TSTP Solution File: SCT162+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SCT162+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 : art05.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 00:22:55 EST 2011
% Result : Theorem 22.76s
% Output : Solution 22.76s
% 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/SystemOnTPTP7640/SCT162+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP7640/SCT162+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP7640/SCT162+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 7764
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% PrfWatch: 3.91 CPU 4.01 WC
% # Preprocessing time : 0.119 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 5.91 CPU 6.02 WC
% # SZS output start CNFRefutation.
% fof(101, axiom,![X1]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),file('/tmp/SRASS.s.p', fact_le__refl)).
% fof(103, axiom,![X6]:![X2]:![X3]:![X4]:(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X3,X2)),X6))<=>(hBOOL(hAPP(hAPP(c_member(X4),X3),X6))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X2),X6)))),file('/tmp/SRASS.s.p', fact_insert__subset)).
% fof(117, axiom,![X23]:![X3]:![X42]:![X4]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(X42,X3)),c_Set_Oimage(X23,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool))))),file('/tmp/SRASS.s.p', fact_rangeI)).
% fof(126, axiom,![X1]:(~(X1=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)),X1))),file('/tmp/SRASS.s.p', fact_gr0I)).
% fof(149, axiom,![X2]:![X4]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),file('/tmp/SRASS.s.p', fact_subset__UNIV)).
% fof(152, axiom,![X2]:![X6]:![X4]:(c_Finite__Set_Ofinite(X4,X6)=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X2),X6))=>c_Finite__Set_Ofinite(X4,X2))),file('/tmp/SRASS.s.p', fact_rev__finite__subset)).
% fof(172, axiom,![X19]:![X37]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X37)))),file('/tmp/SRASS.s.p', fact_less__add__Suc2)).
% fof(205, axiom,![X8]:![X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),hAPP(c_Nat_OSuc,X8)))<=>(X16=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X58]:(X16=hAPP(c_Nat_OSuc,X58)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X58),X8))))),file('/tmp/SRASS.s.p', fact_less__Suc__eq__0__disj)).
% fof(207, axiom,![X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8))<=>?[X43]:X8=hAPP(c_Nat_OSuc,X43)),file('/tmp/SRASS.s.p', fact_gr0__conv__Suc)).
% fof(209, axiom,![X31]:![X42]:![X23]:![X4]:(c_Fun_Oinj__on(X4,X23,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_member(X23),X31),c_Set_Oimage(X4,X23,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))<=>?[X14]:(X31=hAPP(X42,X14)&![X60]:(X31=hAPP(X42,X60)=>X60=X14)))),file('/tmp/SRASS.s.p', fact_range__ex1__eq)).
% fof(230, axiom,![X42]:![X6]:![X23]:![X2]:![X4]:(c_Finite__Set_Ofinite(X4,X2)=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23,tc_HOL_Obool),X6),c_Set_Oimage(X4,X23,X42,X2)))=>c_Finite__Set_Ofinite(X23,X6))),file('/tmp/SRASS.s.p', fact_finite__surj)).
% fof(240, axiom,class_Orderings_Oord(tc_HOL_Obool),file('/tmp/SRASS.s.p', arity_HOL__Obool__Orderings_Oord)).
% fof(246, axiom,![X2]:![X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X4,X2)))=>c_Finite__Set_Ofinite(X4,X2)),file('/tmp/SRASS.s.p', fact_card__ge__0__finite)).
% fof(263, axiom,class_Rings_Ozero__neq__one(tc_Nat_Onat),file('/tmp/SRASS.s.p', arity_Nat__Onat__Rings_Ozero__neq__one)).
% fof(317, axiom,![X19]:~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_OSuc,X19)),file('/tmp/SRASS.s.p', fact_Zero__not__Suc)).
% fof(335, axiom,![X42]:![X4]:![X23]:(c_Set_Oimage(X23,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))<=>![X14]:hAPP(X42,hAPP(c_Hilbert__Choice_Oinv__into(X23,X4,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool)),X42),X14))=X14),file('/tmp/SRASS.s.p', fact_surj__iff__all)).
% fof(348, axiom,![X67]:![X4]:hAPP(c_COMBI(X4),X67)=X67,file('/tmp/SRASS.s.p', help_c__COMBI__1)).
% fof(352, axiom,![X51]:![X42]:![X4]:![X23]:(class_Orderings_Oord(X23)=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X23),X42),X51))<=>![X14]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X23,hAPP(X42,X14)),hAPP(X51,X14))))),file('/tmp/SRASS.s.p', fact_le__fun__def)).
% fof(376, axiom,![X17]:![X18]:(hAPP(c_Nat_OSuc,X18)=hAPP(c_Nat_OSuc,X17)=>X18=X17),file('/tmp/SRASS.s.p', fact_Suc__inject)).
% fof(380, axiom,![X8]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),file('/tmp/SRASS.s.p', fact_less__eq__Suc__le__raw)).
% fof(406, axiom,![X53]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X53),file('/tmp/SRASS.s.p', fact_inj__Suc)).
% fof(407, axiom,![X1]:hAPP(c_Nat_OSuc,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),file('/tmp/SRASS.s.p', fact_Suc__eq__plus1)).
% fof(416, 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(423, axiom,![X2]:![X42]:![X23]:![X15]:![X4]:(hBOOL(hAPP(hAPP(c_member(X4),X15),c_Set_Oimage(X23,X4,X42,X2)))=>hAPP(X42,hAPP(c_Hilbert__Choice_Oinv__into(X23,X4,X2,X42),X15))=X15),file('/tmp/SRASS.s.p', fact_f__inv__into__f)).
% fof(451, axiom,![X42]:![X4]:(c_Finite__Set_Ofinite(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(c_Fun_Oinj__on(X4,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>c_Set_Oimage(X4,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),file('/tmp/SRASS.s.p', fact_finite__UNIV__inj__surj)).
% fof(466, 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(519, axiom,![X4]:(class_Rings_Ozero__neq__one(X4)=>~(c_Groups_Ozero__class_Ozero(X4)=c_Groups_Oone__class_Oone(X4))),file('/tmp/SRASS.s.p', fact_zero__neq__one)).
% fof(982, plain,![X2]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X2)),inference(variable_rename,[status(thm)],[101])).
% cnf(983,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1))),inference(split_conjunct,[status(thm)],[982])).
% fof(989, plain,![X6]:![X2]:![X3]:![X4]:((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X3,X2)),X6)))|(hBOOL(hAPP(hAPP(c_member(X4),X3),X6))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X2),X6))))&((~(hBOOL(hAPP(hAPP(c_member(X4),X3),X6)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X2),X6))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X3,X2)),X6)))),inference(fof_nnf,[status(thm)],[103])).
% fof(990, plain,![X7]:![X8]:![X9]:![X10]:((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X9,X8)),X7)))|(hBOOL(hAPP(hAPP(c_member(X10),X9),X7))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8),X7))))&((~(hBOOL(hAPP(hAPP(c_member(X10),X9),X7)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8),X7))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X9,X8)),X7)))),inference(variable_rename,[status(thm)],[989])).
% fof(991, plain,![X7]:![X8]:![X9]:![X10]:(((hBOOL(hAPP(hAPP(c_member(X10),X9),X7))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X9,X8)),X7))))&(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8),X7))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X9,X8)),X7)))))&((~(hBOOL(hAPP(hAPP(c_member(X10),X9),X7)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8),X7))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X9,X8)),X7)))),inference(distribute,[status(thm)],[990])).
% cnf(994,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3)),X4))),inference(split_conjunct,[status(thm)],[991])).
% fof(1051, plain,![X43]:![X44]:![X45]:![X46]:hBOOL(hAPP(hAPP(c_member(X46),hAPP(X45,X44)),c_Set_Oimage(X43,X46,X45,c_Orderings_Otop__class_Otop(tc_fun(X43,tc_HOL_Obool))))),inference(variable_rename,[status(thm)],[117])).
% cnf(1052,plain,(hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))),inference(split_conjunct,[status(thm)],[1051])).
% fof(1088, plain,![X1]:(X1=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)),X1))),inference(fof_nnf,[status(thm)],[126])).
% fof(1089, plain,![X2]:(X2=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)),X2))),inference(variable_rename,[status(thm)],[1088])).
% cnf(1090,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)],[1089])).
% fof(1180, plain,![X5]:![X6]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[149])).
% cnf(1181,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)],[1180])).
% fof(1193, plain,![X2]:![X6]:![X4]:(~(c_Finite__Set_Ofinite(X4,X6))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X2),X6)))|c_Finite__Set_Ofinite(X4,X2))),inference(fof_nnf,[status(thm)],[152])).
% fof(1194, plain,![X7]:![X8]:![X9]:(~(c_Finite__Set_Ofinite(X9,X8))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X7),X8)))|c_Finite__Set_Ofinite(X9,X7))),inference(variable_rename,[status(thm)],[1193])).
% cnf(1195,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))|~c_Finite__Set_Ofinite(X1,X3)),inference(split_conjunct,[status(thm)],[1194])).
% fof(1266, plain,![X38]:![X39]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X39)))),inference(variable_rename,[status(thm)],[172])).
% cnf(1267,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)],[1266])).
% fof(1398, plain,![X8]:![X16]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),hAPP(c_Nat_OSuc,X8))))|(X16=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X58]:(X16=hAPP(c_Nat_OSuc,X58)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X58),X8)))))&((~(X16=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&![X58]:(~(X16=hAPP(c_Nat_OSuc,X58))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X58),X8)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),hAPP(c_Nat_OSuc,X8))))),inference(fof_nnf,[status(thm)],[205])).
% fof(1399, plain,![X59]:![X60]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))|(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X61]:(X60=hAPP(c_Nat_OSuc,X61)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X59)))))&((~(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&![X62]:(~(X60=hAPP(c_Nat_OSuc,X62))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X59)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))),inference(variable_rename,[status(thm)],[1398])).
% fof(1400, plain,![X59]:![X60]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))|(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(X60=hAPP(c_Nat_OSuc,esk34_2(X59,X60))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_2(X59,X60)),X59)))))&((~(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&![X62]:(~(X60=hAPP(c_Nat_OSuc,X62))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X59)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))),inference(skolemize,[status(esa)],[1399])).
% fof(1401, plain,![X59]:![X60]:![X62]:((((~(X60=hAPP(c_Nat_OSuc,X62))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X59))))&~(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))|(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(X60=hAPP(c_Nat_OSuc,esk34_2(X59,X60))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_2(X59,X60)),X59)))))),inference(shift_quantors,[status(thm)],[1400])).
% fof(1402, plain,![X59]:![X60]:![X62]:((((~(X60=hAPP(c_Nat_OSuc,X62))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X59))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))&(~(X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59)))))&(((X60=hAPP(c_Nat_OSuc,esk34_2(X59,X60))|X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_2(X59,X60)),X59))|X60=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X59))))))),inference(distribute,[status(thm)],[1401])).
% cnf(1404,plain,(X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=hAPP(c_Nat_OSuc,esk34_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)],[1402])).
% fof(1411, plain,![X8]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)))|?[X43]:X8=hAPP(c_Nat_OSuc,X43))&(![X43]:~(X8=hAPP(c_Nat_OSuc,X43))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)))),inference(fof_nnf,[status(thm)],[207])).
% fof(1412, plain,![X44]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))|?[X45]:X44=hAPP(c_Nat_OSuc,X45))&(![X46]:~(X44=hAPP(c_Nat_OSuc,X46))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))),inference(variable_rename,[status(thm)],[1411])).
% fof(1413, plain,![X44]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))|X44=hAPP(c_Nat_OSuc,esk35_1(X44)))&(![X46]:~(X44=hAPP(c_Nat_OSuc,X46))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))),inference(skolemize,[status(esa)],[1412])).
% fof(1414, plain,![X44]:![X46]:((~(X44=hAPP(c_Nat_OSuc,X46))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))|X44=hAPP(c_Nat_OSuc,esk35_1(X44)))),inference(shift_quantors,[status(thm)],[1413])).
% cnf(1415,plain,(X1=hAPP(c_Nat_OSuc,esk35_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)],[1414])).
% fof(1423, plain,![X31]:![X42]:![X23]:![X4]:(~(c_Fun_Oinj__on(X4,X23,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))|((~(hBOOL(hAPP(hAPP(c_member(X23),X31),c_Set_Oimage(X4,X23,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))))|?[X14]:(X31=hAPP(X42,X14)&![X60]:(~(X31=hAPP(X42,X60))|X60=X14)))&(![X14]:(~(X31=hAPP(X42,X14))|?[X60]:(X31=hAPP(X42,X60)&~(X60=X14)))|hBOOL(hAPP(hAPP(c_member(X23),X31),c_Set_Oimage(X4,X23,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))))),inference(fof_nnf,[status(thm)],[209])).
% fof(1424, plain,![X61]:![X62]:![X63]:![X64]:(~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))|((~(hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))|?[X65]:(X61=hAPP(X62,X65)&![X66]:(~(X61=hAPP(X62,X66))|X66=X65)))&(![X67]:(~(X61=hAPP(X62,X67))|?[X68]:(X61=hAPP(X62,X68)&~(X68=X67)))|hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool)))))))),inference(variable_rename,[status(thm)],[1423])).
% fof(1425, plain,![X61]:![X62]:![X63]:![X64]:(~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))|((~(hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))|(X61=hAPP(X62,esk37_4(X61,X62,X63,X64))&![X66]:(~(X61=hAPP(X62,X66))|X66=esk37_4(X61,X62,X63,X64))))&(![X67]:(~(X61=hAPP(X62,X67))|(X61=hAPP(X62,esk38_5(X61,X62,X63,X64,X67))&~(esk38_5(X61,X62,X63,X64,X67)=X67)))|hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool)))))))),inference(skolemize,[status(esa)],[1424])).
% fof(1426, plain,![X61]:![X62]:![X63]:![X64]:![X66]:![X67]:((((~(X61=hAPP(X62,X67))|(X61=hAPP(X62,esk38_5(X61,X62,X63,X64,X67))&~(esk38_5(X61,X62,X63,X64,X67)=X67)))|hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))&(((~(X61=hAPP(X62,X66))|X66=esk37_4(X61,X62,X63,X64))&X61=hAPP(X62,esk37_4(X61,X62,X63,X64)))|~(hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))))|~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))),inference(shift_quantors,[status(thm)],[1425])).
% fof(1427, plain,![X61]:![X62]:![X63]:![X64]:![X66]:![X67]:(((((X61=hAPP(X62,esk38_5(X61,X62,X63,X64,X67))|~(X61=hAPP(X62,X67)))|hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))|~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool)))))&(((~(esk38_5(X61,X62,X63,X64,X67)=X67)|~(X61=hAPP(X62,X67)))|hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))|~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))&((((~(X61=hAPP(X62,X66))|X66=esk37_4(X61,X62,X63,X64))|~(hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool)))))))|~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool)))))&((X61=hAPP(X62,esk37_4(X61,X62,X63,X64))|~(hBOOL(hAPP(hAPP(c_member(X63),X61),c_Set_Oimage(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool)))))))|~(c_Fun_Oinj__on(X64,X63,X62,c_Orderings_Otop__class_Otop(tc_fun(X64,tc_HOL_Obool))))))),inference(distribute,[status(thm)],[1426])).
% cnf(1428,plain,(X4=hAPP(X3,esk37_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)],[1427])).
% fof(1491, plain,![X42]:![X6]:![X23]:![X2]:![X4]:(~(c_Finite__Set_Ofinite(X4,X2))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23,tc_HOL_Obool),X6),c_Set_Oimage(X4,X23,X42,X2))))|c_Finite__Set_Ofinite(X23,X6))),inference(fof_nnf,[status(thm)],[230])).
% fof(1492, plain,![X43]:![X44]:![X45]:![X46]:![X47]:(~(c_Finite__Set_Ofinite(X47,X46))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X45,tc_HOL_Obool),X44),c_Set_Oimage(X47,X45,X43,X46))))|c_Finite__Set_Ofinite(X45,X44))),inference(variable_rename,[status(thm)],[1491])).
% cnf(1493,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))|~c_Finite__Set_Ofinite(X3,X5)),inference(split_conjunct,[status(thm)],[1492])).
% cnf(1510,plain,(class_Orderings_Oord(tc_HOL_Obool)),inference(split_conjunct,[status(thm)],[240])).
% fof(1528, plain,![X2]:![X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X4,X2))))|c_Finite__Set_Ofinite(X4,X2)),inference(fof_nnf,[status(thm)],[246])).
% fof(1529, plain,![X5]:![X6]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X6,X5))))|c_Finite__Set_Ofinite(X6,X5)),inference(variable_rename,[status(thm)],[1528])).
% cnf(1530,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)],[1529])).
% cnf(1549,plain,(class_Rings_Ozero__neq__one(tc_Nat_Onat)),inference(split_conjunct,[status(thm)],[263])).
% fof(1721, plain,![X20]:~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_OSuc,X20)),inference(variable_rename,[status(thm)],[317])).
% cnf(1722,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)),inference(split_conjunct,[status(thm)],[1721])).
% fof(1773, plain,![X42]:![X4]:![X23]:((~(c_Set_Oimage(X23,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))|![X14]:hAPP(X42,hAPP(c_Hilbert__Choice_Oinv__into(X23,X4,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool)),X42),X14))=X14)&(?[X14]:~(hAPP(X42,hAPP(c_Hilbert__Choice_Oinv__into(X23,X4,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool)),X42),X14))=X14)|c_Set_Oimage(X23,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),inference(fof_nnf,[status(thm)],[335])).
% fof(1774, plain,![X43]:![X44]:![X45]:((~(c_Set_Oimage(X45,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))|![X46]:hAPP(X43,hAPP(c_Hilbert__Choice_Oinv__into(X45,X44,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)),X43),X46))=X46)&(?[X47]:~(hAPP(X43,hAPP(c_Hilbert__Choice_Oinv__into(X45,X44,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)),X43),X47))=X47)|c_Set_Oimage(X45,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[1773])).
% fof(1775, plain,![X43]:![X44]:![X45]:((~(c_Set_Oimage(X45,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))|![X46]:hAPP(X43,hAPP(c_Hilbert__Choice_Oinv__into(X45,X44,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)),X43),X46))=X46)&(~(hAPP(X43,hAPP(c_Hilbert__Choice_Oinv__into(X45,X44,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)),X43),esk41_3(X43,X44,X45)))=esk41_3(X43,X44,X45))|c_Set_Oimage(X45,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))),inference(skolemize,[status(esa)],[1774])).
% fof(1776, plain,![X43]:![X44]:![X45]:![X46]:((hAPP(X43,hAPP(c_Hilbert__Choice_Oinv__into(X45,X44,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)),X43),X46))=X46|~(c_Set_Oimage(X45,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool))))&(~(hAPP(X43,hAPP(c_Hilbert__Choice_Oinv__into(X45,X44,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)),X43),esk41_3(X43,X44,X45)))=esk41_3(X43,X44,X45))|c_Set_Oimage(X45,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X45,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))),inference(shift_quantors,[status(thm)],[1775])).
% cnf(1777,plain,(c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),esk41_3(X3,X2,X1)))!=esk41_3(X3,X2,X1)),inference(split_conjunct,[status(thm)],[1776])).
% fof(1815, plain,![X68]:![X69]:hAPP(c_COMBI(X69),X68)=X68,inference(variable_rename,[status(thm)],[348])).
% cnf(1816,plain,(hAPP(c_COMBI(X1),X2)=X2),inference(split_conjunct,[status(thm)],[1815])).
% fof(1825, plain,![X51]:![X42]:![X4]:![X23]:(~(class_Orderings_Oord(X23))|((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X23),X42),X51)))|![X14]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X23,hAPP(X42,X14)),hAPP(X51,X14))))&(?[X14]:~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X23,hAPP(X42,X14)),hAPP(X51,X14))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X23),X42),X51))))),inference(fof_nnf,[status(thm)],[352])).
% fof(1826, plain,![X52]:![X53]:![X54]:![X55]:(~(class_Orderings_Oord(X55))|((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52)))|![X56]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,X56)),hAPP(X52,X56))))&(?[X57]:~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,X57)),hAPP(X52,X57))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52))))),inference(variable_rename,[status(thm)],[1825])).
% fof(1827, plain,![X52]:![X53]:![X54]:![X55]:(~(class_Orderings_Oord(X55))|((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52)))|![X56]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,X56)),hAPP(X52,X56))))&(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,esk42_4(X52,X53,X54,X55))),hAPP(X52,esk42_4(X52,X53,X54,X55)))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52))))),inference(skolemize,[status(esa)],[1826])).
% fof(1828, plain,![X52]:![X53]:![X54]:![X55]:![X56]:(((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,X56)),hAPP(X52,X56)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52))))&(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,esk42_4(X52,X53,X54,X55))),hAPP(X52,esk42_4(X52,X53,X54,X55)))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52))))|~(class_Orderings_Oord(X55))),inference(shift_quantors,[status(thm)],[1827])).
% fof(1829, plain,![X52]:![X53]:![X54]:![X55]:![X56]:(((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,X56)),hAPP(X52,X56)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52))))|~(class_Orderings_Oord(X55)))&((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X55,hAPP(X53,esk42_4(X52,X53,X54,X55))),hAPP(X52,esk42_4(X52,X53,X54,X55)))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X54,X55),X53),X52)))|~(class_Orderings_Oord(X55)))),inference(distribute,[status(thm)],[1828])).
% cnf(1830,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk42_4(X4,X3,X2,X1))),hAPP(X4,esk42_4(X4,X3,X2,X1))))),inference(split_conjunct,[status(thm)],[1829])).
% cnf(1831,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5)),hAPP(X4,X5)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))),inference(split_conjunct,[status(thm)],[1829])).
% fof(1912, plain,![X17]:![X18]:(~(hAPP(c_Nat_OSuc,X18)=hAPP(c_Nat_OSuc,X17))|X18=X17),inference(fof_nnf,[status(thm)],[376])).
% fof(1913, plain,![X19]:![X20]:(~(hAPP(c_Nat_OSuc,X20)=hAPP(c_Nat_OSuc,X19))|X20=X19),inference(variable_rename,[status(thm)],[1912])).
% cnf(1914,plain,(X1=X2|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2)),inference(split_conjunct,[status(thm)],[1913])).
% fof(1923, plain,![X9]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X9)),inference(variable_rename,[status(thm)],[380])).
% cnf(1924,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)],[1923])).
% fof(2004, plain,![X54]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X54),inference(variable_rename,[status(thm)],[406])).
% cnf(2005,plain,(c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)),inference(split_conjunct,[status(thm)],[2004])).
% fof(2006, plain,![X2]:hAPP(c_Nat_OSuc,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),inference(variable_rename,[status(thm)],[407])).
% cnf(2007,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)],[2006])).
% cnf(2032,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)],[416])).
% fof(2055, plain,![X2]:![X42]:![X23]:![X15]:![X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X15),c_Set_Oimage(X23,X4,X42,X2))))|hAPP(X42,hAPP(c_Hilbert__Choice_Oinv__into(X23,X4,X2,X42),X15))=X15),inference(fof_nnf,[status(thm)],[423])).
% fof(2056, plain,![X43]:![X44]:![X45]:![X46]:![X47]:(~(hBOOL(hAPP(hAPP(c_member(X47),X46),c_Set_Oimage(X45,X47,X44,X43))))|hAPP(X44,hAPP(c_Hilbert__Choice_Oinv__into(X45,X47,X43,X44),X46))=X46),inference(variable_rename,[status(thm)],[2055])).
% cnf(2057,plain,(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,X4,X1),X5))=X5|~hBOOL(hAPP(hAPP(c_member(X3),X5),c_Set_Oimage(X2,X3,X1,X4)))),inference(split_conjunct,[status(thm)],[2056])).
% fof(2156, plain,![X42]:![X4]:(~(c_Finite__Set_Ofinite(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))|(~(c_Fun_Oinj__on(X4,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))|c_Set_Oimage(X4,X4,X42,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),inference(fof_nnf,[status(thm)],[451])).
% fof(2157, plain,![X43]:![X44]:(~(c_Finite__Set_Ofinite(X44,c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool))))|(~(c_Fun_Oinj__on(X44,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool))))|c_Set_Oimage(X44,X44,X43,c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X44,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[2156])).
% cnf(2158,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)],[2157])).
% cnf(2205,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)],[466])).
% fof(2371, plain,![X4]:(~(class_Rings_Ozero__neq__one(X4))|~(c_Groups_Ozero__class_Ozero(X4)=c_Groups_Oone__class_Oone(X4))),inference(fof_nnf,[status(thm)],[519])).
% fof(2372, plain,![X5]:(~(class_Rings_Ozero__neq__one(X5))|~(c_Groups_Ozero__class_Ozero(X5)=c_Groups_Oone__class_Oone(X5))),inference(variable_rename,[status(thm)],[2371])).
% cnf(2373,plain,(c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ozero__neq__one(X1)),inference(split_conjunct,[status(thm)],[2372])).
% cnf(2571,plain,(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(spm,[status(thm)],[2373,1549,theory(equality)])).
% cnf(2584,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)],[1924,2205,theory(equality)])).
% cnf(2587,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)],[1914,2205,theory(equality)])).
% cnf(3098,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)],[1267,2007,theory(equality)])).
% cnf(4012,plain,(hBOOL(hAPP(hAPP(c_member(X1),X3),c_Set_Oimage(X4,X1,c_COMBI(X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))),inference(spm,[status(thm)],[1052,1816,theory(equality)])).
% cnf(4525,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)],[1195,1181,theory(equality)])).
% cnf(8832,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2)))|~class_Orderings_Oord(tc_HOL_Obool)),inference(spm,[status(thm)],[1831,1181,theory(equality)])).
% cnf(8841,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2)))|$false),inference(rw,[status(thm)],[8832,1510,theory(equality)])).
% cnf(8842,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2)))),inference(cn,[status(thm)],[8841,theory(equality)])).
% cnf(25188,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2)))),inference(rw,[status(thm)],[1530,2584,theory(equality)])).
% cnf(25189,plain,(hAPP(c_Nat_OSuc,esk35_1(X1))=X1|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))),inference(rw,[status(thm)],[1415,2584,theory(equality)])).
% cnf(25192,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))),inference(rw,[status(thm)],[1090,2584,theory(equality)])).
% cnf(25532,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),inference(spm,[status(thm)],[25188,2032,theory(equality)])).
% cnf(25540,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))|$false),inference(rw,[status(thm)],[25532,983,theory(equality)])).
% cnf(25541,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)],[25540,theory(equality)])).
% cnf(25564,plain,(hAPP(c_Nat_OSuc,esk35_1(X1))=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1),inference(spm,[status(thm)],[25189,25192,theory(equality)])).
% cnf(29172,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1)),inference(spm,[status(thm)],[4525,25541,theory(equality)])).
% cnf(31577,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))|~class_Orderings_Oord(tc_HOL_Obool)),inference(spm,[status(thm)],[1830,8842,theory(equality)])).
% cnf(31647,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))|$false),inference(rw,[status(thm)],[31577,1510,theory(equality)])).
% cnf(31648,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),inference(cn,[status(thm)],[31647,theory(equality)])).
% cnf(31671,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),inference(spm,[status(thm)],[994,31648,theory(equality)])).
% cnf(38011,plain,(hAPP(c_Nat_OSuc,esk34_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)],[1404,3098,theory(equality)])).
% cnf(38073,plain,(hAPP(c_Nat_OSuc,esk34_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)],[38011,2571,theory(equality)])).
% cnf(38128,plain,(esk34_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)],[2587,38073,theory(equality)])).
% cnf(38283,plain,(esk34_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)],[38128,25564,theory(equality)])).
% cnf(104455,plain,(hAPP(c_COMBI(X1),hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_COMBI(X1)),X4))=X4),inference(spm,[status(thm)],[2057,4012,theory(equality)])).
% cnf(104515,plain,(hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_COMBI(X1)),X4)=X4),inference(rw,[status(thm)],[104455,1816,theory(equality)])).
% cnf(104729,plain,(c_Set_Oimage(X1,X2,c_COMBI(X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_COMBI(X3),esk41_3(c_COMBI(X3),X2,X1))!=esk41_3(c_COMBI(X3),X2,X1)),inference(spm,[status(thm)],[1777,104515,theory(equality)])).
% cnf(104779,plain,(c_Set_Oimage(X1,X2,c_COMBI(X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|$false),inference(rw,[status(thm)],[104729,1816,theory(equality)])).
% cnf(104780,plain,(c_Set_Oimage(X1,X2,c_COMBI(X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),inference(cn,[status(thm)],[104779,theory(equality)])).
% cnf(130659,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X3,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|~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(spm,[status(thm)],[1493,104780,theory(equality)])).
% cnf(130718,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X3,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|$false),inference(rw,[status(thm)],[130659,31648,theory(equality)])).
% cnf(130719,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X3,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),inference(cn,[status(thm)],[130718,theory(equality)])).
% cnf(130960,plain,(c_Finite__Set_Ofinite(X1,X2)),inference(spm,[status(thm)],[130719,29172,theory(equality)])).
% cnf(131362,plain,(c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|$false|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),inference(rw,[status(thm)],[2158,130960,theory(equality)])).
% cnf(131363,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)],[131362,theory(equality)])).
% cnf(135088,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)],[131363,2005,theory(equality)])).
% cnf(136082,plain,(hAPP(c_Nat_OSuc,esk37_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)],[1428,135088,theory(equality)])).
% cnf(136147,plain,(hAPP(c_Nat_OSuc,esk37_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1|$false|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),inference(rw,[status(thm)],[136082,2005,theory(equality)])).
% cnf(136148,plain,(hAPP(c_Nat_OSuc,esk37_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1|$false|$false),inference(rw,[status(thm)],[136147,31671,theory(equality)])).
% cnf(136149,plain,(hAPP(c_Nat_OSuc,esk37_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))=X1),inference(cn,[status(thm)],[136148,theory(equality)])).
% cnf(136233,plain,(X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),inference(spm,[status(thm)],[1722,136149,theory(equality)])).
% cnf(136790,plain,(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1),inference(sr,[status(thm)],[38283,136233,theory(equality)])).
% cnf(136791,plain,($false),inference(sr,[status(thm)],[136790,136233,theory(equality)])).
% cnf(136792,plain,($false),136791,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 6043
% # ...of these trivial : 199
% # ...subsumed : 3724
% # ...remaining for further processing: 2120
% # Other redundant clauses eliminated : 655
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 24
% # Backward-rewritten : 139
% # Generated clauses : 99087
% # ...of the previous two non-trivial : 89720
% # Contextual simplify-reflections : 550
% # Paramodulations : 98327
% # Factorizations : 17
% # Equation resolutions : 721
% # Current number of processed clauses: 1307
% # Positive orientable unit clauses: 327
% # Positive unorientable unit clauses: 33
% # Negative unit clauses : 73
% # Non-unit-clauses : 874
% # Current number of unprocessed clauses: 58441
% # ...number of literals in the above : 165563
% # Clause-clause subsumption calls (NU) : 126098
% # Rec. Clause-clause subsumption calls : 90915
% # Unit Clause-clause subsumption calls : 8608
% # Rewrite failures with RHS unbound : 344
% # Indexed BW rewrite attempts : 10126
% # Indexed BW rewrite successes : 279
% # Backwards rewriting index: 1130 leaves, 2.78+/-7.403 terms/leaf
% # Paramod-from index: 268 leaves, 2.37+/-5.699 terms/leaf
% # Paramod-into index: 1001 leaves, 2.53+/-5.999 terms/leaf
% # -------------------------------------------------
% # User time : 5.254 s
% # System time : 0.144 s
% # Total time : 5.398 s
% # Maximum resident set size: 0 pages
% PrfWatch: 7.74 CPU 7.90 WC
% FINAL PrfWatch: 7.74 CPU 7.90 WC
% SZS output end Solution for /tmp/SystemOnTPTP7640/SCT162+1.tptp
%
%------------------------------------------------------------------------------