,X3)
& ! [X66] :
( X22 = hAPP(X2,X66)
=> X66 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_range__eqI,axiom,
! [X14,X10,X8,X2,X22] :
( X22 = hAPP(X2,X8)
=> hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_less__irrefl__nat,axiom,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_finite,axiom,
! [X12,X10] :
( class_Finite__Set_Ofinite(X10)
=> c_Finite__Set_Ofinite(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_injh,axiom,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injh) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X56] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X56)
<=> ? [X17] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_finite__imageD,axiom,
! [X12,X2,X14,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oimage(X14,X10,X2,X12))
=> ( c_Fun_Oinj__on(X14,X10,X2,X12)
=> c_Finite__Set_Ofinite(X14,X12) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(fact_inj__on__def,axiom,
! [X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> ! [X38] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),X12))
=> ( hAPP(X2,X3) = hAPP(X2,X38)
=> X3 = X38 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_UNIV__I,axiom,
! [X8,X10] : hBOOL(hAPP(hAPP(c_member(X10),X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(c_0_10,plain,
! [X1365,X1366,X1367,X1368,X1370,X1371] :
( ( X1365 = hAPP(X1366,esk34_4(X1365,X1366,X1367,X1368))
| ~ hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) )
& ( X1365 != hAPP(X1366,X1370)
| X1370 = esk34_4(X1365,X1366,X1367,X1368)
| ~ hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) )
& ( X1365 = hAPP(X1366,esk35_5(X1365,X1366,X1367,X1368,X1371))
| X1365 != hAPP(X1366,X1371)
| hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) )
& ( esk35_5(X1365,X1366,X1367,X1368,X1371) != X1371
| X1365 != hAPP(X1366,X1371)
| hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,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_11,plain,
! [X1409,X1410,X1411,X1412,X1413] :
( X1413 != hAPP(X1412,X1411)
| hBOOL(hAPP(hAPP(c_member(X1410),X1413),c_Set_Oimage(X1409,X1410,X1412,c_Orderings_Otop__class_Otop(tc_fun(X1409,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
cnf(c_0_12,plain,
( X3 = esk34_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_10]) ).
cnf(c_0_13,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_11]) ).
fof(c_0_14,plain,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(c_0_15,plain,
! [X916,X917] :
( ~ class_Finite__Set_Ofinite(X917)
| c_Finite__Set_Ofinite(X917,X916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
cnf(c_0_16,plain,
( X1 = esk34_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_12,c_0_13]) ).
cnf(c_0_17,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_injh]) ).
fof(c_0_18,plain,
! [X780] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X780),X780)),
inference(variable_rename,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X1603,X1605,X1606,X1607] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1603)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1605),X1603))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1605),esk41_1(X1603))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X1606,X1607)),X1606))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1606) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X1606,X1607)),X1607))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1606) ) ),
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_finite__nat__set__iff__bounded])])])])])]) ).
fof(c_0_20,plain,
! [X1423,X1424,X1425,X1426] :
( ~ c_Finite__Set_Ofinite(X1426,c_Set_Oimage(X1425,X1426,X1424,X1423))
| ~ c_Fun_Oinj__on(X1425,X1426,X1424,X1423)
| c_Finite__Set_Ofinite(X1425,X1423) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
cnf(c_0_21,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
cnf(c_0_23,plain,
( X1 = esk34_4(X2,v_h____,tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi)
| X2 != hAPP(v_h____,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_24,plain,
! [X323,X324,X325,X326,X327,X328,X329,X330,X331,X332] :
( ( ~ c_Fun_Oinj__on(X326,X325,X324,X323)
| ~ hBOOL(hAPP(hAPP(c_member(X326),X327),X323))
| ~ hBOOL(hAPP(hAPP(c_member(X326),X328),X323))
| hAPP(X324,X327) != hAPP(X324,X328)
| X327 = X328 )
& ( hBOOL(hAPP(hAPP(c_member(X332),esk11_4(X329,X330,X331,X332)),X329))
| c_Fun_Oinj__on(X332,X331,X330,X329) )
& ( hBOOL(hAPP(hAPP(c_member(X332),esk12_4(X329,X330,X331,X332)),X329))
| c_Fun_Oinj__on(X332,X331,X330,X329) )
& ( hAPP(X330,esk11_4(X329,X330,X331,X332)) = hAPP(X330,esk12_4(X329,X330,X331,X332))
| c_Fun_Oinj__on(X332,X331,X330,X329) )
& ( esk11_4(X329,X330,X331,X332) != esk12_4(X329,X330,X331,X332)
| c_Fun_Oinj__on(X332,X331,X330,X329) ) ),
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_25,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk41_1(X1)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X117,X118] : hBOOL(hAPP(hAPP(c_member(X118),X117),c_Orderings_Otop__class_Otop(tc_fun(X118,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
cnf(c_0_28,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_20]) ).
cnf(c_0_29,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
esk34_4(hAPP(v_h____,X1),v_h____,tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi) = X1,
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( hAPP(X1,esk11_4(X2,X1,X3,X4)) = hAPP(X1,esk12_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk11_4(X1,X2,X3,X4) != esk12_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk41_1(X1)),X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,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_27]) ).
cnf(c_0_35,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
c_Fun_Oinj__on(X1,X2,v_h____,X3),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]),c_0_32]) ).
cnf(c_0_37,plain,
~ 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_34]) ).
cnf(c_0_38,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT166+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.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 15:46:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 1.90/1.97 % Version : CSE_E---1.5
% 1.90/1.97 % Problem : theBenchmark.p
% 1.90/1.97 % Proof found
% 1.90/1.97 % SZS status Theorem for theBenchmark.p
% 1.90/1.97 % SZS output start Proof
% See solution above
% 1.90/1.98 % Total time : 1.364000 s
% 1.90/1.98 % SZS output end Proof
% 1.90/1.98 % Total time : 1.390000 s
%------------------------------------------------------------------------------