TSTP Solution File: SCT161+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT161+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 : n031.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 1.08s 1.17s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 165
% Syntax : Number of formulae : 195 ( 13 unt; 156 typ; 0 def)
% Number of atoms : 106 ( 28 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 111 ( 44 ~; 46 |; 9 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 350 ( 136 >; 214 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-6 aty)
% Number of functors : 124 ( 124 usr; 20 con; 0-6 aty)
% Number of variables : 110 ( 14 sgn; 55 !; 1 ?; 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_Nat_Onat: $i ).
tff(decl_25,type,
v_h____: $i ).
tff(decl_26,type,
tc_HOL_Obool: $i ).
tff(decl_27,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_29,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_30,type,
hBOOL: $i > $o ).
tff(decl_31,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_32,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_33,type,
c_member: $i > $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,
c_Orderings_Oord__class_Oless: $i > $i ).
tff(decl_38,type,
v_Lab____: $i ).
tff(decl_39,type,
v_Lba____: $i ).
tff(decl_40,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_41,type,
class_Orderings_Otop: $i > $o ).
tff(decl_42,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_43,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_45,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_46,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
v_F: $i ).
tff(decl_48,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_49,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_50,type,
c_COMBK: ( $i * $i ) > $i ).
tff(decl_51,type,
c_fequal: $i ).
tff(decl_52,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_53,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_54,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_55,type,
class_Orderings_Oord: $i > $o ).
tff(decl_56,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_57,type,
c_COMBI: $i > $i ).
tff(decl_58,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(decl_59,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(decl_60,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
c_Arrow__Order__Mirabelle_Oabove: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Product__Type_OPair: ( $i * $i ) > $i ).
tff(decl_63,type,
v_a____: $i ).
tff(decl_64,type,
v_b____: $i ).
tff(decl_65,type,
c_Arrow__Order__Mirabelle_Odictator: ( $i * $i ) > $o ).
tff(decl_66,type,
c_SetInterval_Oord_OgreaterThanAtMost: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
c_SetInterval_Oord_OatLeastLessThan: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
c_SetInterval_Oord_OgreaterThanLessThan: ( $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
c_SetInterval_Oord_OatLeastAtMost: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
c_SetInterval_Oord_OgreaterThan: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
c_SetInterval_Oord_OlessThan: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
c_SetInterval_Oord_OatMost: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
c_SetInterval_Oord_OatLeast: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_75,type,
c_Fun_Othe__inv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_76,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_77,type,
c_Recdef_Osame__fst: ( $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(decl_79,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(decl_80,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(decl_81,type,
tc_sum: ( $i * $i ) > $i ).
tff(decl_82,type,
tc_Option_Ooption: $i > $i ).
tff(decl_83,type,
c_Wellfounded_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(decl_84,type,
c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
tff(decl_86,type,
c_Finite__Set_Ofolding__image__simple__idem: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_87,type,
c_Nat_OSuc: $i ).
tff(decl_88,type,
c_fFalse: $i ).
tff(decl_89,type,
c_HOL_Obool_Obool__size: $i > $i ).
tff(decl_90,type,
c_fTrue: $i ).
tff(decl_91,type,
c_Nat_Onat_Onat__case: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
c_Wellfounded_Omax__extp: ( $i * $i * $i * $i ) > $o ).
tff(decl_93,type,
c_Wellfounded_Omax__ext: ( $i * $i ) > $i ).
tff(decl_94,type,
c_SetInterval_Oord__class_OgreaterThan: ( $i * $i ) > $i ).
tff(decl_95,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(decl_97,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_98,type,
class_Orderings_Obot: $i > $o ).
tff(decl_99,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_100,type,
class_Groups_Ozero: $i > $o ).
tff(decl_101,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_102,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_103,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_104,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_105,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_106,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_107,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_108,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_109,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_110,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_111,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_112,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_113,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_114,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_115,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_116,type,
c_Finite__Set_Ofolding__one__idem: ( $i * $i * $i ) > $o ).
tff(decl_117,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_118,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
v_Sledgehammer_058p__2: $i ).
tff(decl_120,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_121,type,
esk2_0: $i ).
tff(decl_122,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_123,type,
esk4_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_124,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk9_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_129,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_130,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_131,type,
esk12_0: $i ).
tff(decl_132,type,
esk13_0: $i ).
tff(decl_133,type,
esk14_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_134,type,
esk15_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_135,type,
esk16_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
esk17_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_137,type,
esk18_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_138,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_140,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk23_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_143,type,
esk24_1: $i > $i ).
tff(decl_144,type,
esk25_1: $i > $i ).
tff(decl_145,type,
esk26_1: $i > $i ).
tff(decl_146,type,
esk27_1: $i > $i ).
tff(decl_147,type,
esk28_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_148,type,
esk29_1: $i > $i ).
tff(decl_149,type,
esk30_1: $i > $i ).
tff(decl_150,type,
esk31_1: $i > $i ).
tff(decl_151,type,
esk32_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_152,type,
esk33_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_153,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk35_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_155,type,
esk36_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_156,type,
esk37_1: $i > $i ).
tff(decl_157,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk39_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_159,type,
esk40_1: $i > $i ).
tff(decl_160,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk42_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_162,type,
esk43_1: $i > $i ).
tff(decl_163,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_165,type,
esk46_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_166,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_169,type,
esk50_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_170,type,
esk51_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_171,type,
esk52_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_172,type,
esk53_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_173,type,
esk54_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_174,type,
esk55_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_175,type,
esk56_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_176,type,
esk57_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_177,type,
esk58_4: ( $i * $i * $i * $i ) > $i ).
fof(fact_finite__code,axiom,
! [X25,X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X84,X83] :
( ( class_Finite__Set_Ofinite(X83)
& class_Finite__Set_Ofinite(X84) )
=> class_Finite__Set_Ofinite(tc_prod(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(fact_range__ex1__eq,axiom,
! [X26,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X26),c_Set_Oimage(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
<=> ? [X3] :
( X26 = hAPP(X2,X3)
& ! [X27] :
( X26 = hAPP(X2,X27)
=> X27 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_range__eqI,axiom,
! [X7,X5,X4,X2,X26] :
( X26 = hAPP(X2,X4)
=> hBOOL(hAPP(hAPP(c_member(X5),X26),c_Set_Oimage(X7,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_inj__Suc,axiom,
! [X58] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_finite__imageD,axiom,
! [X25,X2,X7,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X7,X5,X2,X25))
=> ( c_Fun_Oinj__on(X7,X5,X2,X25)
=> c_Finite__Set_Ofinite(X7,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_inj__on__def,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
=> ! [X32] :
( hBOOL(hAPP(hAPP(c_member(X5),X32),X25))
=> ( hAPP(X2,X3) = hAPP(X2,X32)
=> X3 = X32 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_infinite__UNIV__nat,axiom,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(c_0_9,plain,
! [X663,X664] :
( ~ class_Finite__Set_Ofinite(X664)
| c_Finite__Set_Ofinite(X664,X663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(c_0_10,plain,
! [X1728,X1729] :
( ~ class_Finite__Set_Ofinite(X1729)
| ~ class_Finite__Set_Ofinite(X1728)
| class_Finite__Set_Ofinite(tc_prod(X1729,X1728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
cnf(c_0_11,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( class_Finite__Set_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite(X1)
| ~ class_Finite__Set_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( c_Finite__Set_Ofinite(tc_prod(X1,X2),X3)
| ~ class_Finite__Set_Ofinite(X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]) ).
fof(c_0_15,plain,
! [X205,X206,X207,X208,X210,X211] :
( ( X205 = hAPP(X206,esk3_4(X205,X206,X207,X208))
| ~ hBOOL(hAPP(hAPP(c_member(X207),X205),c_Set_Oimage(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool))) )
& ( X205 != hAPP(X206,X210)
| X210 = esk3_4(X205,X206,X207,X208)
| ~ hBOOL(hAPP(hAPP(c_member(X207),X205),c_Set_Oimage(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool))) )
& ( X205 = hAPP(X206,esk4_5(X205,X206,X207,X208,X211))
| X205 != hAPP(X206,X211)
| hBOOL(hAPP(hAPP(c_member(X207),X205),c_Set_Oimage(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool))) )
& ( esk4_5(X205,X206,X207,X208,X211) != X211
| X205 != hAPP(X206,X211)
| hBOOL(hAPP(hAPP(c_member(X207),X205),c_Set_Oimage(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X208,X207,X206,c_Orderings_Otop__class_Otop(tc_fun(X208,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_16,plain,
! [X357,X358,X359,X360,X361] :
( X361 != hAPP(X360,X359)
| hBOOL(hAPP(hAPP(c_member(X358),X361),c_Set_Oimage(X357,X358,X360,c_Orderings_Otop__class_Otop(tc_fun(X357,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
cnf(c_0_17,plain,
( c_Finite__Set_Ofinite(tc_prod(X1,tc_HOL_Obool),X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( X3 = esk3_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_15]) ).
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_16]) ).
fof(c_0_20,plain,
! [X1118] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1118),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
cnf(c_0_21,plain,
( c_Finite__Set_Ofinite(tc_prod(tc_prod(X1,X2),tc_HOL_Obool),X3)
| ~ class_Finite__Set_Ofinite(X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_22,plain,
( X1 = esk3_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,
! [X908,X909,X910,X911] :
( ~ c_Finite__Set_Ofinite(X911,c_Set_Oimage(X910,X911,X909,X908))
| ~ c_Fun_Oinj__on(X910,X911,X909,X908)
| c_Finite__Set_Ofinite(X910,X908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
cnf(c_0_25,plain,
( c_Finite__Set_Ofinite(tc_prod(tc_prod(X1,tc_HOL_Obool),tc_HOL_Obool),X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_26,plain,
( X1 = esk3_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_27,plain,
! [X275,X276,X277,X278,X279,X280,X281,X282,X283,X284] :
( ( ~ c_Fun_Oinj__on(X278,X277,X276,X275)
| ~ hBOOL(hAPP(hAPP(c_member(X278),X279),X275))
| ~ hBOOL(hAPP(hAPP(c_member(X278),X280),X275))
| hAPP(X276,X279) != hAPP(X276,X280)
| X279 = X280 )
& ( hBOOL(hAPP(hAPP(c_member(X284),esk9_4(X281,X282,X283,X284)),X281))
| c_Fun_Oinj__on(X284,X283,X282,X281) )
& ( hBOOL(hAPP(hAPP(c_member(X284),esk10_4(X281,X282,X283,X284)),X281))
| c_Fun_Oinj__on(X284,X283,X282,X281) )
& ( hAPP(X282,esk9_4(X281,X282,X283,X284)) = hAPP(X282,esk10_4(X281,X282,X283,X284))
| c_Fun_Oinj__on(X284,X283,X282,X281) )
& ( esk9_4(X281,X282,X283,X284) != esk10_4(X281,X282,X283,X284)
| c_Fun_Oinj__on(X284,X283,X282,X281) ) ),
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_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_24]) ).
cnf(c_0_29,plain,
c_Finite__Set_Ofinite(tc_prod(tc_prod(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool),X1),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_30,plain,
esk3_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = X1,
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( hAPP(X1,esk9_4(X2,X1,X3,X4)) = hAPP(X1,esk10_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk9_4(X1,X2,X3,X4) != esk10_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__nat]) ).
cnf(c_0_34,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_prod(tc_prod(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool),X3,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,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_30,c_0_31]),c_0_30]),c_0_32]) ).
cnf(c_0_36,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SCT161+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 : n031.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 17:07:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 1.08/1.17 % Version : CSE_E---1.5
% 1.08/1.17 % Problem : theBenchmark.p
% 1.08/1.17 % Proof found
% 1.08/1.17 % SZS status Theorem for theBenchmark.p
% 1.08/1.17 % SZS output start Proof
% See solution above
% 1.08/1.19 % Total time : 0.594000 s
% 1.08/1.19 % SZS output end Proof
% 1.08/1.19 % Total time : 0.617000 s
%------------------------------------------------------------------------------