TSTP Solution File: SCT159+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT159+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 : 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 14:11:22 EDT 2023
% Result : Theorem 3.17s 3.30s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 148
% Syntax : Number of formulae : 217 ( 40 unt; 124 typ; 0 def)
% Number of atoms : 192 ( 33 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 172 ( 73 ~; 68 |; 11 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 281 ( 115 >; 166 *; 0 +; 0 <<)
% Number of predicates : 40 ( 38 usr; 2 prp; 0-6 aty)
% Number of functors : 86 ( 86 usr; 8 con; 0-8 aty)
% Number of variables : 172 ( 36 sgn; 91 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_25,type,
c_Finite__Set_Ocard: ( $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_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_29,type,
hBOOL: $i > $o ).
tff(decl_30,type,
class_Orderings_Otop: $i > $o ).
tff(decl_31,type,
c_member: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
class_Groups_Ozero: $i > $o ).
tff(decl_33,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_34,type,
v_F: $i ).
tff(decl_35,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_36,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_37,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_38,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_39,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(decl_40,type,
tc_Option_Ooption: $i > $i ).
tff(decl_41,type,
tc_sum: ( $i * $i ) > $i ).
tff(decl_42,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_43,type,
tc_Nat_Onat: $i ).
tff(decl_44,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_45,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_46,type,
c_Fun_Othe__inv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_47,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_48,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_49,type,
class_Orderings_Obot: $i > $o ).
tff(decl_50,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_51,type,
class_Orderings_Oord: $i > $o ).
tff(decl_52,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_53,type,
c_fequal: $i > $i ).
tff(decl_54,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_SetInterval_Oord_OatMost: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
c_SetInterval_Oord_OatLeast: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
c_SetInterval_Oord_OlessThan: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
c_SetInterval_Oord_OgreaterThan: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
c_SetInterval_Oord_OatLeastAtMost: ( $i * $i * $i * $i ) > $i ).
tff(decl_60,type,
c_SetInterval_Oord_OgreaterThanLessThan: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
c_SetInterval_Oord_OgreaterThanAtMost: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
c_SetInterval_Oord_OatLeastLessThan: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
c_Nat_OSuc: $i ).
tff(decl_64,type,
c_Finite__Set_Ofolding__one__idem: ( $i * $i * $i ) > $o ).
tff(decl_65,type,
c_Finite__Set_Ofolding__image__simple__idem: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_66,type,
c_SetInterval_Oord__class_OgreaterThan: ( $i * $i ) > $i ).
tff(decl_67,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_70,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_71,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_72,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_73,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_74,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_75,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_76,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_77,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_78,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_79,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_80,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_81,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_82,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_83,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_84,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_85,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_86,type,
c_SetInterval_Oord__class_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_88,type,
c_fTrue: $i ).
tff(decl_89,type,
c_HOL_Obool_Obool__size: $i > $i ).
tff(decl_90,type,
tc_Product__Type_Ounit: $i ).
tff(decl_91,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_92,type,
class_Groups_Oone: $i > $o ).
tff(decl_93,type,
c_fFalse: $i ).
tff(decl_94,type,
c_Int_Oring__1__class_OInts: $i > $i ).
tff(decl_95,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_96,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_97,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_Set_Othe__elem: ( $i * $i ) > $i ).
tff(decl_99,type,
c_Finite__Set_Ofolding__one: ( $i * $i * $i ) > $o ).
tff(decl_100,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
v_thesis____: $o ).
tff(decl_102,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_103,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
esk5_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_108,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_109,type,
esk8_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_110,type,
esk9_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_111,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk12_1: $i > $i ).
tff(decl_114,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk14_1: $i > $i ).
tff(decl_116,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk18_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_120,type,
esk19_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk22_1: $i > $i ).
tff(decl_124,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk24_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
esk25_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_127,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
esk30_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_132,type,
esk31_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
esk32_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_134,type,
esk33_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_135,type,
esk34_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_137,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_140,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_141,type,
esk40_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_142,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk44_3: ( $i * $i * $i ) > $i ).
fof(fact_finite,axiom,
! [X4,X6] :
( class_Finite__Set_Ofinite(X6)
=> c_Finite__Set_Ofinite(X6,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_order__trans,axiom,
! [X23,X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X23)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_Suc__le__mono,axiom,
! [X34,X29] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),hAPP(c_Nat_OSuc,X34))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_card__mono,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X6,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_card__UNIV__unit,axiom,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_subset__UNIV,axiom,
! [X4,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
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_not__less__eq__eq,axiom,
! [X29,X34] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_le0,axiom,
! [X25] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_card__seteq,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X7),c_Finite__Set_Ocard(X6,X4))
=> X4 = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_mem__def,axiom,
! [X4,X8,X6] :
( c_member(X6,X8,X4)
<=> hBOOL(hAPP(X4,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_top1I,axiom,
! [X8,X6] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_eq__mem,axiom,
! [X9,X8,X6] :
( c_member(X6,X8,c_fequal(X9))
<=> X8 = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(help_c__fequal__1,axiom,
! [X9,X8] :
( ~ hBOOL(hAPP(c_fequal(X8),X9))
| X8 = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_less__le__not__le,axiom,
! [X9,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(fact_bot__apply,axiom,
! [X8,X5,X6] :
( class_Orderings_Obot(X6)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,X6)),X8) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_card__gt__0__iff,axiom,
! [X4,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X6,X4))
<=> ( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
& c_Finite__Set_Ofinite(X6,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(fact_emptyE,axiom,
! [X13,X6] : ~ c_member(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(help_c__fequal__2,axiom,
! [X9,X8] :
( X8 != X9
| hBOOL(hAPP(c_fequal(X8),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(c_0_24,plain,
! [X114,X115] :
( ~ class_Finite__Set_Ofinite(X115)
| c_Finite__Set_Ofinite(X115,X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(c_0_25,plain,
! [X382,X383,X384,X385] :
( ~ class_Orderings_Opreorder(X385)
| ~ c_Orderings_Oord__class_Oless__eq(X385,X384,X383)
| ~ c_Orderings_Oord__class_Oless__eq(X385,X383,X382)
| c_Orderings_Oord__class_Oless__eq(X385,X384,X382) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(c_0_26,plain,
! [X895,X896] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X896),hAPP(c_Nat_OSuc,X895))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X896,X895) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X896,X895)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X896),hAPP(c_Nat_OSuc,X895)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(c_0_27,plain,
! [X431,X432,X433] :
( ~ c_Finite__Set_Ofinite(X433,X432)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X433,tc_HOL_Obool),X431,X432)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X433,X431),c_Finite__Set_Ocard(X433,X432)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
cnf(c_0_28,plain,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]) ).
cnf(c_0_29,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
fof(c_0_30,plain,
! [X719,X720] : c_Orderings_Oord__class_Oless__eq(tc_fun(X720,tc_HOL_Obool),X719,c_Orderings_Otop__class_Otop(tc_fun(X720,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
cnf(c_0_31,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
fof(c_0_33,plain,
! [X29,X34] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
cnf(c_0_34,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(c_0_37,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_41,plain,
! [X498] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X498),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(c_0_42,plain,
! [X891,X892] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X892,X891)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X891),X892) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X891),X892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X892,X891) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_43,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_44,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),c_0_40])]) ).
cnf(c_0_45,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_46,plain,
! [X428,X429,X430] :
( ~ c_Finite__Set_Ofinite(X430,X429)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X430,tc_HOL_Obool),X428,X429)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X430,X429),c_Finite__Set_Ocard(X430,X428))
| X428 = X429 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
cnf(c_0_47,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1),hAPP(c_Nat_OSuc,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
fof(c_0_49,plain,
! [X576,X577,X578] :
( ( ~ c_member(X578,X577,X576)
| hBOOL(hAPP(X576,X577)) )
& ( ~ hBOOL(hAPP(X576,X577))
| c_member(X578,X577,X576) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(c_0_50,plain,
! [X81,X82] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X82,tc_HOL_Obool)),X81)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_51,plain,
( X3 = X2
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_36])]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_54,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,plain,
( c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_38]),c_0_39])]),c_0_40])]) ).
cnf(c_0_57,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_58,plain,
! [X245,X246,X247] :
( ( ~ c_member(X247,X246,c_fequal(X245))
| X246 = X245 )
& ( X246 != X245
| c_member(X247,X246,c_fequal(X245)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
cnf(c_0_59,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
( c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1),X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_61,plain,
! [X9,X8] :
( ~ hBOOL(hAPP(c_fequal(X8),X9))
| X8 = X9 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
cnf(c_0_62,plain,
( X2 = X3
| ~ c_member(X1,X2,c_fequal(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1),X2)
| c_member(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_64,plain,
! [X9,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_65,plain,
! [X1670,X1671] :
( ~ hBOOL(hAPP(c_fequal(X1671),X1670))
| X1671 = X1670 ),
inference(variable_rename,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
hBOOL(c_fTrue),
inference(split_conjunct,[status(thm)],[help_c__fTrue__1]) ).
cnf(c_0_67,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_fequal(X2)),X3) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_68,plain,
! [X203,X204,X205] :
( ~ class_Orderings_Obot(X205)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X204,X205)),X203) = c_Orderings_Obot__class_Obot(X205) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(c_0_69,plain,
! [X233,X234,X235] :
( ( c_Orderings_Oord__class_Oless__eq(X235,X234,X233)
| ~ c_Orderings_Oord__class_Oless(X235,X234,X233)
| ~ class_Orderings_Opreorder(X235) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X235,X233,X234)
| ~ c_Orderings_Oord__class_Oless(X235,X234,X233)
| ~ class_Orderings_Opreorder(X235) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X235,X234,X233)
| c_Orderings_Oord__class_Oless__eq(X235,X233,X234)
| c_Orderings_Oord__class_Oless(X235,X234,X233)
| ~ class_Orderings_Opreorder(X235) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
fof(c_0_70,plain,
! [X471,X472] :
( ( X471 != c_Orderings_Obot__class_Obot(tc_fun(X472,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X472,X471)) )
& ( c_Finite__Set_Ofinite(X472,X471)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X472,X471)) )
& ( X471 = c_Orderings_Obot__class_Obot(tc_fun(X472,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X472,X471)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X472,X471)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).
fof(c_0_71,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(c_0_72,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_fequal(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_fequal(c_fTrue)),X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_74,plain,
! [X13,X6] : ~ c_member(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
cnf(c_0_75,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
fof(c_0_77,plain,
! [X1672,X1673] :
( X1673 != X1672
| hBOOL(hAPP(c_fequal(X1673),X1672)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
cnf(c_0_78,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_fequal(c_fTrue)),X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_82,plain,
! [X514,X515] : ~ c_member(X515,X514,c_Orderings_Obot__class_Obot(tc_fun(X515,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[c_0_74]) ).
cnf(c_0_83,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,plain,
( hBOOL(hAPP(c_fequal(X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_85,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_36])]) ).
cnf(c_0_86,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_fequal(c_fTrue)),X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_73]) ).
cnf(c_0_87,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_88,plain,
( c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_54,c_0_83]) ).
cnf(c_0_89,plain,
hBOOL(hAPP(c_fequal(X1),X1)),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_90,plain,
c_fequal(c_fTrue) = c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_40])]) ).
cnf(c_0_91,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_83]),c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT159+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n003.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 14:59:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 3.17/3.30 % Version : CSE_E---1.5
% 3.17/3.30 % Problem : theBenchmark.p
% 3.17/3.30 % Proof found
% 3.17/3.30 % SZS status Theorem for theBenchmark.p
% 3.17/3.30 % SZS output start Proof
% See solution above
% 3.27/3.31 % Total time : 2.717000 s
% 3.27/3.31 % SZS output end Proof
% 3.27/3.31 % Total time : 2.736000 s
%------------------------------------------------------------------------------