TSTP Solution File: SCT163+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SCT163+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Mon Mar 7 00:23:59 EST 2011
% Result : Theorem 39.84s
% Output : Solution 39.84s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP13309/SCT163+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% WARNING: TreeLimitedRun lost 0.50s, total lost is 0.50s
% found
% SZS status THM for /tmp/SystemOnTPTP13309/SCT163+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP13309/SCT163+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 13433
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% PrfWatch: 3.92 CPU 4.01 WC
% PrfWatch: 5.91 CPU 6.02 WC
% PrfWatch: 7.90 CPU 8.02 WC
% PrfWatch: 9.89 CPU 10.03 WC
% PrfWatch: 11.88 CPU 12.03 WC
% PrfWatch: 13.87 CPU 14.04 WC
% PrfWatch: 15.86 CPU 16.04 WC
% # Preprocessing time : 0.120 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 17.84 CPU 18.05 WC
% PrfWatch: 19.84 CPU 20.05 WC
% PrfWatch: 21.83 CPU 22.06 WC
% PrfWatch: 23.82 CPU 24.06 WC
% # SZS output start CNFRefutation.
% fof(10, axiom,![X11]:![X7]:![X9]:(hBOOL(hAPP(hAPP(c_member(X9),X7),X11))<=>hBOOL(hAPP(X11,X7))),file('/tmp/SRASS.s.p', fact_mem__def)).
% fof(28, axiom,![X16]:(~(X16=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16))),file('/tmp/SRASS.s.p', fact_neq0__conv)).
% fof(67, axiom,![X11]:![X2]:![X28]:![X9]:(c_Fun_Oinj__on(X9,X28,X2,X11)<=>![X3]:(hBOOL(hAPP(hAPP(c_member(X9),X3),X11))=>![X36]:(hBOOL(hAPP(hAPP(c_member(X9),X36),X11))=>(hAPP(X2,X3)=hAPP(X2,X36)=>X3=X36)))),file('/tmp/SRASS.s.p', fact_inj__on__def)).
% fof(74, axiom,![X11]:![X14]:![X9]:(hBOOL(hAPP(hAPP(c_member(X9),X14),X11))=>c_Set_Oinsert(X9,X14,X11)=X11),file('/tmp/SRASS.s.p', fact_insert__absorb)).
% fof(104, axiom,![X12]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X12)),file('/tmp/SRASS.s.p', fact_le__refl)).
% fof(108, axiom,![X16]:![X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X16)))<=>(X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X41]:(X17=hAPP(c_Nat_OSuc,X41)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X16))))),file('/tmp/SRASS.s.p', fact_less__Suc__eq__0__disj)).
% fof(110, axiom,![X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16))<=>?[X42]:X16=hAPP(c_Nat_OSuc,X42)),file('/tmp/SRASS.s.p', fact_gr0__conv__Suc)).
% fof(122, axiom,![X10]:![X14]:![X9]:hBOOL(hAPP(hAPP(c_member(X9),X14),c_Set_Oinsert(X9,X14,X10))),file('/tmp/SRASS.s.p', fact_insertI1)).
% fof(125, axiom,![X16]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X16)),file('/tmp/SRASS.s.p', fact_less__eq__Suc__le__raw)).
% fof(146, axiom,![X7]:![X11]:![X6]:![X9]:(hBOOL(hAPP(c_Set_Oinsert(X9,X6,X11),X7))<=>(X6=X7|hBOOL(hAPP(X11,X7)))),file('/tmp/SRASS.s.p', fact_insert__code)).
% fof(149, axiom,![X20]:![X33]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X33)))),file('/tmp/SRASS.s.p', fact_less__add__Suc2)).
% fof(180, axiom,![X50]:![X51]:(hAPP(c_Nat_OSuc,X51)=hAPP(c_Nat_OSuc,X50)<=>X51=X50),file('/tmp/SRASS.s.p', fact_nat_Oinject)).
% fof(204, axiom,![X62]:![X9]:hAPP(c_COMBI(X9),X62)=X62,file('/tmp/SRASS.s.p', help_c__COMBI__1)).
% fof(206, axiom,![X11]:![X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X9,X11)))=>c_Finite__Set_Ofinite(X9,X11)),file('/tmp/SRASS.s.p', fact_card__ge__0__finite)).
% fof(217, axiom,![X11]:![X9]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),file('/tmp/SRASS.s.p', fact_subset__UNIV)).
% fof(248, axiom,![X7]:![X9]:hBOOL(hAPP(hAPP(c_member(X9),X7),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),file('/tmp/SRASS.s.p', fact_UNIV__I)).
% fof(251, axiom,c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),file('/tmp/SRASS.s.p', fact_One__nat__def)).
% fof(253, axiom,![X12]:hAPP(c_Nat_OSuc,X12)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),file('/tmp/SRASS.s.p', fact_Suc__eq__plus1)).
% fof(298, axiom,![X20]:~(hAPP(c_Nat_OSuc,X20)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),file('/tmp/SRASS.s.p', fact_Suc__neq__Zero)).
% fof(374, axiom,![X72]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X72),file('/tmp/SRASS.s.p', fact_inj__Suc)).
% fof(403, axiom,![X13]:![X2]:![X28]:![X9]:(c_Fun_Oinj__on(X9,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_member(X28),X13),c_Set_Oimage(X9,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))))<=>?[X3]:(X13=hAPP(X2,X3)&![X79]:(X13=hAPP(X2,X79)=>X79=X3)))),file('/tmp/SRASS.s.p', fact_range__ex1__eq)).
% fof(422, axiom,![X10]:![X11]:![X9]:(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))=>(c_Finite__Set_Ofinite(X9,X10)=>c_Finite__Set_Ofinite(X9,X11))),file('/tmp/SRASS.s.p', fact_finite__subset)).
% fof(499, 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('/tmp/SRASS.s.p', fact_card__UNIV__unit)).
% fof(514, 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('/tmp/SRASS.s.p', fact_finite__UNIV__inj__surj)).
% fof(522, axiom,![X11]:![X2]:![X28]:![X9]:(c_Finite__Set_Ofinite(X9,c_Set_Oimage(X28,X9,X2,X11))=>(c_Fun_Oinj__on(X28,X9,X2,X11)=>c_Finite__Set_Ofinite(X28,X11))),file('/tmp/SRASS.s.p', fact_finite__imageD)).
% fof(647, plain,![X11]:![X7]:![X9]:((~(hBOOL(hAPP(hAPP(c_member(X9),X7),X11)))|hBOOL(hAPP(X11,X7)))&(~(hBOOL(hAPP(X11,X7)))|hBOOL(hAPP(hAPP(c_member(X9),X7),X11)))),inference(fof_nnf,[status(thm)],[10])).
% fof(648, plain,![X12]:![X13]:![X14]:((~(hBOOL(hAPP(hAPP(c_member(X14),X13),X12)))|hBOOL(hAPP(X12,X13)))&(~(hBOOL(hAPP(X12,X13)))|hBOOL(hAPP(hAPP(c_member(X14),X13),X12)))),inference(variable_rename,[status(thm)],[647])).
% cnf(649,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X3,X2))),inference(split_conjunct,[status(thm)],[648])).
% fof(729, plain,![X16]:((X16=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16)))|~(X16=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),inference(fof_nnf,[status(thm)],[28])).
% fof(730, plain,![X17]:((X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)))|~(X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),inference(variable_rename,[status(thm)],[729])).
% cnf(732,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(split_conjunct,[status(thm)],[730])).
% fof(867, plain,![X11]:![X2]:![X28]:![X9]:((~(c_Fun_Oinj__on(X9,X28,X2,X11))|![X3]:(~(hBOOL(hAPP(hAPP(c_member(X9),X3),X11)))|![X36]:(~(hBOOL(hAPP(hAPP(c_member(X9),X36),X11)))|(~(hAPP(X2,X3)=hAPP(X2,X36))|X3=X36))))&(?[X3]:(hBOOL(hAPP(hAPP(c_member(X9),X3),X11))&?[X36]:(hBOOL(hAPP(hAPP(c_member(X9),X36),X11))&(hAPP(X2,X3)=hAPP(X2,X36)&~(X3=X36))))|c_Fun_Oinj__on(X9,X28,X2,X11))),inference(fof_nnf,[status(thm)],[67])).
% fof(868, plain,![X37]:![X38]:![X39]:![X40]:((~(c_Fun_Oinj__on(X40,X39,X38,X37))|![X41]:(~(hBOOL(hAPP(hAPP(c_member(X40),X41),X37)))|![X42]:(~(hBOOL(hAPP(hAPP(c_member(X40),X42),X37)))|(~(hAPP(X38,X41)=hAPP(X38,X42))|X41=X42))))&(?[X43]:(hBOOL(hAPP(hAPP(c_member(X40),X43),X37))&?[X44]:(hBOOL(hAPP(hAPP(c_member(X40),X44),X37))&(hAPP(X38,X43)=hAPP(X38,X44)&~(X43=X44))))|c_Fun_Oinj__on(X40,X39,X38,X37))),inference(variable_rename,[status(thm)],[867])).
% fof(869, plain,![X37]:![X38]:![X39]:![X40]:((~(c_Fun_Oinj__on(X40,X39,X38,X37))|![X41]:(~(hBOOL(hAPP(hAPP(c_member(X40),X41),X37)))|![X42]:(~(hBOOL(hAPP(hAPP(c_member(X40),X42),X37)))|(~(hAPP(X38,X41)=hAPP(X38,X42))|X41=X42))))&((hBOOL(hAPP(hAPP(c_member(X40),esk3_4(X37,X38,X39,X40)),X37))&(hBOOL(hAPP(hAPP(c_member(X40),esk4_4(X37,X38,X39,X40)),X37))&(hAPP(X38,esk3_4(X37,X38,X39,X40))=hAPP(X38,esk4_4(X37,X38,X39,X40))&~(esk3_4(X37,X38,X39,X40)=esk4_4(X37,X38,X39,X40)))))|c_Fun_Oinj__on(X40,X39,X38,X37))),inference(skolemize,[status(esa)],[868])).
% fof(870, plain,![X37]:![X38]:![X39]:![X40]:![X41]:![X42]:((((~(hBOOL(hAPP(hAPP(c_member(X40),X42),X37)))|(~(hAPP(X38,X41)=hAPP(X38,X42))|X41=X42))|~(hBOOL(hAPP(hAPP(c_member(X40),X41),X37))))|~(c_Fun_Oinj__on(X40,X39,X38,X37)))&((hBOOL(hAPP(hAPP(c_member(X40),esk3_4(X37,X38,X39,X40)),X37))&(hBOOL(hAPP(hAPP(c_member(X40),esk4_4(X37,X38,X39,X40)),X37))&(hAPP(X38,esk3_4(X37,X38,X39,X40))=hAPP(X38,esk4_4(X37,X38,X39,X40))&~(esk3_4(X37,X38,X39,X40)=esk4_4(X37,X38,X39,X40)))))|c_Fun_Oinj__on(X40,X39,X38,X37))),inference(shift_quantors,[status(thm)],[869])).
% fof(871, plain,![X37]:![X38]:![X39]:![X40]:![X41]:![X42]:((((~(hBOOL(hAPP(hAPP(c_member(X40),X42),X37)))|(~(hAPP(X38,X41)=hAPP(X38,X42))|X41=X42))|~(hBOOL(hAPP(hAPP(c_member(X40),X41),X37))))|~(c_Fun_Oinj__on(X40,X39,X38,X37)))&((hBOOL(hAPP(hAPP(c_member(X40),esk3_4(X37,X38,X39,X40)),X37))|c_Fun_Oinj__on(X40,X39,X38,X37))&((hBOOL(hAPP(hAPP(c_member(X40),esk4_4(X37,X38,X39,X40)),X37))|c_Fun_Oinj__on(X40,X39,X38,X37))&((hAPP(X38,esk3_4(X37,X38,X39,X40))=hAPP(X38,esk4_4(X37,X38,X39,X40))|c_Fun_Oinj__on(X40,X39,X38,X37))&(~(esk3_4(X37,X38,X39,X40)=esk4_4(X37,X38,X39,X40))|c_Fun_Oinj__on(X40,X39,X38,X37)))))),inference(distribute,[status(thm)],[870])).
% cnf(872,plain,(c_Fun_Oinj__on(X1,X2,X3,X4)|esk3_4(X4,X3,X2,X1)!=esk4_4(X4,X3,X2,X1)),inference(split_conjunct,[status(thm)],[871])).
% cnf(873,plain,(c_Fun_Oinj__on(X1,X2,X3,X4)|hAPP(X3,esk3_4(X4,X3,X2,X1))=hAPP(X3,esk4_4(X4,X3,X2,X1))),inference(split_conjunct,[status(thm)],[871])).
% fof(902, plain,![X11]:![X14]:![X9]:(~(hBOOL(hAPP(hAPP(c_member(X9),X14),X11)))|c_Set_Oinsert(X9,X14,X11)=X11),inference(fof_nnf,[status(thm)],[74])).
% fof(903, plain,![X15]:![X16]:![X17]:(~(hBOOL(hAPP(hAPP(c_member(X17),X16),X15)))|c_Set_Oinsert(X17,X16,X15)=X15),inference(variable_rename,[status(thm)],[902])).
% cnf(904,plain,(c_Set_Oinsert(X1,X2,X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))),inference(split_conjunct,[status(thm)],[903])).
% fof(1010, plain,![X13]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13),X13)),inference(variable_rename,[status(thm)],[104])).
% cnf(1011,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1))),inference(split_conjunct,[status(thm)],[1010])).
% fof(1021, plain,![X16]:![X17]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X16))))|(X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X41]:(X17=hAPP(c_Nat_OSuc,X41)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X16)))))&((~(X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&![X41]:(~(X17=hAPP(c_Nat_OSuc,X41))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X16)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X16))))),inference(fof_nnf,[status(thm)],[108])).
% fof(1022, plain,![X42]:![X43]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))|(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X44]:(X43=hAPP(c_Nat_OSuc,X44)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X42)))))&((~(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&![X45]:(~(X43=hAPP(c_Nat_OSuc,X45))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X42)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))),inference(variable_rename,[status(thm)],[1021])).
% fof(1023, plain,![X42]:![X43]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))|(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(X43=hAPP(c_Nat_OSuc,esk6_2(X42,X43))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk6_2(X42,X43)),X42)))))&((~(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&![X45]:(~(X43=hAPP(c_Nat_OSuc,X45))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X42)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))),inference(skolemize,[status(esa)],[1022])).
% fof(1024, plain,![X42]:![X43]:![X45]:((((~(X43=hAPP(c_Nat_OSuc,X45))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X42))))&~(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))|(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(X43=hAPP(c_Nat_OSuc,esk6_2(X42,X43))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk6_2(X42,X43)),X42)))))),inference(shift_quantors,[status(thm)],[1023])).
% fof(1025, plain,![X42]:![X43]:![X45]:((((~(X43=hAPP(c_Nat_OSuc,X45))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X42))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))&(~(X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42)))))&(((X43=hAPP(c_Nat_OSuc,esk6_2(X42,X43))|X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk6_2(X42,X43)),X42))|X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X42))))))),inference(distribute,[status(thm)],[1024])).
% cnf(1027,plain,(X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=hAPP(c_Nat_OSuc,esk6_2(X2,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))),inference(split_conjunct,[status(thm)],[1025])).
% fof(1034, plain,![X16]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16)))|?[X42]:X16=hAPP(c_Nat_OSuc,X42))&(![X42]:~(X16=hAPP(c_Nat_OSuc,X42))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16)))),inference(fof_nnf,[status(thm)],[110])).
% fof(1035, plain,![X43]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)))|?[X44]:X43=hAPP(c_Nat_OSuc,X44))&(![X45]:~(X43=hAPP(c_Nat_OSuc,X45))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)))),inference(variable_rename,[status(thm)],[1034])).
% fof(1036, plain,![X43]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)))|X43=hAPP(c_Nat_OSuc,esk7_1(X43)))&(![X45]:~(X43=hAPP(c_Nat_OSuc,X45))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)))),inference(skolemize,[status(esa)],[1035])).
% fof(1037, plain,![X43]:![X45]:((~(X43=hAPP(c_Nat_OSuc,X45))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)))|X43=hAPP(c_Nat_OSuc,esk7_1(X43)))),inference(shift_quantors,[status(thm)],[1036])).
% cnf(1038,plain,(X1=hAPP(c_Nat_OSuc,esk7_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)],[1037])).
% fof(1079, plain,![X15]:![X16]:![X17]:hBOOL(hAPP(hAPP(c_member(X17),X16),c_Set_Oinsert(X17,X16,X15))),inference(variable_rename,[status(thm)],[122])).
% cnf(1080,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3)))),inference(split_conjunct,[status(thm)],[1079])).
% fof(1103, plain,![X17]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),inference(variable_rename,[status(thm)],[125])).
% cnf(1104,plain,(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1))),inference(split_conjunct,[status(thm)],[1103])).
% fof(1174, plain,![X7]:![X11]:![X6]:![X9]:((~(hBOOL(hAPP(c_Set_Oinsert(X9,X6,X11),X7)))|(X6=X7|hBOOL(hAPP(X11,X7))))&((~(X6=X7)&~(hBOOL(hAPP(X11,X7))))|hBOOL(hAPP(c_Set_Oinsert(X9,X6,X11),X7)))),inference(fof_nnf,[status(thm)],[146])).
% fof(1175, plain,![X12]:![X13]:![X14]:![X15]:((~(hBOOL(hAPP(c_Set_Oinsert(X15,X14,X13),X12)))|(X14=X12|hBOOL(hAPP(X13,X12))))&((~(X14=X12)&~(hBOOL(hAPP(X13,X12))))|hBOOL(hAPP(c_Set_Oinsert(X15,X14,X13),X12)))),inference(variable_rename,[status(thm)],[1174])).
% fof(1176, plain,![X12]:![X13]:![X14]:![X15]:((~(hBOOL(hAPP(c_Set_Oinsert(X15,X14,X13),X12)))|(X14=X12|hBOOL(hAPP(X13,X12))))&((~(X14=X12)|hBOOL(hAPP(c_Set_Oinsert(X15,X14,X13),X12)))&(~(hBOOL(hAPP(X13,X12)))|hBOOL(hAPP(c_Set_Oinsert(X15,X14,X13),X12))))),inference(distribute,[status(thm)],[1175])).
% cnf(1178,plain,(hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))|X2!=X4),inference(split_conjunct,[status(thm)],[1176])).
% fof(1186, plain,![X34]:![X35]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X35)))),inference(variable_rename,[status(thm)],[149])).
% cnf(1187,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))))),inference(split_conjunct,[status(thm)],[1186])).
% fof(1307, plain,![X50]:![X51]:((~(hAPP(c_Nat_OSuc,X51)=hAPP(c_Nat_OSuc,X50))|X51=X50)&(~(X51=X50)|hAPP(c_Nat_OSuc,X51)=hAPP(c_Nat_OSuc,X50))),inference(fof_nnf,[status(thm)],[180])).
% fof(1308, plain,![X52]:![X53]:((~(hAPP(c_Nat_OSuc,X53)=hAPP(c_Nat_OSuc,X52))|X53=X52)&(~(X53=X52)|hAPP(c_Nat_OSuc,X53)=hAPP(c_Nat_OSuc,X52))),inference(variable_rename,[status(thm)],[1307])).
% cnf(1310,plain,(X1=X2|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2)),inference(split_conjunct,[status(thm)],[1308])).
% fof(1401, plain,![X63]:![X64]:hAPP(c_COMBI(X64),X63)=X63,inference(variable_rename,[status(thm)],[204])).
% cnf(1402,plain,(hAPP(c_COMBI(X1),X2)=X2),inference(split_conjunct,[status(thm)],[1401])).
% fof(1405, plain,![X11]:![X9]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X9,X11))))|c_Finite__Set_Ofinite(X9,X11)),inference(fof_nnf,[status(thm)],[206])).
% fof(1406, plain,![X12]:![X13]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X13,X12))))|c_Finite__Set_Ofinite(X13,X12)),inference(variable_rename,[status(thm)],[1405])).
% cnf(1407,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2)))),inference(split_conjunct,[status(thm)],[1406])).
% fof(1428, plain,![X12]:![X13]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X12),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[217])).
% cnf(1429,plain,(hBOOL(hAPP(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)],[1428])).
% fof(1502, plain,![X10]:![X11]:hBOOL(hAPP(hAPP(c_member(X11),X10),c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[248])).
% cnf(1503,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),inference(split_conjunct,[status(thm)],[1502])).
% cnf(1510,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)],[251])).
% fof(1513, plain,![X13]:hAPP(c_Nat_OSuc,X13)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)),inference(variable_rename,[status(thm)],[253])).
% cnf(1514,plain,(hAPP(c_Nat_OSuc,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),inference(split_conjunct,[status(thm)],[1513])).
% fof(1654, plain,![X21]:~(hAPP(c_Nat_OSuc,X21)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(variable_rename,[status(thm)],[298])).
% cnf(1655,plain,(hAPP(c_Nat_OSuc,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(split_conjunct,[status(thm)],[1654])).
% fof(1911, plain,![X73]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X73),inference(variable_rename,[status(thm)],[374])).
% cnf(1912,plain,(c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)),inference(split_conjunct,[status(thm)],[1911])).
% fof(2008, plain,![X13]:![X2]:![X28]:![X9]:(~(c_Fun_Oinj__on(X9,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))))|((~(hBOOL(hAPP(hAPP(c_member(X28),X13),c_Set_Oimage(X9,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))))))|?[X3]:(X13=hAPP(X2,X3)&![X79]:(~(X13=hAPP(X2,X79))|X79=X3)))&(![X3]:(~(X13=hAPP(X2,X3))|?[X79]:(X13=hAPP(X2,X79)&~(X79=X3)))|hBOOL(hAPP(hAPP(c_member(X28),X13),c_Set_Oimage(X9,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))))))),inference(fof_nnf,[status(thm)],[403])).
% fof(2009, plain,![X80]:![X81]:![X82]:![X83]:(~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))|((~(hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|?[X84]:(X80=hAPP(X81,X84)&![X85]:(~(X80=hAPP(X81,X85))|X85=X84)))&(![X86]:(~(X80=hAPP(X81,X86))|?[X87]:(X80=hAPP(X81,X87)&~(X87=X86)))|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))))),inference(variable_rename,[status(thm)],[2008])).
% fof(2010, plain,![X80]:![X81]:![X82]:![X83]:(~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))|((~(hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|(X80=hAPP(X81,esk42_4(X80,X81,X82,X83))&![X85]:(~(X80=hAPP(X81,X85))|X85=esk42_4(X80,X81,X82,X83))))&(![X86]:(~(X80=hAPP(X81,X86))|(X80=hAPP(X81,esk43_5(X80,X81,X82,X83,X86))&~(esk43_5(X80,X81,X82,X83,X86)=X86)))|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))))),inference(skolemize,[status(esa)],[2009])).
% fof(2011, plain,![X80]:![X81]:![X82]:![X83]:![X85]:![X86]:((((~(X80=hAPP(X81,X86))|(X80=hAPP(X81,esk43_5(X80,X81,X82,X83,X86))&~(esk43_5(X80,X81,X82,X83,X86)=X86)))|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))&(((~(X80=hAPP(X81,X85))|X85=esk42_4(X80,X81,X82,X83))&X80=hAPP(X81,esk42_4(X80,X81,X82,X83)))|~(hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))))|~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))),inference(shift_quantors,[status(thm)],[2010])).
% fof(2012, plain,![X80]:![X81]:![X82]:![X83]:![X85]:![X86]:(((((X80=hAPP(X81,esk43_5(X80,X81,X82,X83,X86))|~(X80=hAPP(X81,X86)))|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))&(((~(esk43_5(X80,X81,X82,X83,X86)=X86)|~(X80=hAPP(X81,X86)))|hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))|~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))&((((~(X80=hAPP(X81,X85))|X85=esk42_4(X80,X81,X82,X83))|~(hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))))|~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))&((X80=hAPP(X81,esk42_4(X80,X81,X82,X83))|~(hBOOL(hAPP(hAPP(c_member(X82),X80),c_Set_Oimage(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool)))))))|~(c_Fun_Oinj__on(X83,X82,X81,c_Orderings_Otop__class_Otop(tc_fun(X83,tc_HOL_Obool))))))),inference(distribute,[status(thm)],[2011])).
% cnf(2013,plain,(X4=hAPP(X3,esk42_4(X4,X3,X2,X1))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))),inference(split_conjunct,[status(thm)],[2012])).
% fof(2075, plain,![X10]:![X11]:![X9]:(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)))|(~(c_Finite__Set_Ofinite(X9,X10))|c_Finite__Set_Ofinite(X9,X11))),inference(fof_nnf,[status(thm)],[422])).
% fof(2076, plain,![X12]:![X13]:![X14]:(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X13),X12)))|(~(c_Finite__Set_Ofinite(X14,X12))|c_Finite__Set_Ofinite(X14,X13))),inference(variable_rename,[status(thm)],[2075])).
% cnf(2077,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X1,X3)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))),inference(split_conjunct,[status(thm)],[2076])).
% cnf(2318,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)],[499])).
% fof(2361, plain,![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)))),inference(fof_nnf,[status(thm)],[514])).
% fof(2362, plain,![X10]:![X11]:(~(c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))))|(~(c_Fun_Oinj__on(X11,X11,X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))))|c_Set_Oimage(X11,X11,X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[2361])).
% cnf(2363,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_Fun_Oinj__on(X1,X1,X2,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)))),inference(split_conjunct,[status(thm)],[2362])).
% fof(2387, plain,![X11]:![X2]:![X28]:![X9]:(~(c_Finite__Set_Ofinite(X9,c_Set_Oimage(X28,X9,X2,X11)))|(~(c_Fun_Oinj__on(X28,X9,X2,X11))|c_Finite__Set_Ofinite(X28,X11))),inference(fof_nnf,[status(thm)],[522])).
% fof(2388, plain,![X29]:![X30]:![X31]:![X32]:(~(c_Finite__Set_Ofinite(X32,c_Set_Oimage(X31,X32,X30,X29)))|(~(c_Fun_Oinj__on(X31,X32,X30,X29))|c_Finite__Set_Ofinite(X31,X29))),inference(variable_rename,[status(thm)],[2387])).
% cnf(2389,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Fun_Oinj__on(X1,X3,X4,X2)|~c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2))),inference(split_conjunct,[status(thm)],[2388])).
% cnf(2454,plain,(hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2))),inference(er,[status(thm)],[1178,theory(equality)])).
% cnf(2595,plain,(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(spm,[status(thm)],[1655,1510,theory(equality)])).
% cnf(2603,plain,(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),inference(spm,[status(thm)],[1104,1510,theory(equality)])).
% cnf(2606,plain,(X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)),inference(spm,[status(thm)],[1310,1510,theory(equality)])).
% cnf(2688,plain,(c_Set_Oinsert(X1,X2,X3)=X3|~hBOOL(hAPP(X3,X2))),inference(spm,[status(thm)],[904,649,theory(equality)])).
% cnf(3060,plain,(c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),inference(spm,[status(thm)],[904,1503,theory(equality)])).
% cnf(3070,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))))),inference(spm,[status(thm)],[1187,1514,theory(equality)])).
% cnf(6335,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),inference(spm,[status(thm)],[2077,1429,theory(equality)])).
% cnf(6856,plain,(hAPP(c_COMBI(X1),esk4_4(X2,c_COMBI(X1),X3,X4))=esk3_4(X2,c_COMBI(X1),X3,X4)|c_Fun_Oinj__on(X4,X3,c_COMBI(X1),X2)),inference(spm,[status(thm)],[1402,873,theory(equality)])).
% cnf(7109,plain,(esk4_4(X2,c_COMBI(X1),X3,X4)=esk3_4(X2,c_COMBI(X1),X3,X4)|c_Fun_Oinj__on(X4,X3,c_COMBI(X1),X2)),inference(rw,[status(thm)],[6856,1402,theory(equality)])).
% cnf(25212,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2)))),inference(rw,[status(thm)],[1407,2603,theory(equality)])).
% cnf(25213,plain,(hAPP(c_Nat_OSuc,esk7_1(X1))=X1|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))),inference(rw,[status(thm)],[1038,2603,theory(equality)])).
% cnf(25216,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))),inference(rw,[status(thm)],[732,2603,theory(equality)])).
% cnf(25463,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),inference(spm,[status(thm)],[25212,2318,theory(equality)])).
% cnf(25471,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))|$false),inference(rw,[status(thm)],[25463,1011,theory(equality)])).
% cnf(25472,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))),inference(cn,[status(thm)],[25471,theory(equality)])).
% cnf(25494,plain,(hAPP(c_Nat_OSuc,esk7_1(X1))=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1),inference(spm,[status(thm)],[25213,25216,theory(equality)])).
% cnf(26825,plain,(c_Set_Oinsert(X1,X2,c_Set_Oinsert(X3,X2,X4))=c_Set_Oinsert(X3,X2,X4)),inference(spm,[status(thm)],[2688,2454,theory(equality)])).
% cnf(30951,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1)),inference(spm,[status(thm)],[6335,25472,theory(equality)])).
% cnf(30959,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2)),inference(spm,[status(thm)],[2389,30951,theory(equality)])).
% cnf(37496,plain,(hAPP(c_Nat_OSuc,esk6_2(hAPP(c_Nat_OSuc,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),inference(spm,[status(thm)],[1027,3070,theory(equality)])).
% cnf(37557,plain,(hAPP(c_Nat_OSuc,esk6_2(hAPP(c_Nat_OSuc,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)),inference(sr,[status(thm)],[37496,2595,theory(equality)])).
% cnf(37628,plain,(esk6_2(hAPP(c_Nat_OSuc,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(spm,[status(thm)],[2606,37557,theory(equality)])).
% cnf(37736,plain,(esk6_2(X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1),inference(spm,[status(thm)],[37628,25494,theory(equality)])).
% cnf(46554,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X3,X2,X4)))),inference(spm,[status(thm)],[1080,26825,theory(equality)])).
% cnf(59385,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),inference(spm,[status(thm)],[46554,3060,theory(equality)])).
% cnf(444288,plain,(c_Fun_Oinj__on(X4,X3,c_COMBI(X1),X2)),inference(csr,[status(thm)],[7109,872])).
% cnf(444289,plain,(c_Finite__Set_Ofinite(X1,X2)),inference(spm,[status(thm)],[30959,444288,theory(equality)])).
% cnf(444413,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))|$false|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),inference(rw,[status(thm)],[2363,444289,theory(equality)])).
% cnf(444414,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_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),inference(cn,[status(thm)],[444413,theory(equality)])).
% cnf(448469,plain,(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),inference(spm,[status(thm)],[444414,1912,theory(equality)])).
% cnf(453952,plain,(hAPP(c_Nat_OSuc,esk42_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1|~c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),inference(spm,[status(thm)],[2013,448469,theory(equality)])).
% cnf(454011,plain,(hAPP(c_Nat_OSuc,esk42_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1|$false|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),inference(rw,[status(thm)],[453952,1912,theory(equality)])).
% cnf(454012,plain,(hAPP(c_Nat_OSuc,esk42_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1|$false|$false),inference(rw,[status(thm)],[454011,59385,theory(equality)])).
% cnf(454013,plain,(hAPP(c_Nat_OSuc,esk42_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1),inference(cn,[status(thm)],[454012,theory(equality)])).
% cnf(454123,plain,(X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(spm,[status(thm)],[1655,454013,theory(equality)])).
% cnf(455123,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1),inference(sr,[status(thm)],[37736,454123,theory(equality)])).
% cnf(455124,plain,($false),inference(sr,[status(thm)],[455123,454123,theory(equality)])).
% cnf(455125,plain,($false),455124,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 14458
% # ...of these trivial : 347
% # ...subsumed : 10895
% # ...remaining for further processing: 3216
% # Other redundant clauses eliminated : 2039
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 36
% # Backward-rewritten : 198
% # Generated clauses : 327298
% # ...of the previous two non-trivial : 299881
% # Contextual simplify-reflections : 1447
% # Paramodulations : 325053
% # Factorizations : 23
% # Equation resolutions : 2166
% # Current number of processed clauses: 2289
% # Positive orientable unit clauses: 435
% # Positive unorientable unit clauses: 43
% # Negative unit clauses : 112
% # Non-unit-clauses : 1699
% # Current number of unprocessed clauses: 221893
% # ...number of literals in the above : 708546
% # Clause-clause subsumption calls (NU) : 223464
% # Rec. Clause-clause subsumption calls : 167237
% # Unit Clause-clause subsumption calls : 12547
% # Rewrite failures with RHS unbound : 496
% # Indexed BW rewrite attempts : 13598
% # Indexed BW rewrite successes : 372
% # Backwards rewriting index: 1638 leaves, 2.77+/-8.187 terms/leaf
% # Paramod-from index: 379 leaves, 2.58+/-7.002 terms/leaf
% # Paramod-into index: 1431 leaves, 2.58+/-6.967 terms/leaf
% # -------------------------------------------------
% # User time : 16.238 s
% # System time : 0.483 s
% # Total time : 16.720 s
% # Maximum resident set size: 0 pages
% PrfWatch: 24.37 CPU 25.18 WC
% FINAL PrfWatch: 24.37 CPU 25.18 WC
% SZS output end Solution for /tmp/SystemOnTPTP13309/SCT163+1.tptp
%
%------------------------------------------------------------------------------